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[3081] In this docket, the Postal Service proposes to use a survey designed to produce engineered time standards to replace a survey that the Commission has used since Docket No. R87-1 to apportion the accrued costs of city delivery carrier street time activity to basic functions. It also renews challenges that it first made in Docket No. R97-1 to the established methods by which the Commission estimates volume variable runtime, and elemental and coverage-related load time. For reasons explained below, the Commission finds the engineered time standards survey results to be unsuitable for use in ratemaking. It also rejects the Postal Service's renewed challenges to the established methods for estimating volume variable route time, access time, and elemental and coverage-related load time.
[3082] UPS witness Luciani introduced three proposals to modify the treatment of parcel costs. He proposes that the time carriers spend sorting and loading parcels in their trucks at the DDU be calculated as in-office time. Currently, these costs are treated as support costs and have much lower volume variability than in-office time. Further, Luciani proposes that the labor costs for routes designated as "Exclusive Parcel Routes" be totally attributed to the Zoned Parcel Post mail subclass. Lastly, he proposes that elemental load costs for parcel shaped mail be distributed to subclasses on the basis of weight. As discussed below, the Commission rejects these proposals based on evidence introduced into the record that shows these costs should continue to be handled as in recent dockets. See Sections 5, 8 and 9.
[3083] Witness Nelson, on behalf of the Publications Group, proposes to alter the analysis he conducted for the Postal Service in R97-1 regarding the variability of Motorized Letter Routes. This led witness Baron to present supplemental testimony on behalf of the Postal Service that disputes witness Nelson's proposal and then proceeds to develop arguments for totally eliminating this variable cost element. The Commission finds merit in witness Nelson's proposal but rejects witness Baron's arguments. This is discussed in Section 7.
[3084] The Commission's Opinion in Docket No. R97-1 comments as follows on the data parties were forced to rely upon to attribute city delivery carrier street time costs.
[T]he basic data on which city delivery carrier cost attribution must rely come largely from obsolete special studies that no longer conform to current delivery operations or the current state of analysis.
[3085] This opinion was soon echoed by the Data Quality Study which suggested the Postal Service ascertain if the Service's Engineered Standards/Delivery Redesign (ES) project might provide a more up-to-date source of suitable data. However, the Data Quality Study did not specifically recommend that the Postal Service and the Commission use the ES data. A.T Kearney, Data Quality Study, Technical Report #4: Alternative Approaches for Data Collection, April 16, 1999 at 53-56. According to MPA witness Hay, who was one of the contributors, the authors of the Data Quality Study merely recommended that the ES data be reviewed to determine its interim usefulness until new data could be provided. Tr. 27/13091-92.
[3086] The Commission does not collect postal data. That task belongs exclusively to the Postal Service and its contractors. By Docket No. R97-1, almost all of the critical estimates that the Commission was forced to use were derived from samples that were 8 to 12 years old. Carrier street time was divided among its principal components (street support time, travel time, run time and load time) using proportions taken from the Street Time Sampling (STS) survey. This survey was conducted in 1986. Run time was subdivided into access time and route time with variabilities taken from a regression fit to data from the Curbline and Foot Access Test (CAT/FAT). The most recent CAT/FAT test experiment was conducted in 1989. Load time was separated into elemental volume-variable load time and coverage-related load time using elasticities taken from regressions fit to the Load Time Variability (LTV) study. The data for this study were collected in 1985.
[3087] Not only were these data old, they were somewhat inconsistent. Both the STS and LTV samples can be used to derive carrier street time proportions but the actual load times derived from these two sets of data are different. Witness Crowder who recommended adoption of the LTV proportions noticed this in Docket R97-1. After considering the reasons for the differences in the load times derived from the two studies, the Commission concluded that the differences were likely to be proportional. Consequently, it would still be proper to marry load time variabilities taken from regressions on the LTV data with a load time cost pool determined by the STS proportions. PRC Op. R97-1, Appendix K.
[3088] In the current proceeding the Postal Service proposes that the ES data be used to replace the STS and LTV samples. This would be accomplished, first, by using carrier street time proportions derived from the ES data by USPS witnesses Baron and Raymond, and, second, by replacing the stop-level load time regressions fit to the LTV data with route-level load time regressions fit to the ES data. Taken together, the proposals would avoid the possibility of a mismatch in the applied definitions of load time that arises when different samples are used to apportion carrier street time and estimate load time volume variability.
[3089] The Commission rejects both of the Service's ES proposals. Postal Service witnesses have not fit satisfactory route-level regressions to the ES data. An examination of the regressions reveals a basic flaw in the econometrics: among the "explanatory" variables for load time are variables that cannot be measured without knowing load time. In effect, load time has been used to explain load time. This is a fundamental technical error that makes the ES variability estimates meaningless. For this reason the Commission must continue to use the stop-level regressions fit to the LTV sample.
[3090] This means that to apply the LTV-derived variabilities to load times calculated using the ES proportions, the Commission must be satisfied that the same definition of load time has been applied to collect and compile both data sets. Unfortunately, this does not appear to be the case. The collection and compilation of load time proportions in accordance with the Postal Service's and Commission's definition of load time was not a designed purpose of the ES survey. Most of the precautions that should have been taken to obtain a random, or at least representative, sample were omitted. The sample is too small to be reweighted. And the ES data collectors were not informed of the precise distinction between loading and access activities that the Postal Service and the Commission apply to carrier street time. Apparently, as a result, the ES load time proportions turn out to be much higher than the proportions found in the more carefully conducted STS and LTV surveys.
[3091] The Postal Service proposes to use proportions from the ES survey tallies rather than the STS proportions to divide carrier street time into its components. This switch has been the subject of a considerable proportion of the testimony in this proceeding. The reason for this interest is obvious: the ES proportions are quite different from the STS proportions, as can be seen from Table 3-2, taken from the testimony of MPA witness Crowder. Tr. 32/16179.
[3092] The increase in the load time proportion converts into a $980 million increase in load time costs according to witness Crowder. Id. at 16146. The Commission's established methods for estimating volume variability and attributing load time and access costs would convert a very large part of this increase into attributable costs. In Docket No. R97-1 about 70 percent of load time cost was attributable in the test year.
[3093] The Postal Service's proposal and supporting testimony is to be found mostly in the testimony and library references of Postal Service witnesses Baron and Raymond. NAA witness Kent also supported the Service's proposal in rebuttal testimony. The proposal's principal critics are Periodical mailers' witnesses Crowder and Hay. Witness Crowder has provided the Commission with a particularly detailed analysis and critique of the ES survey. On Brief, the OCA supports the use of the ES data in place of STS data. OCA Brief at 133-135.
[3094] The collection and initial processing of the ES data are described by witness Raymond. He is the President and CEO of the Postal Service contractor responsible for designing and executing the ES survey. USPS-T-13 at 1-2. Witness Raymond's direct testimony is limited to a detailed account of the mechanics of the sample selection and data collection procedures. It is apparent from his testimony that the ES survey was not designed to collect carrier-street time data for rate making. This does not mean that the ES data are automatically unsuitable, but it does mean that the ES survey has to fortuitously meet some unanticipated standards for sample design and data collection. It is the application of unanticipated standards by Periodical witnesses Crowder and Hay that forms the basis of most of the data collection and load time measurement criticisms discussed in their testimony. These issues are: 1) Did the ES data collectors apply the correct definitions of load and run time? 2) Were the data collectors all applying the same definitions? 3) Were the collectors accurate in recording the information related to load time? 4) Does the information collected for a tally always map correctly into load time, run time, etc.?
[3095] Correct definitions of load and run time. There is no evidence on the record to indicate that ES data collectors knew the correct distinction between load time and run time, which is that load time begins when the carrier stops before a receptacle or door and ends as he begins to move away. Witness Hay states the distinction as follows "the load time begins at the moment that the letter carrier's feet stop moving at the end of a walk and ends at the moment that the foot is lifted to start away from a stop." Tr. 27/13083-89. Witness Crowder argues that the generic terms such as "point of delivery" and "delivery/collect" corresponding to the bar codes that collectors scanned to record a tally are somewhat imprecise and interpretable. Tr. 32/16158-61. Nevertheless, the information was collected for the purpose of identifying exactly the activity of the carrier at the moment of the tally. The data were recorded according to a bar code scheme that was sufficiently detailed in design to distinguish load time from run time activities. And most of the bar code labels do not seem to be as interpretable as witness Crowder claims. In short, the system may have worked well enough to produce load time and run time tallies according to a fairly uniform common sense interpretation of the bar codes even though the collectors plainly could not have been deliberately applying the correct specific accepted rate-making definitions of load and run time.
[3096] Consistent application of definitions by data collectors. Witness Crowder argues that data collectors had no written instructions, Id. at 16154, that there was a high rate of turnover among the data collectors during the survey, Id. at 16158, and that replacements were trained "on-the-job" Ibid. Witness Hay notes the absence of training manuals and log-books, and that training did not emphasize the distinction between run time and load time. Tr. 27/13088-89.
[3097] Witness Raymond in his rebuttal testimony disputes most of these points. He specifically denies that the training of the collectors was deficient, that extensive training was even needed, and that replacement collectors were not trained. Tr. 39/17909-10. From witness Raymond's rebuttal testimony it appears that the ES data collectors were adequately trained to be efficient and effective tally takers using the bar code scanning system devised for the survey. However, the training seems to have left the collectors to interpret the bar codes for themselves. Without a set of written instructions accompanying the bar codes, it is difficult to imagine how the data collectors could have done anything else. In practice the data collectors probably did not apply the same definitions of load and run time, but the result may have been just an avoidable increase in the noise in the tally data.
[3098] Accuracy of the collectors in recording load time? On this question witness Crowder argues that work sampling was not the central purpose of the ES survey. Tr. 32/16152-53 and that the data collectors were very busy with tasks other than work sampling Id. at 16154-56. Witness Hay also argues that the industrial engineering standards applied by witness Raymond are inappropriate for cost studies. Tr. 27/13086-87. Witness Raymond has responded that work sampling was a central purpose of the ES survey. Tr. 39/17907 and that the data collectors were not too overworked to accurately record the tallies Id. at 17908. On this question the record includes a curious attempt by witness Crowder to ascertain the accuracy of the ES load time percentages for specific routes by examining nine videotapes of carriers taken by the ES data collectors. Tr. 32/16186-88. Witness Raymond points out so many problems with the videotapes that it appears that witness Crowder analysis is of little help. Tr. 39/17911-17. The collectors were not as accurate as they might have been nor was the survey very well designed to collect economic data, but the result here, as before, may just be unnecessary noise in the observations. We also note that unlike the MODS data used by USPS witness Bozzo to estimate mail processing variabilities, the ES data were screened for errors as it was collected. USPS-T-13 at 13.
[3099] Mapping the information collected for a tally correctly into load time and run time. Witness Crowder argues that this has not occurred. Witness Raymond mapped the ES tallies into STS carrier street time categories following instructions from witness Baron. In principle every possible tally would be assigned to an STS category. In practice it appears that many kinds of tallies never occurred in the sample. Witness Crowder's objections to the procedure are that the ES code definitions are broad, imprecise, and failed to specify breakpoints, that witnesses Baron and Raymond cannot assign tallies to STS categories without imposing their own interpretations on the ES codes, that 3 location codes and 5 activity codes are "vague and interchangeable," and that no analyst could identify precisely the STS category for some of the tallies Tr. 32/16162-64. Witness Raymond's rebuttal is that "anomolous" sic load time tallies were rare in the sample and had mostly been categorized correctly. The miss-categorization of tallies is a likely source of error in the ES tallies, but the extent of miss-categorization is not firmly determined on the record.
[3100] The Commission's overall impression of the ES tallies, and the way that they were collected and categorized, agrees with witness Hay's assertions that the ES tallies were made to answer a different set of questions than those that were asked by the ES survey. Tr. 27/13086. With the same effort the Postal Service could easily have collected a much larger and more accurate sample for estimating carrier street time proportions if it had planned to do so at the outset. While the design and execution of the ES survey does limit the applicability of results for rate cases, the data do serve some useful purposes in understanding carrier route operations and designing new studies that can estimate street time proportions with greater confidence.
[3101] The design of a sample for the purpose of estimating carrier street time proportions should be driven by the requirements imposed by the use of the estimates in rate making. Witness Hay describes in a general way how the requirements relate to the size and selection rules for the sample. Id. at 13080-84. He says that the sampling frame should be designed, and random sampling undertaken within the frame, so that the sample will be representative of the population to which the estimates apply. Sampling should be random but "pure randomness is rarely attained in practice." The sample must be large enough to provide estimates with an acceptable error. Witness Hay describes alternative sampling plans: systematic sampling, stratified sampling and cluster sampling.
[3102] The ES sampling plan was none of the above. The consideration that controlled its design was convenience. The ES sample design is described by witness Raymond USPS-T-13 at 7-9 and is roundly criticized by witness Crowder. Tr. 32/16165-78. There were two phases to the sampling. In phase 1, the ten geographic regions each chose 3 to 5 sites (zip codes). Ten additional sites were chosen at random. Routes were chosen randomly at the sites. In phase 2 managers of the 10 geographic regions choose test sites and 8 additional sites were chosen randomly. Again, routes were chosen randomly at the sites. Altogether witness Raymond reported that 340 routes were surveyed. It later was discovered that more routes had been surveyed but the results had not been included in the ES data.
[3103] Under witness Raymond's design most of the observed ES route-days turn out to have been selected non-randomly. This fact is immediately apparent from two tables compiled by witness Crowder. Id. at 16166. Only 101 out of 845 route-days were selected randomly and the sample was mostly drawn from a limited number of metropolitan areas. Four cities accounted for 55 percent of the observed route-days. The amount of data that was collected but excluded from the ES sample was 175 route-days.
[3104] The ad hoc nature of the ES sampling plan and the unexplained deletion of route-days brings up questions that would not have arisen if the design had been conventional. The questions that arise are 1) Is the sample representative of the population? 2) Is the sample large enough? and 3) Does it matter for the proposed use of the sample?
[3105] Representativeness of the sample. Witness Crowder's analysis shows that the ES sample will not be representative of the population of city carrier routes. In her own words "Mr. Raymond's sample is not representative of the entire system of USPS letter routes and, in fact, is biased toward routes with a larger proportion of in office and load time." The sample is heavily weighted towards residential curbline routes. Id. at 16174. The ES sample favored larger ZIP codes in more densely populated areas. Id. at 16175. The ES sampled sites averaged 26 routes per site while the national average is 14. Id. at 16174. The ES sample is biased towards regions in the South and West and away from regions in the North and East. Id. at 16175. In fact the geographic distribution of ES routes is very different from the geographic distribution of routes in the system. According to witness Crowder "Almost 85 percent of the ES foot routes come from the New York Metro, Pacific and Great Lakes regions while only 48 percent of total system foot routes are in those regions." Id. at 16176. Delivery types are somewhat different for the ES sample and the total system. The ES sample is biased towards residential NDCBU and residential central and away from other types. Id. at 16177.
[3106] Size of sample. A sample that was large enough might be reweighted to overcome the sampling biases discovered by witness Crowder. Witness Baron does a limited reweighting of the sample for this purpose. Witness Crowder points out, however, that the ES sample is much too small to be reweighted to eliminate many of the biases that make it unrepresentative. The 340 foot routes sampled are only about 0.5 percent of the routes in the system. As an example of what happens when the sample is reweighted she cites one ES foot route in the New York Metro region which, under witness Baron's reweighting, "accounts for approximately half of the weighted load time proportion calculated for all foot routes." Id. at 16176. The small size of the sample would leave an appreciable amount of sampling error in witness Baron's estimates of carrier street time proportions even if the ES sample had been random. Witness Baron in response to an ADVO interrogatory to witness Raymond provided standard errors and confidence intervals for the proportions. ADVO/USPS-T13-23 (Tr. 18/7107). The calculations are made with formulas that assume random sampling.
[3107] Significance of flawed sample design. In his response to the ADVO interrogatory witness Baron attempts to dismiss concerns about the apparent non-randomness of the ES sampling plan by citing a result found in Cochran, Sampling Techniques, John Wiley & Sons, 1977 at 158-159. In essence, the result is this. If the routes found at the sites (zip codes) are random samples from a superpopulation of possible routes, then any scheme for selecting sites produces a random sample of routes from the superpopulation. If the routes found at a Zip Code are random then witness Raymond's plan for selecting sites is as good as any other plan. Unfortunately, Cochran's result is not applicable to the routes found at the Service's Zip Codes. The routes at a zip code are not randomly drawn from a superpopulation. They are found at the site because of geography, demographics, mail flows and the Postal Service's organization of its network.
[3108] Witness Hay states that "no confidence levels can be ascribed to these data because no sample design was made." Tr. 27/13092. This appears to the Commission to be a reasonable assessment of the effect of the ES sampling plan on the carrier street time proportions proposed by the Postal Service. Accordingly, the Commission is unable to rely on ES data to attribute the costs of city delivery carrier street time.
[3109] Compatibility issues arise when the ES proportions are combined with LTV-based variabilities. These compatibility issues are essentially the same as the STS versus LTV compatibility issues that arose in Docket No. R97-1. In Docket No. R97-1 the Commission concluded that the differences in carrier street times found between the STS and LTV surveys were proportional. The definitions of the components of carrier street time for the two surveys were identical. The survey methods, however, differed in ways that suggested that carriers went at a faster pace in the LTV survey. If this was the only difference, then MTV elasticities could be used with STS proportions.
[3110] Both witness Crowder and witness Baron have concluded that the combination of ES proportions and LTV variabilities is a mismatch. Witness Crowder has shown that the differences between the ES and STS load and run time percentages are too large to be accounted for by sampling error or by changes in the way carriers deliver mail that have occurred over the interval of time from 1986, when the STS data were collected, and 1998, when the last of the ES data were collected. Tr. 32/16179-85. The testimony offered by USPS witness Kingsley USPS-T-10 cannot explain changes of the magnitude found between the two samples. Regarding growth in cluster boxes, witness Crowder notes that MDR stops are only 7.6 percent of all stops in the system. Regarding replacement of foot routes with motorized routes, she observes that foot routes converted to park and loop are only 10 percent of the total and that curbline routes have increased only slightly since 1986. Regarding the introduction of Delivery Point Sequencing (DPS), she says that DPS letters do not add time at load. Regarding increasing volume per delivery, she replies that average volume per delivery has increased from 5.03 to 5.44 pieces, too little to explain much of the increase in load time. Regarding mail mix effects she shows that mail mix has hardly changed since 1986.
[3111] The explanations that survive witness Crowder's analysis are that the STS and ES surveys applied different definitions of load and run time, and that the ES (or STS) proportions came from biased samples. In his rebuttal testimony witness Baron proposes to resolve the compatibility issue by deriving variabilities from the ES data Tr. 43/18701-708. In effect, the Postal Service proposes to redefine load and run time to conform to the implicit consensus definitions applied by collectors as they took the ES sample. This is not a change that the Commission would be willing to make even if the Service had been successful in estimating variabilities from the ES sample. The STS definition cited by witness Hay is correct and clear. The implicit ES definition is unclear and may be incorrect. As it is, the proposal is moot because witness Baron's ES route level load time regressions are fatally defective.
[3112] The Postal Service's proposal to use route-level load time variabilities from regressions fit to the ES sample appeared late in the proceedings. The fully developed proposal is not found until one reaches the rebuttal testimony of witness Baron. Id. at 18695-713. In its initial filing the Postal Service used the ES data only to replace the STS proportions. In his direct testimony, witness Baron recommended applying LTV variabilities to load times derived with the ES proportions. Most of the testimony of non-postal parties in this proceeding is directed to the Postal Service's original proposal. For example, MPA witness Crowder fit regressions to the ES data for another purpose before the ES data set in the Service's original filing had been supplemented with delivered volumes by shape, accountables and collectables for the routes in the ES sample. Tr. 32/16196-206.
[3113] The Postal Service's econometrics began to emerge from UPS interrogatories directed to witness Baron. At this point the Service provided the disclosures required by our rules for econometric evidence and some additional discussion in a set of unsponsored library references. USPS-LR-I-310, LR-I-386 and LR-I-402. The regressions that witness Baron regards as providing the most accurate variabilities are found in USPS-LR-I-402. From his rebuttal testimony it appears that witness Baron is the author of LR-I-402, and may have authored the other library references as well.
[3114] USPS-LR-I-310 describes how the ES tallies were combined with other volume and delivery information to create a sample for the econometrics. Out of 971 ES route-day records, 758 could be matched to time, volume, and delivery point records. Load time for the routes in the ES sample was not actually measured as part of the ES survey. Instead, it must be estimated using the ES tallies and clocked street time for the carriers on the sampled routes. Several route records were deleted from the sample because the estimated load times were zero or very close to zero. The data assembly process described in LR-I-310 will leave estimates of load time with sampling errors, but the deletions should not impart a bias if they are random. The ES sample, however, is not particularly large, so the regressions must produce moderately good fits to provide statistically reliable estimates of load time variability.
[3115] The first attempt to fit a route-level regression to the ES sample used an equation patterned after the Commission's stop-level LTV regressions. The defective result is described in LR-I-310: "virtually all estimated regression coefficients are not statistically significant", "the estimated coefficients for volumes are both insignificant and small in absolute value", "the estimated elasticities of load time with respect to volume are essentially zero for flats, parcels, and accountables," and, "the overall equation seems to perform poorly as the R-square statistic from the regression is only 31 percent." USPS-LR-I-310 at 8.
[3116] The solution to the poor fit chosen by the author of LR-I-310 is to include in the regression a set of dummy variables defined to allow the regression line to "shift" for those observations that have very high load times relative to the shape volumes.
Including these dummy variables in the regression permitted estimation of the true volume - load time relationship. Each such dummy variable was set equal to one for all observations for which the load time per piece (by shape, and for accountables) fell within the upper 10 percent of the distribution of all observations of load time per piece. The dummy variable was set equal to zero for all other observations.
[3117] All of the regressions, except for the first, include these dummy variables, or similar ones, which differ only in the choice of the upper tail percentage of the distribution. These dummy variables all plainly use load time in their measurement. Since load time is also the dependent variable of the regression, the device that the Postal Service has employed to improve the fit of its equations to the ES sample is, constructively, to use load time to explain load time. This is not acceptable econometric practice in this instance because the equations have been fit by a method, least squares, that requires rather fundamentally that explanatory variables be exogenous (determined independently of the dependent variable). The dummy variables used in the Postal Service's regressions are not exogenous because they cannot be measured without knowing in advance the load times for the routes.
[3118] All of the statistical properties of the Postal Service's various regression experiments are grossly inflated by the presence of the improper dummy variables. This includes all of the t-values, F-statistics, and R-squares witness Baron cites to support his proposed use of the ES regressions, generally, and cites as reasons for selecting the particular one he uses to calculate his proposed variabilities. The statistical importance of the dummies can be seen from the t-values that are attached to their estimated coefficients. See, for example, Tr. 43/18706, Table 3D. The t-values for the dummies named "load time/letters dummy," "load time/flats dummy," and "load time/accountables dummy," range from 6.00 to 8.99. The t-value for the "load time/parcel dummy" is 3.84. The largest t-value for any other variable is 4.72. Without the improper dummies, the Postal Service's equation fits to the ES sample would be expected to have approximately the same statistical and economic properties as the original failed regression described in LR-I-310.
[3119] The Commission uses an established model of load time variability that is derived from the testimony of technical witnesses in Docket No. R90-1. The basic elements of the model consist of sub-models that are used to identify and combine the components of volume-variable load time at the stop level and at the system level. A third basic element of the model is the mathematics that shows how the variabilities that are derived from stop-level samples relate to the parameters of the stop-level and system-level submodels. A description of the established stop-level submodel is presented in Docket No. R90-1. The system-level model is shown in a derivation by witness Crowder in her response in R97-1 to Notice Of Inquiry No. 3. The connection between the submodels is described in general terms in the Commission's R97-1 Recommended Decision.
[3120] The following mathematical description of the established model reaffirms that the three components of the model fit together as parts of a logically consistent single entity. The description also shows how the equations which the Postal Service and the Commission fit to data from the Postal Service's Load Time Variability (LTV) study correspond to a component of the stop level submodel and relate to a component of the system level submodel.
[3121] Load time at a stop,
, is a function
of volume at the stop,
, and the number of actual deliveries that are made at the stop, A. In practice, the stop level submodel is applied to three kinds of stops. These are Single Delivery Residential (SDR), Multiple Delivery Residential (MDR) and Business and Mixed (BAM) stops. SDR stops have exactly one actual delivery, but MDR and BAM stops can have more than one actual delivery. The function,
, is defined for a range
and
for MDR and BAM stops. If volume by shape types, accountables and collectables at the stop are zero, then actual deliveries are also zero and the stop would not actually occur. Mathematically, the Commission's Conceptual Stop Level Load Time Function is:
[3122] The Conceptual Stop Level Load Time Function is an inconvenient equation to fit to the Postal Service's LTV sample for two reasons. First, one of the principal variables, actual deliveries
, was omitted from the sample. Instead of actual deliveries, the LTV sample recorded possible deliveries,
, for the stops included in the sample. The second reason the function,
, is inconvenient is that actual deliveries is itself volume-variable. We would certainly expect as the volume at an MDR or BAM stop increased that the number of actual deliveries would increase until it reached the number of possible deliveries at the stop. This fact makes actual deliveries an inconvenient variable to use as a control in an econometric fit of a load time equation because the volume variability of load time cannot be extracted from the result simply by using the partial derivative with respect to the volume,
.
[3123] The difficulties with the Conceptual Stop Level Load Time Function are overcome by transforming it. The transformation is a transformation of variables that is made mathematically by directly substituting for the variable actual deliveries,
, a function relating actual deliveries to its determinants. These determinants are volume at the stop,
, and the number of possible deliveries at the stop,
. This function is described in the R97-1 testimony of witness Baron. USPS-T-12 at 20-21. However, the function actually has much earlier origins in the testimony of USPS witness Bradley in Docket No. R94-1. USPS-T-5 at 49-50. We use the following general statement of the Actual Deliveries Function:
[3124] The substitution for
in the function
leaves a function,
, that we may call the Applied Stop Level Load Time Function. The terminology is appropriate because the function,
, corresponds in form to the equations that have been specified and fit econometrically to the LTV sample.
[3125] The Applied Stop Level Load Time Function,
, corresponds to the load time functions shown by witness Baron in his R97-1 testimony and is repeated as his equations (1) and (2) in his current testimony. USPS-T-12 at 4-5. These functions are specified as separable quadratics in
and
, not
. The equations, as they are fit to the LTV sample, also include other non-volume variable controls in the form of dummy variables for receptacle and container type. It must be noted that volume per stop is actually a vector,
, of volumes by shape category, accountables and collections. This complicates the application of the mathematics without altering the model in any essential way. For simplicity, in describing the established model we shall present the mathematics as though
is a single variable rather than a vector. In actual applications derivatives with respect to
become partial derivatives with respect to the components of the vector,
, and some of the equations involve sums of terms rather than a single term.
[3126] The volume variability of load time follows from the definition of the elasticity of load time with respect to volume. This definition is:
is marginal load time. Marginal load time is just the partial derivative ofwith respect to
(or the elements of the vector
) because the remaining variables in the Applied Stop Level Load Time Function are all non-volume variable. These variables are possible deliveries,
, and a collection of non-volume variable dummies. When we say that possible deliveries are non-volume variable it means that the Commission assumes that:
[3127] Rearranging the definition of
shows that all of the volume variable load time,
, in the load time for a single stop is accounted for by
.
This equation also holds for a particular shape, accountables or collectibles, i.e., for any element of a vector,.
[3128] Load time at a stop is cleanly partitioned into volume variable,
, and non-volume variable,
, components by the Commission's Stop Level Load Time Sub-model:
[3129] The mathematics that produces this partition does not impose any condition other than first-order differentiability on the Applied Stop Level Load Time Function. In particular, the mathematics does not require that the function
be linear in
. The equation forms used to fit
to the LTV sample are non-linear quadratic forms, and the parameters for the nonlinear components that emerge from the fits for the three kinds of stops, taken together, are different from zero at high levels of significance. If the function
is nonlinear then marginal load time,
and non-volume variable load time,
, will not be fixed constants. They will themselves be functions of volume at the stop,
.
[3130] The volume variable load time at a stop includes both a direct and an indirect effect. Differentiating the Conceptual Stop Level Load Time Function,
, with respect to
has to produce the same result as taking the partial derivative of the Applied Stop Level Load Time Function,
:
[3131] Actual deliveries are a function of volume, so the function-of-a-function rule is applied to obtain the second term. Multiplying through by
produces an equation for volume variable load time with two components:
[3132] The components are, first, the direct effect of volume on stop level load time with actual deliveries held constant, and, second, an indirect "deliveries" effect that operates on load time through the number of actual deliveries. The second effect arises because a change will affect load time indirectly by changing the number of deliveries. An increase in the number of actual deliveries can be expected to increase load time even if the volume at the stop remains fixed.
[3133] The Commission's calculations of volume variable costs and the attribution of these costs to subclasses is all done at the system level, that is, for the Postal Service as an entity. Prior to R97-1 this was done somewhat naively by applying the estimated volume variabilities derived from the stop level econometrics. In Docket No. R97-1 witness Crowder presented testimony in response to the Commission's NOI No. 3 that showed that the Commission's method was mathematically sound. The Commission's System level Load Time Sub-model is taken directly from witness Crowder's R97-1 testimony.
[3134] Total system load time is equal to average load time per stop,
, times the number of stops in the system,
.
[3135] The components of the equation are:
[3136] The average load time at a stop is assumed to be a function,
, of average volume per stop,
, and, possibly, other variables that are non-volume variable and need not be shown specifically as arguments for that reason. The function
is the Average Stop Level Load Time Function. The function,
, is not assumed to be the same as the Conceptual Stop Level Load Time Equation,
, or the Applied Stop Level Load Time Function,
, but is obviously closely related to them. Also, the number of stops in the system,
, may be a function of total volume in the system,
.
[3137] System-level volume variability is the elasticity of total system load time,
, with respect to total system volume,
:
[3138] The derivative in this expression is obtained by differentiating the equation for total system load time:
[3139] The elasticity,
, of the number of stops,
, with respect to total system volume,
, is defined as:
[3140] Substituting in the expression for system-level volume variability and using
gives:
[3141] The elasticity,
, of average load time per stop,
, with respect to average volume per stop,
, is called "elemental load time variability" and is defined as:
[3142] Substituting
in the equation for system level volume variability gives:
[3143] It can be seen from Crowder's equation that system level volume variability is composed of two distinct effects. These are, first, the elemental load time variability
, and, second, a coverage-related stops effect
that is the effect of the variability of stops on the residual from the elemental load time effect.
[3144] Nothing is assumed about the Average Stop Level Load Time Function in the derivation of Crowder's equation except that the function
exists over the necessary range (the same range as the functions
and
), and is first-order differentiable with respect to average volume per stop,
, over its range. The function does not have to be linear in
. The functions
and
are nonlinear in
so it would not be appropriate if the mathematics required that
be linear.
[3145] Nothing material in the mathematics changes when the System-level Load Time Sub-model is applied separately to load times for SDR, MDR and BAM stops. The mathematics is also essentially unchanged if
and
are vectors of volumes by shape, accountables and collections. Derivatives with respect to
and
become partial derivatives with respect to the elements of the vectors, the elemental load and stop elasticities are separately defined for the elements of the vectors, and Crowder's equation holds separately for each shape, accountables and collectables. Total elemental volume variable load time is the sum of the elemental volume variable load time by shape, accountables and collectables.
[3146] The Commission attributes elemental load time to subclasses by summing the elemental volume-variable load times for the several shapes, accountables and collectables.
This sum of volume variable load times is attributed to subclasses by applying carrier street time distribution keys. The Commission attributes part of the remainder to subclasses by applying single-subclass stop proportions to the sum of the residuals. In practice, the Commission performs this arithmetic simply by adding to carrier access costs the residual of load time costs obtained by deducting elemental volume variable load time costs from total load time costs. Load time costs that are not attributed by this two step method become part of institutional costs.
[3147] This method generally attributes a sum of load time carrier costs to subclasses that is greater than the amount that would be attributed on the basis of the sum of the volume-variable stops effects by shape etc.:
[3148] The Commission's System-level Load Time Variability Model was the basis for the Commission's Docket No. R97-1 explanations of the two components of load time variability.
The established analysis divides load time into two categories, each with its own driver. "Elemental" load time is that portion of total load time that varies directly with volume. Its cost driver is volume, expressed as pieces per stop. "Coverage-related" load time is the amount of accrued load time that remains after elemental load time is identified and deducted. Its intermediate cost driver is the number of stops that are covered. The number of stops that are covered, in turn, is driven by volume.
[3149] The Applied Stop Level Load Time Function,
, from the Stop-level Sub-model and the Average Stop Level Load Time Function,
, from the System-level Sub-model are not the same function, but are mathematically related. Let
be the continuous probability density function for volume per stop over the population of stops. Then average load time per stop
, by definition, is the expected value of stop-level load time,
:
[3150] Terms with derivatives higher than the second-order are truncated and are zero in any case for the quadratic forms used to fit
to the LTV sample. Substituting the Taylor's series expansion within the integral and moving the value of the function and derivatives that are evaluated at the mean outside the integrals produces:
[3151] The integrals on the right-hand side are reduced term by term using the standard properties of a continuous probability density function. These properties can be found in any basic mathematical statistics text and are 1) that the integral of
over its range is 1, 2) that the first moment of
is the population average (mean) of
, and, 3) that the second moment of
about the mean is the variance of
. These properties are stated mathematically as follows:
[3152] Substituting for the integrals and simplifying the result leaves the following equation:
[3153] This is the relationship between the Average Stop Level Load Time Function,
, and the Applied Stop Level Load Time Function,
, when
and its derivatives are evaluated at the average volume per stop. If the function
is a quadratic, the function
is exact because the Taylor's series has no terms higher than the second order. The function
will be a very close approximation anyway if
is a symmetric distribution since all of the odd moments about the mean are zero for such a distribution.
[3154] Notice that the two functions
and
differ by an amount that is fixed because the third-order derivative of
is assumed to be zero and because the variance of the probability density function
is a fixed value that is independent of the mean. The derivatives of the functions
and
are interchangeable in the definition of elemental load time variability:
[3155] The elemental load time variability used by the Commission and by the Postal Service is actually an approximation that is exact only if
. The approximation is the elasticity computed from the Applied Stop Level Load Time Function
at the point that corresponds to the average volume per stop
:
[3156] This approximation is a convenience statistically because
is easier to compute than
.
[3157] The Commission's method is to compute elemental load time variability separately for SDR, MDR and BAM stops. The information used for each stop type is, first, an econometric fit of the Applied Stop Level Load Time Function
and, second, the average volume per stop,
. This is all the information that is needed to apply the approximation. If average load time,
is known or can be estimated from other information, then the accuracy of the calculation could be improved by substituting
for
. The accuracy of the calculation also depends upon the success of the econometrics in fitting functions to the LTV sample for each stop type.
[3158] If
is a vector of volumes per stop by shape etc., then all of the variances and covariances of the multivariate probability density function
are involved in the relationship between
and
:
[3159] where
is the covariance of
and
. The assumptions of the multi-variate case are analogous to the assumptions of the single-variate case. The Taylor's series expansion that is used in the multi-variate case is assumed to have no partial derivatives higher than the second order and all of the elements of the variance-covariance matrix of the multivariate probability density function are independent of the vector of means. Therefore, the multivariate analogue of the Average Stop Level Load Time Function also differs from the multivariate Applied Stop Level Load Time Function by a fixed amount. All of the rest of the mathematics follows with partial derivatives with respect to the components of the vector
replacing the derivative of
with respect to
.
[3160] The mathematics of the established Load Time Variability Model can be applied with only definitional changes to a model whose basic behavioral functions are defined at the route level rather than the stop level. The functions
,
,
and
would all be redefined at the route level with the number of system routes, say
, replacing the number of system stops,
. All of the necessary changes are straightforward, for example, volume per stop,
, would have to be redefined as volume per route and
as load time per route.
[3161] Postal Service witness Baron has proposed several changes to the Commission's method for determining the volume variable component of load time costs. These proposals are motivated by witness Baron's belief that the established Load Time Variability Model is flawed. In each instance the perceived flaw corresponds to a proposal made by witness Baron in testimony given in Docket No. R97-1 that was rejected by the Commission.
[3162] The Postal Service's methodological proposals are:
· That the Commission deduct a predetermined amount of fixed time per stop from load time per stop and add it to access time.
· That the Commission include in elementary load time volume variability a new "deliveries" effect that arises from regarding possible stops as actual stops in the load time regressions.
· That the Commission no longer add the residual of load time, after the deduction of elemental volume-variable load time, to access time. The entire residual of load time cost would become a part of institutional cost.
[3163] The Commission rejects the Service's methodological proposals again for reasons that differ little from the reasons stated in the R97-1 Recommended Decision. PRC Op. R97-1, paras. 3253-3307.
[3164] Witness Baron reiterates at many points a belief that only an identifiable fixed component of load time at a stop should be included in the amount of load time that the Commission adds to access time. The load time that the Commission adds to access time is the residual labeled "coverage related" in the Commission's System-level Load Time Model. Acceptance of witness Baron's proposal would cause a considerable reduction in the amount of load time that the Commission regards as coverage-related, and a commensurate reduction in the load time that is ultimately attributed to subclasses using the single subclass stops proportions.
[3165] Witness Baron's proposal is motivated by a misreading of the Commission's R90-1 Recommended Decision where we described coverage-related load time as "independent of the amount of mail delivered at a stop." PRC Op. R97-1, paras. 3276-3280. According to witness Baron the Postal Service also regards coverage-related load time as "independent" of volume: "the Postal Service has consistently asserted that the stops effect of volume on load time equals the increase in time that results from the accessing of a new stop. The Postal Service regards this block of time as independent of the amount and mix of volume delivered at that stop." USPS-T-12 at 7. Witness Baron uniformly interprets "independent" as meaning "fixed" for all possible levels of volume although there is nothing in the Commission's past decisions to justify such a strict interpretation.
[3166] Witness Baron's proposal was analyzed at length in the Commission's R97-1 Recommended Decision and it was rejected. PRC Op. R97-1, paras. 3258-3285. Witness Baron's testimony in the present proceeding reargues his R97-1 proposal while adding nothing that is new. The proposal is still based entirely on the belief that coverage-related load time should only contain load time that is fixed per stop. Witness Baron's own summation of his arguments can be found in his rebuttal testimony: 1.) "the residual violates the premise of the fixed-time at stops definition", 2.) "the residual is the correct measure of coverage-related load time only if the load time equation defines load time as a strictly linear function of volume", and, 3.) "according to the residual formula, BY 1998 coverage-related load time per stop equaled 6.65 seconds per SDR stop, 17.35 seconds per BAM stop, and 39.90 seconds per MDR stop. These estimates are much too high to qualify as realistic predictions of fixed stop time." Tr. 43/18683-85.
[3167] The basic technical error in witness Baron's proposal is that it conflicts with Crowder's equation except in the special case when the Conceptual, Applied and Average Stop-Level Load Time Functions,
,
and
, are all linear. The mathematics that produces Crowder's equation is, at the same time, a proof that the coverage-related stops effect is found by applying the stops elasticity
to the whole residual
, not just to a fixed part of it as proposed by witness Baron. Therefore, witness Baron's proposal is invalid mathematics. Witness Baron's error can be seen easily by considering the load time that would be saved if the system lost a stop but the volume at the stop was redistributed so that total system volume remained the same. The load time that would be saved would be all of the load time at the stop minus the elemental load time that would have to be added to handle the added volume at the remaining stops. This is exactly the residual found in Crowder's equation. The residual includes the fixed load time described by witness Baron, but it also includes the accumulated effects of the curvature of the functions
,
and
when they are nonlinear in
.
[3168] OCA witness Ewen presents residual load time cost estimates in Table 2. Tr. 25/12031. They show the difference between witness Baron's proposed fixed load time costs and the residual load time costs that arise from an application of the established method to information from the R97-1 record and the Postal Service's response to OCA interrogatory. OCA/USPS-T12-8. Witness Baron's fixed load time costs are only $260,244,000 (Ibid. line 2, column (b) "Postal Service Methodology") while the amount of the residual in Crowder's equation is $1,104,406,000 (Ibid. line 6, column (a) "PRC Methodology"). In addition, the Postal Service methodology treats only a small percentage, 7.3 percent, of the fixed load time costs as volume variable. The Commission's use of single subclass stops proportions provides a basis for attributing 17.5 percent of the larger residual. Ultimately, the Postal Service adds only $18,933,000 of load costs to its volume-variable costs for coverage related load time. The Commission's method adds $192,807,000 to attributable costs for the same effect.
[3169] The large difference between witness Baron's fixed load time cost and the established method's residual occurs because the Applied Stop Level Load Time Function used by the Commission is highly non-linear. To begin with, the functional forms used in the econometrics to fit the function,
, are quadratics that are separable in
and
, meaning that there are no cross-products between these variables USPS-T-12 at 4-5. When the quadratic forms are fit to the LTV sample many of the squares and cross-products between the components of the vector,
, of volumes by shape etc. receive statistically significant coefficients. The effects of these nonlinearities can be seen wherever the fitted functions are used. For example, witness Ewen shows that the "inferred stops effect" corresponding to the vertical intercept for the receptacle dummy with the lowest coefficient is negative for all three stop types. Tr. 25/12036-38. Witness Baron's own comparisons of the average FY 1998 predicted load time to the load time predicted for the average volume stop exhibit the effects of nonlinearity quite clearly for MDR and BAM stops USPS-T-12 at 17-18.
[3170] Witness Baron's method for estimating fixed load time would be unacceptable to the Commission even if it were prepared to accept his proposal in principle. His estimates of fixed load times were produced using the kind of ad hoc procedure that our rules for econometric evidence are designed to exclude. Witness Baron describes his procedure as follows:
To summarize, this procedure measures the stops effect as the minimum of the load times recorded during the 1985 load-time field test at stops receiving only one letter piece. I estimated this minimum for each stop type as the average of the lowest quintile of these observed load times.
[3171] As an estimator, witness Baron's procedure is neither efficient nor unbiased. It is inefficient because it utilizes only a small part of the applicable sample. For example, only 1373 of 16,037 SDR stops are one letter stops. Tr. 43/18685. It is biased because there is no reason to expect that the distribution of the load times of the lowest quintile of one-letter stops is centered at the fixed load time for all stops. All of this and other faults are evident from witness Ewen's analysis of witness Baron's estimation methods. Tr. 25/12038-42. A "revised" procedure described by witness Baron in his rebuttal testimony Tr. 43/18685-94 is ad hoc and seems to have most of the same flaws identified by witness Ewen in the original procedure.
[3172] Crowder's Equation. Witness Baron resurrects an argument, made in his R97-1 rebuttal testimony, in an attempt to discredit Crowder's equation. His argument can be analyzed in terms of the notation and mathematics of the Commission's established model. This argument is that the average load time at a stop,
, is unequal to the value of the Applied Stop Level Load Time Function,
, when the function is evaluated at the average volume per stop,
. USPS-T-12 at 9-16. The two are likely to be unequal "due to the substantial non-linearity in the load time regressions" as stated by witness Baron. Although it is certainly true that
and
are unequal for the fitted equations used by the Commission, the derivation of Crowder's equation is not dependant on the assumption that the functions
and
are linear or the same as claimed by witness Baron.
[3173] In his direct testimony witness Baron provides a derivation of Crowder's equation using the function
instead of the function
. He observes that the two functions are not equivalent, asserts that the function
does not exist, and claims that Crowder's equation is incorrect. Witness Baron's basic mathematical error here is his mistaken belief that the Average Stop Level Load Time Function,
, used in the Commission's derivation of Crowder's equation does not exist. Witness Baron's own words (but using the Commission's notation for the functions
and
) are as follows:
The claim that even though(where
is one of the load-time regressions), some other functional relationship
exists, is also incorrect. This claim asserts that an equation exists quantifying average load time over all stops as a function of average volume per stop. In reality, there is no alternative
function to substitute for
. For a functional relationship to exist between
and
, each average volume per stop (
) must produce a unique corresponding value for average load time per stop (
). Clearly, this requirement is violated. Each unique value for
can be produced by a virtually infinite number of differing allocations of mail volume across total, system-wide stops. Moreover, because of the non-linearity of the relationship between load time and volume at any one stop, each such allocation of volume across multiple stops produces a different value of
. Thus, for any
,
will take on many differing values. Since a functional relationship requires that
equal only one value for each
,
cannot be a function of
.
[3174] The function
not only exists, its approximate form is known for a very large class of functions,
, and probability densities,
, and its exact form is known for the quadratics used in the Commission's "load-time regressions". When
is a simple variable (rather than a vector) this form is:
[3175] When
is a vector with elements indexed
,
the form becomes:
[3176] The existence of the function
was pointed out by the Commission in the R97-1 Recommended Decision. PRC Op. R97-1, paras. 3283-3289. Its derivation which is shown above requires only an elementary knowledge of mathematical statistics. The problem with witness Baron's "explanation" of why the function cannot exist is that both
and
are mathematical expectations defined by integrals involving a continuous probability density function
. His explanation is actually an attempt to apply verbal logic to solve a problem in the integral calculus and reaches an incorrect conclusion.
[3177] Witness Baron's failure to recognize the existence of the function
leads to another erroneous assertion about Crowder's equation. Witness Baron believes that Crowder's equation is valid only if the function
is linear in
. Actually, the functions
and
will be identical if either
is linear in
or the second-order moments about the mean of
are all zero
for all
. If
is linear then
will be linear which would certainly simplify the mathematics of the established Load Time Variability Model, but the linearity assumption is not necessary and does not hold for the regression equations used by the Commission.
[3178] The Conceptual Stop Level Load Time Functions,
, for MDR and BAM stops include actual deliveries,
, as a variable. Actual deliveries is solved out to produce the Applied Stop Level Load Time Function,
, that is actually fit to the LTV survey data. The Applied Stop Level Load Time Function is more convenient because it represents all stop-level volume effects with the single variable
, since possible deliveries,
, is non-volume variable.
[3179] That the function
and not the function
was used with the LTV sample was clear in witness Baron's R97-1 Direct Testimony and is evident in any case from the LTV sample itself. Possible deliveries,
, is the variable that is recorded for stops in the LTV data set. In his R97-1 testimony witness Baron incorrectly resubstituted
for
in the Applied Stop Level Load Time Functions for MDR and BAM stops. This error is repeated in his testimony in this proceeding. According to witness Baron "[t]he Postal Service also views the deliveries variables in the MDR and BAM load time equations as actual deliveries" USPS-T-12 at 19-22.
[3180] The effect of this error on witness Baron's load time variabilities is described by witness Crowder "All volume-related stop level effects are already captured by the volume coefficients in the model. Thus, his approach amounts to attributing some of the stop level time twice and is clearly excessive and inappropriate." Tr. 32/16191-93. This assessment is confirmed by the mathematics. The function
is obtained in the established Stop-Level Sub-Model by making the substitution
in the function
:
[3181] Resubstituting
for
as done by witness Baron leaves:
[3182] Differentiating with respect to
gives:
[3183] Since
is close to one, the deliveries effect, is almost double-counted:
[3184] The elemental load time variability used by the Commission and by the Postal Service is an approximation that is exact only if
. The approximation uses
instead of
and is identical to the load time elasticity of volume per stop computed on the function
at the point corresponding to average volume per stop,
:
[3185] This approximation is a convenience statistically because
is easier to compute than
. An exact calculation of elemental load time variability is obtained when
is used instead of
because the derivatives of
and
are the same:
[3186] Witness Baron sees that
and
are unequal (USPS-T-12 Attachment A at 38-39) but fails to see that the derivatives of
and
are the same. This is understandable since witness Baron failed to recognize that the function H even existed. Witness Baron also cites some essentially irrelevant testimony by witness Bradley in R90-1 that `evaluation of a cost function at the mean volume level provides, necessarily, an unbiased estimator of the true volume variability'. USPS-T-12 at 39 citing R90-1, USPS-RT-2 at 10. All that this means is that
is an unbiased estimate. It says nothing about
as an approximation for
.
[3187] Witness Baron regards the approximation used by the Commission as a fatal flaw in the established Load Time Variability Model. In reality, it is a convenient but unnecessary approximation that can be dispensed with any time that the Postal Service wants to take the trouble. Witness Baron's direct testimony includes an elaborate and unnecessary quantitative demonstration that
and
are unequal using data from the 1998 Carrier Cost System (CCS). USPS-T-12 at 16-18. The average of the predicted load times by stop type from witness Baron's Table 1 are estimates of
that could be used to eliminate the approximation used by the Commission. Witness Baron's calculations demonstrate that the Postal Service collects with the CCS all the information it needs to improve the accuracy of the elemental load time variabilities,
, used with the established method.
[3188] Witness Baron does not calculate volume variability correctly for his own proposal. Deducting a fixed amount from average load time per stop and adding it to access time as he proposes requires a change in the calculation of the elasticity,
, that witness Baron uses as his volume variability. To avoid an error, this elasticity must be computed after the Applied Stop Level Load Time Function,
has been shifted downward for the deduction of the fixed time. In Docket No. R97-1, and again in R2000-1, witness Baron fails to make the necessary change in his calculation of
which is calculated from the unshifted function
. The change is easy to make. In order to avoid an error in the amount of volume variable load time that emerges from his calculations, witness Baron must multiply the elasticity
by
where
is the fixed amount he deducts from load time per stop. Without this correction his method produces volume variable load times that are too low.
[3189] Next, we note that we can find nothing in the testimony of witness Crowder in this case to support witness Baron's assertion, repeated on Brief by the Postal Service, that witness Crowder now believes that the mathematics of the System-level Load Time Sub-model presented in her R97-1 Response to Notice Of Inquiry No. 3 is incorrect. In his rebuttal testimony witness Baron claims that "Ms. Crowder's new mathematical derivation provides a critical validation of my Docket No. R2000-1 analysis showing that the residual measure of coverage-related load time is valid if and only if the load time is linear." Tr. 43/18680 (emphasis added). An entire subsection of the Postal Service's Initial Brief is entitled "Witness Crowder, upon whose prior testimony the Commission based its system-wide approach to coverage related load time, has now confirmed the correctness of Mr. Baron's approach." Postal Service Brief at V-87 to V-91.
[3190] The sole basis for witness Baron's assertion appears be his own analysis of a route-level model presented by witness Crowder in response to a USPS interrogatory USPS/MPA-T5-2 (Tr. 32/16233-39). The mathematics of the Commission's established Load Time Variability Model does not change in any essential way when route-level functions replace the stop level functions of the established model. Witness Crowder's route level counterpart of the Conceptual Stop Level Load Time Function is a route-level load time function:
[3191]
is load time on the route,
is route volume,
is a function for average "unit piece handling and loading costs at the delivery point",
is a function for actual stops,
is possible stops and f is fixed stop time. Witness Crowder notes that when the route-level load time function is fit to the Engineering Standards (ES) data it is in a form in which
has been solved out:
[3192] This is the route-level counterpart of the Applied Stop Level Load Time Function. Possible stops,
, is analogous to possible deliveries,
, in the stop-level model.
is a non-volume variable control that is needed along with others to correctly fit the function. Witness Crowder observes that:
route-level load time variability measured from such a model must be of the reduced form, which must include all volume effects detailed on the right hand side, including all coverage-related effects initiated by the volume change.
[3193] Her "coverage-related" effects at the route-level are equivalent to the delivery effects at the stop level that are imbedded in the stop-level elasticity
. At the system level load time is equal to average load time per route times the number of routes in the system, say
. The number of routes,
, will vary with volume just as the number of stops varies with volume in the established model. If we define a function for the average load time per route as
then:
is the starting point for the system level submodel. All of the rest of the mathematics for the established model follows, including Crowder's equation. Elemental volume variability is the route-level load time elasticity of volume,. The coverage effect is the result of applying the elasticity of
with respect to volume, call it
, to the residual
.
[3194] Witness Baron's attempt to derive coverage-related load time for witness Crowder's route-level model is found in Attachment A to his rebuttal testimony Tr. 43/18729-33. From beginning to end, through five pages of mathematics, witness Baron completely fails to recognize that load time at the route level must be multiplied by the number of routes to get system load time. As a result, his analysis never reaches the system level where Crowder's equation is derived.
[3195] City carrier letter route costs are divided into several functions. Traversing a route is referred to as route time; deviating from the route to reach a point of delivery or collection is referred to as access time; loading the mail in a receptacle, collecting mail and/or interacting with a customer for accountable mail is referred to as load time. The remaining activities are characterized as support costs. The latter function includes the costs of carriers loading mail into their delivery trucks and driving to their routes.1 The data and special studies used to divide the city carrier letter route costs into functions are described in USPS-LR-I-1 and in the R97-1 Decision, Chapter III, Section B.
[3196] The portion of load time that varies with the volume of mail delivered at stops is referred to as elemental load cost. Regressions of volume on load time, by shape and accountable activity, are used to calculate the elemental load costs. These costs are treated as 100 percent volume variable. They are distributed by shape and accountable activity to subclasses according to the distribution of mail pieces from the City Carrier Cost System annual sample of routes.2 Coverage related load time costs is the remaining difference after subtracting the elemental load costs from the total accrued load costs. The attributable portion of coverage related load cost is the proportion of stops that are single subclass stops.
[3197] UPS witness Luciani observes that, in calculating avoided costs, Postal Service Witness Daniel distributes city carrier elemental load cost by weight within the First Class Presort and Standard (A) mail categories. Witness Luciani concludes that if
weight is a proper basis for reflecting cost differences within the narrow ranges from one ounce up to thirteen ounces for First Class Mail Presort and from one ounce up to sixteen ounces for Standard Mail (A), then it surely should be used in the case of the more significant weight differences between the lighter weight and the heavier weight classes of mail.
[3198] He proposes that the distribution key for parcels be the "product of average weight and volume data from the City Carrier Cost System for each subclass of parcel shaped items." 11781. He obtains the average weight for First-Class and Standard (A) parcels from cost studies performed by witness Daniel. He uses billing determinant to estimate the average weight for parcels for other subclasses. 11777. Applying the Commission's attribution method to BY 1998 data witness Luciani's proposed distribution key would increase attributable costs by $19.1 million for Priority Mail, and $54.2 million for Zoned Parcel Post over the estimates in the Service's initial filing. The attributable costs of First-Class and Standard A mail would be reduced by $25.3 million and $50.3 million, respectively. 11782.
[3199] Citing testimony by witnesses Daniel and Baron, Postal Service witness Kay asserts that shape is the major reason that one piece of mail takes longer to load than another piece, and is the only load-cost causing factor cited on the record. Tr. 39/17760. Furthermore, witness Kay claims that the weight studies cited by UPS only provide an upper bound for the effects of weight on city carrier costs within rate categories. Witness Kay argues that larger items of the same shape may be assumed to be heavier, but the reverse may also be true. In summary, the Postal Service does not believe that the effect of weight on load costs has been demonstrated on the record. It opposes witness Luciani's proposal to use weight as a distribution key.
[3200] In the Commission's view it is plausible that weight is a major factor determining the time it takes to load parcels. It as at least as likely that the dimensions of the piece have a strong effect on loading time and the correlation with weight is unknown. The Commission is sympathetic with witness Luciani's argument, but data are lacking to support a shift to weight as the sole basis for the distributing costs to subclasses for parcel shaped pieces. It may be that weight should provide a basis for distributing the load costs of letter and flat size mail. Although the Commission rejects the Luciani proposal for lack of data, it urges the Postal Service to study the effect of weight on the costs of elemental load time.
[3201] City Carrier street time on letter routes is apportioned to its constituent functions in proportion to tallies gathered in the 1986 Street Time Survey (STS). One of those functions is runtime, defined as the time that it takes a carrier to travel between stops on his route. Under the established analysis, runtime is decomposed into "route time," defined as the time that a carrier requires to traverse his route without deviating from it to access delivery points, and "access time," defined as the time that a carrier spends deviating from his route to access delivery points. Regression analysis is used to identify the portion of runtime that varies with the number of stops covered. That portion is then multiplied by the single subclass stop ratio to estimate the attributable portion of access time costs. The portion of runtime that does not vary with the number of stops accessed is generally regarded as fixed route time, which is treated as an institutional cost. A small portion of route time on motorized letter routes, however, is estimated to be volume variable, and therefore attributable.
[3202] Elasticities of runtime with respect to covered stops are derived from regression analysis of data collected in a 1988 survey known as the Curbline Access Time and Foot Access Time (CAT/FAT) Study. This study evaluated carrier activity on a random sample of 438 city carrier routes: 161 curbline routes, 78 foot routes, and 199 park and loop routes. In an experimental simulation, carriers were observed traveling over a designated portion of each test route five different times, accessing a different percentage of possible stops on each run. The carriers delivered no mail, but paused at each stop to mark a data collection sheet. Of the five experimental runs conducted on each route, one was at 100 percent coverage, one at 90 percent, and one each at 80 percent, 70 percent, and 60 percent. For each run, data collectors recorded the time expended by the carrier (i.e. the runtime) at the various levels of coverage.3
[3203] The established runtime variability model has been in use since Docket No. R901. It is a more general version of the model proposed in that docket by Postal Service witness Colvin in USPST7, and proposed again in Docket No. R97-1 and in this docket by witness Baron. The established model has the following specification:
where there areroutes, indexed by
; 5 runs for each route, indexed by
; and 8 route types, indexed by
.
[3204] The established model form is quadratic. The cost driver is STOPS. A separate slope coefficient is estimated for the STOPS squared variable for each route. In addition, a separate intercept coefficient is estimated for each combination of run and route type.
[3205] Because each test route in the CAT/FAT study had unique characteristics, dummy variables were included to control for route-specific factors. To control for any "learning curve" effect that would influence running time, a dummy variable was included to control for the run number. The model is estimated separately for three route groups - curbline, foot, and park & loop - producing one regression for each group. See PRC Op. R90-1, para. 3052, and PRC LR-10.
[3206] Witness Baron proposes to restrict the established model to require all of the STOPS and STOPS squared coefficients to be equal across all routes, and to require all of the run number coefficients to be equal across all route types. The model that the Postal Service proposes has the following specification:
[3207] As in Docket No. R97-1, witness Baron advocates imposing a single, common slope coefficient on the STOPS and STOPS squared terms, which assumes that the individual route coefficients are equal. He also advocates imposing a common slope coefficient on each run number variable, which assumes that the individual route type coefficients are equal.
[3208] In PRC Op. R901, paras. 3053-3054, the Commission explained why it believed that the Postal Service should have tested these restrictions statistically to see if they were consistent with the data, rather than simply adopting those assumptions a priori. The Commission noted that variations in the FAT/CAT data across routes and route types due to variations in their physical characteristics were to be expected and should be tested. The Commission tested the significance of such variations by generalizing the Postal Service's model to allow the coefficients of the STOPS and STOPS squared terms to vary by individual route. It found that this variation was statistically significant at the .01 confidence level, and that taking this variation into account significantly improved the fit of the Postal Service's model.
[3209] In Docket No. R97-1, witness Baron offered several reasons for not adopting the more general, better fitting model. He argued for example, that highly correlated route-specific coefficients that have passed an F-test for joint statistical significance should nevertheless be selectively discarded according to their individual t-statistics. The Commission interpreted his comments as recommending that they be discarded during the modelling process. In this docket, he comments that he had advocated that they be discarded after the modelling process, at the time that the elasticity of runtime is evaluated. USPS-T-12 at 25. The Commission's interpretation of witness Baron's comments stands corrected. However, selectively ignoring the coefficients of highly correlated, jointly significant variables at the evaluation stage is no more legitimate than selectively discarding those variables during the specification stage of the modeling priocess.
[3210] In Docket No. R97-1, witness Baron argued that the results of the more general model were implausible. He pointed out that some STOPS coefficients were negative and some STOPS squared coefficients were positive, contrary to his expectations. The Commission commented that the focus should be on whether the combination of the STOPS and STOPS squared coefficients yield plausible results at the average number of stops. In this docket, witness Baron argues that the combination of these coefficients is not plausible for certain routes. He reports that 21.1 percent of the route-specific elasticities of curbline route running time with respect to actual MDR stops is negative, 1.9 percent is between 0.00 and 0.10, and 5.0 percent is greater than 2.00. For park and loop routes, he reports that 18.6 percent of the elasticities with respect to MDR stops is negative, 3.5 percent is between 0.00 and 0.10, and 7.5 percent is greater than 2.00. He reports that the elasticities that result from the restricted model are in a tighter range without the implausible extremes. Id. at 27.
[3211] The elasticity estimates produced by the more general model will be less precise, and will have a wider range of results in terms of individual route elasticities than the restricted model. A more relevant consideration than the plausibility of each individual route elasticity is whether the general model yields a more reliable estimate of elasticity at the mean for a route group. For the reasons discussed in Docket No. R97-1, the Commission concludes that the risk of imprecision in the more general model is less than the risk of bias in the restricted model. PRC Op. R97-1, paras. 3250-3252. Artificially constraining coefficients for routes to be equal, as witness Baron recommends, might produce more plausible results for individual routes, but does so at the risk of getting a biased estimate at the mean for a route group, which is the estimate of interest.
[3212] In Docket No. R97-1, despite its lower R squared statistic, witness Baron argued that the restricted model fit the data better than the more general model. In this docket, witness Baron concedes that generalizing the model significantly improves the R sqaured statistic while it eliminates the omitted-variables bias that exists in the restricted model. He argues, nevertheless, that
no measures were used to actually quantify the magnitude of any biases in the quadratic model. The amount of bias could be small. The careful analyst is clearly justified in refusing to uncritically regard these biases as high enough to warrant serious concern, and in refusing to regard the F Test as a conclusive guideline that must dictate the correct choice among competing regression models.
[3213] He contends that both the degree of bias in the coefficient estimates and the precision of those estimates must be measured in order to decide how to resolve the precision/bias trade off. Id. at 30, fn. 38. He fails to do this, however. He shows how much generalizing the Postal Service model improves the R square statistic, and characterizes the improvement as "modest." He doesn't characterize, let alone quantify, the amount of precision that is lost. Id. at 29. More tellingly, he ignores the Commission's discussion of the adjusted R squared statistic that is designed to take into account the loss of efficiency that results from adding explanatory variables. He makes no comment on the Commission's observation that the adjusted R square statistic for the more general model is higher than for the Postal Service model, indicating that the more general model removes bias with a relatively minor the loss of precision. PRC Op. R97-1, para. 3251, fn. 35.
[3214] Witness Baron is correct that in arguing that when econometric modelling presents a trade off between precision and bias in the estimate of interest, each case must be evaluated on its facts. The choice made is a judgment call. If the data for these route groups were taken from small samples, the risk of imprecision might be greater than the risk of omitted variables bias. Because the route group data comes from relatively large samples, however, omitted variables bias appears to present the greater risk.
[3215] For the reasons discussed above, the Commission rejects witness Baron's criticisms of the established runtime variability model.
[3216] The Postal Service's data collection systems provide estimates for the amount of time city carriers spend driving on a route. As volume increases, the driving time may change due to the addition of parking points for the formation of new walking loops and the addition of dismounts to deliver high volumes at individual stops. In R90-1, a variability factor was first adopted to calculate volume variable driving time costs. In Docket No. R97-1, the Commission adopted USPS witness Nelson's proposal for modifying the analysis of driving time on Motorized Letter Routes.
[3217] The R97-1 analysis by witness Nelson is based on a 1996 Motorized Letter Route survey in which supervisors classified looping/dismount parking points as being established due to volume/weight or due to other factors. Witness Nelson then classified the loop parking points caused by volume/weight as 100 percent volume variable and the other loop parking points as 0 percent volume variable. Dismounts established due to factors other than volume/weight were judged to be fixed relative to volume and given a 0 percent volume variability factor. For dismounts considered to be caused by volume/weight, witness Nelson assumes that their variability is equal to the weighted average of the first three variabilities (40.99 percent). This approach results in a 32.15 percent average variability for loop stops, 40.99 percent for dismounts due to volume/weight, and a total Motorized Letter Route variability of 40.99 percent. The following table summarizes the calculations. R97-1 Tr. 4/1347-49 and 1353.
[3218] For this docket, witness Nelson was asked by MPA to reexamine his R97-1 Motorized Letter Route variability analysis. This review led to a conclusion that the interactions of loop parking points and dismounts are not taken into consideration in the R97-1 calculation of the volume variability.
Basically, stops that would become new volume-driven dismounts in the presence of a volume increase are currently served on loops. The conversion of such stops from loop delivery points to (volume-driven) dismounts as volume increases moderates the need to add looping points. If the analysis assumes that a volume increase on volume-driven loops is accommodated entirely by an equal percentage increase in the number of loop parking points, none of the stops on those loops will need to be converted to dismounts, and the number of volume-driven dismounts will not change. In light of these considerations, if the 100 percent figure is used for volume-driven looping points, it would be most reasonable to treat volume-driven dismounts as fixed (i.e., 0 percent variable).
[3219] Employing this logic reduces the dismount variability to zero, leaving only the loop variability of 32.15 percent to contribute to the Motorized Letter Route variability.
[3220] Witness Nelson claims in this docket that "routine loops that are established on the basis of volume/weight were treated as 100 percent because of the constraints on the formation of such loops imposed by the 35-lb. weight limit on carrier satchel loads." Id. at 13415. The 35-lb. argument appears to be new in this docket. It is not found in the reference to R97-1, Tr. 4/1353, that Nelson cites in his testimony as the authority for his specific computation of the Motorized Letter Route variability. Tr. 28/13415.
[3221] Postal Service witness Baron disagrees with witness Nelson's logic regarding the creation of new dismount stops. He presents a new analysis that supports a variability of zero for Motorized Letter Routes. Witness Baron argues that there is no reason to assume, as Nelson does, that a new dismount stop generated by a volume increase will fall at an existing parking point on an existing loop. He argues that the dismount could fall on a non-loop segment of an existing route, and not become a parking point for a new or existing loop. Lastly, witness Baron argues that it is blatantly contradictory for witness Nelson to assume "the volume variability of `volume-driven dismounts' should be regarded as 0 percent. He argues that if 'volume-driven' dismounts are, indeed, volume driven, then the variability of these dismounts must be greater than 0 percent." Tr. 43/18725-26.
[3222] Having challenged witness Nelson's proposed variability for dismounts, Baron turns to an analysis of what the variability of the loop and dismount parking points should be. He challenges witness Nelson's assumption that a 100 percent variability for loop parking points is implied by the 35-lb. weight limit on carrier satchel loads. Baron uses data from 1,270 records of satchel weight measurements taken during the Engineered Standards. See USPS-LR-I-329 for the data. Each record lists the weight of one mail satchel that a data collector weighed at a loop parking point prior to the carrier beginning the loop. The average satchel weight is calculated to be 11.33 pounds with only 2 exceeding 30 pounds. From this data on satchel weight, witness Baron concludes "that, for all practical purposes, there is a zero probability that a marginal (say one percent) increase in volume... would increase the weight of mail to an extent that a new loop parking point would be required. The clear implication is that the variability of loop [parking] points with respect to mail volume is likewise zero." Tr. 43/18727.
[3223] Baron observes that carriers almost never respond to a volume and weight increases at a dismount stop by adding a new vehicle parking point. Lastly, he states that, `to the extent the carrier does anything at all differently due to the volume and weight increase, he is most likely to convert the stop into a loop [parking point]." Id. at 18728. This would seem to agree with witness Nelson's assumption that a new dismount stop is likely to become a loop parking point.
[3224] Witness Baron relies on Engineered Standards data that the Commission declines to use for other purposes in this docket. Setting this issue aside, to treat the average weight of 11.33 pounds as valid does not necessarily imply that the variability of loop parking points is zero. For example, other factors, such as shape or the ability to accommodate various bundles, may lead to a change in loop structure as volume increases. The fact remains that the Motorized Letter Route survey introduced in R97-1 does indicate that supervisors regard 32 percent of the stops as caused by volume/weight. While the variability of these stops may be less than the 100 percent assumed by Nelson in R97-1, assuming that it is zero would not be consistent with the supervisors' experience. Also, as witness Baron observed when critiquing witness Nelson's testimony, "[i]f 'volume-driven' dismounts are, indeed, volume driven, then the variability of these dismounts must be greater than 0 percent." Id. at 18725-26. The Commission will retain the 32.15 percent variability for parking points on loops. Analyzing only loop parking point variability can support this much variability. It is likely that dismounts contribute some additional variability.
[3225] It is reasonable that many of the new dismounts will fall on loops and be counted in the variability for the loop parking points. Conceivably some new dismounts could occur at non-loop route segments. If so, it would increase the number of actual dismounts. While no estimate is provided on what percent of new dismounts would occur on non-loop segments, witness Baron implies it will be rare, since he claims the most likely outcome of a volume/weigh increase is to convert a stop to a loop parking point. Because the variability of dismounts would appear to be small, the Commission accepts witness Nelson's position that the variability of dismounts is zero. While this may not be precisely correct, it is offset by the likelihood that the use of 100 percent variability for the loop parking points is overstated.
[3226] For these reasons, the Commission accepts for purposes of this docket a variability of 32.15 percent for Motorized Letter Route parking points.
[3227] City carriers, working in their delivery unit offices, sort letter and flat-shaped mail that is not in delivery point sequence when provided to the delivery unit. The accrued sorting time is part of the Segment 6 in-office cost in the Cost and Revenue Account System. In-office sorting costs are treated as 100 percent volume variable. USPS-LR-I-1 at 6-2. Some small parcel shaped mail that can fit in the sorting bins are sorted in the office and included in Segment 6. Other parcels, however, are taken to the carrier's truck in a hamper, or some other type of container, without sorting it in delivery sequence. Once at the truck, parcels are loaded and organized in a manner that assists the carrier to easily select them for delivery once on the route. The time loading the truck, or unloading, at parking points, is part of the support component of Segments 6 and 7. Support costs are apportioned to office time and each of the street time functions (route, collection, access and load). The apportioned support costs are then attributed and distributed in the same manner as the associated function. Id. at 7-9.
[3228] UPS proposes that the time spent loading parcels at the truck be deleted from the support component and added to the in-office component. This loading time would thereby take on a much higher variability. UPS witness Luciani derives
parcel sequencing costs by multiplying the cost per piece for sequencing parcels by the volume of parcels delivered in each subclass as estimated by Postal Service Witness Harahush. The cost per piece for sequencing parcels was obtained by multiplying the city carrier wage rate by the city carrier sequencing time per parcel taken from the Postal Service's confidential Engineered Standards study. The Engineered Standards study is based on time standards rather than actual observations. In practice, city carriers are likely not yet meeting those time standards since they reflect more efficient operating procedures than are now used, Tr. 19/8122-23 (Raymond), and thus the cost per piece for sequencing parcels obtained using the results of the time standards study is a conservatively low estimate.
[3229] Total attributable costs increase due to the higher volume variability of in-office costs. The resulting change in costs for each subclass is shown in Exhibit UPS-T-5C, filed under protective custody due to the use of the results from the Engineered Standards study.
[3230] Witness Kay of the Postal Service rebuts the UPS proposal on several grounds. She contends that:
1 Arranging of parcels is not equivalent to the detailed; delivery sequence sort that a carrier performs in the office based on the testimony of witnesses Raymond and Kingsley. Tr. 39/17763.
2 The use of a proposed, individual standard from the Engineered Standards study is not in isolation a valid measure of the time taken to sort a parcel under current carrier procedures. Costs for this function could be higher or lower when a full set of standards are introduced. Id. at 17764-65.
3 Time standards are an average cost per piece; they are not marginal costs per piece. Time standards must be multiplied by a variability to make them applicable to cost attribution. Id. at 17765.
4 Variability of in-office sorting is inappropriate for parcels, since in-office sorting is mainly of letters and flats, which are quite distinct from parcels. Ibid.
[3231] The Commission finds the Service's concerns credible. In particular, the use of potential standards from the Engineered Standards project is speculative. The existence of a proposed standard is not equivalent to evidence from operations on the time actually taken to arrange parcel shaped pieces at the truck. Likewise, the variability of the costs, if they could be determined, needs to be better specified. Therefore, the Commission rejects the current UPS proposal and recommends that the Service conduct a special study to determine the cost of sorting parcel shaped mail.
[3232] City carrier street time costs are divided into letter routes and special purpose routes for purposes of analysis. The latter consists of nine types of special routes, one of which is designated as "Exclusive Parcel Post".4 The costs of each special purpose route can be individually identified in the Postal Service's cost accounting systems. For the purposes of calculating attributable costs, however, special purpose routes are treated as a single group. Tr. 6/2663-65.
[3233] On the assumption that the parcel routes deliver Parcel Post subclass mail, witness Luciani proposes that the entire cost of the Exclusive Parcel Routes be treated as product specific costs and be attributed to the Parcel Post subclass. Since witness Mehan applies the same attribution and distribution factors to all parcel routes, the Service attributes some Exclusive Parcel Post route costs to the Parcel Post subclass.
[3234] Given this situation Witness Luciani proposes what is characterized as a conservative attribution procedure. Namely, he proposes to assign to Parcel Post the difference between the total cost of the Exclusive Parcel Post Routes and the total Special Purpose Route costs attributed to Parcel Post. By UPS calculations this amount is $26.5 million. Tr. 25/11786.
[3235] On rebuttal, witness Kay extracts data from the Docket No. R97-1 C study, to demonstrate that only 11.9 percent of the pieces delivered on Exclusive Parcel Post Routes are Standard (B), Parcel Post Zoned mail. Tr. 39/17769-70. In short, witness Kay demonstrates that the name of the route does not indicate that a particular subclass of mail is delivered on that route.
[3236] Given the distribution of mail on Special Purpose Routes presented by witness Kay, it does not appear reasonable to assign all the Exclusive Parcel Post route costs to the Parcel Post subclass. Consequently, the Commission declines to accept witness Luciani's proposed attribution of these costs. It might be useful, however, if the Service could rename these routes in future versions of LR-I-1, Summary Description of USPS Development of Costs by Segments and Components, in order to avoid further confusion of this kind.
1Detailed definitions of each function are given in LR-I-1, Summary Description of USPS Development of Costs by Segments and Components at 7-2.
2The City Carrier Cost System involves an on-going sample of every tenth stop on a sample of randomly selected routes. USPS-LR-I-16 at 2-3.
3Details of the CAT/FAT test implementation, field instructions, and data collection and recording were presented in Docket No. R90-1, Exhibit USPS-7A, and USPS-LR-F-187 through F-190.
 Postal Rate Commission http://www.prc.gov Voice: (202) 789-6800 Fax: (202) 789-6886 prc-admin@prc.gov |
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is a vector of volumes by shapes etc. indexed by 
, then:
is quite small for most kinds of stops and most kinds of mail. 
at the average volume per stop, 
, is:
routes, indexed by 
; 5 runs for each route, indexed by 
.