Compu & 0,~s RPS, Vol 4. pp. 235-246. Pergamon Press. I?77 Printed in Great Britain

OPERATIONS RESEARCH IN POSTAL SERVICES-A SURVEY*

JATINDER N. D. GUPTA? and LEROY J. KRAJEWSKIS

Faculty of Management Sciences, College of Administrative Sciences, The Ohio State University, Columbus, Ohio 43210, U.S.A.

Scope and purpose-The postal services throughout the world are spending considerable amounts of labor and resources to meet the customer demand in the area of hard-copy communications transfer. In spite of several efforts to improve the services and reduce costs, postal services are a topic of frequent public criticism. Rarely do the revenues earned by postal services equal (or exceed) its costs. This paper describes several problem areas where emerging operations research/management science approaches can be beneficial to the study of postal decision problems. This survey of operations research applications is )y no means exhaustive. It is representative of several efforts in the world to resolve postal issues and it is designed to open up the means of communication for further reporting and research. The paper will be useful to those professionals who wish to gain insights into postal services and to researchers who may want to seek problem areas for future developments of theories and techniques.

Abstract-The collection, processing and delivery of letters and packages comprise one of the largest service industries in the world. This paper provides a broad survey of the application of operations research techniques to analyze and resolve decision problems forced by postal managers in various countries. The problem areas considered include: forecasting, cost and revenue analysis, postal network design, manpower planning and scheduling, maintenance, and service characteristic measurement. The paper concludes with a brief description of the efforts to train postal managers in the use of operations research in their decision-making functions.

INTRODUCTION

The primary purpose of a postal system is to transmit hard-copy written communications from one point to another in an acceptable manner. This system is quite old and evolved as a piece-meal effort over several centuries in various countries. In the United States, for example, the first official postal route was inaugurated in 1775 and since then, the US. Postal Service has become a multi-billion dollar organization employing nearly 700,000 persons to handle about 100 billion pieces of mail every year. As the demand for postal services grew since 1775, new routes and post offices were added to the network without much concern for the effect on the total system. The basic goal of the postal services, till recently, had been to move the mail without much concern about costs or charges to public since the revenues did not need to cover costs. It is only recently (since 1970) that the cost considerations have explicitly entered the postal decision-making process.

The consideration of costs in postal decisions creates several problems. Often, a cost reduction program, especially in times of inflation, is associated with the decrease in the quality of service. This gives enough cause for public criticism and dissatisfaction. Yet, to our knowledge, no postal service in the world has shown its capabilities to recover costs and maintain an adequate level of service characteristics. Perhaps the tradition of government- managed postal services as monopoly is not suitable to achieve the goals and purposes of the postal system. Whatever the case may be, a careful study of postal problems can be useful to arrive at sound operational and strategic decisions.

*The view expressed here are those of the authors and should not be interpreted as necessarily those of their respective organizations.

tJatinder N. D. Gupta is currently General Manager, Information Technology Division, Office of Information Requirements and Technology, MIS Department, U.S. Postal Service. Washinaton. D.C. He holds a B.E. (Mech.) from Universitv of Delhi. M. Tech (IELGR) from Indian Institute of Technology, Kharagpur, India, and Ph.D. from Texas Tech University.‘Dr. Gupta has taught at Texas Tech, University of Alabama in Huntsville, Alabama A&M University, and Sangamon State University. He is the author of more than 30 research papers and is the co-author of an introductorv text: Ooerarions Research in Decision Making.

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fLeRoy J. Krajewski is Professor of Management Sciences, College of Administrative Science at the Ohio State University. He received his Ph.D. in Production Management from the University of Wisconsin-Madison. He is the author of papers appearing in Management Science, Bell J&rr~ol of Economics and Management, Decision Sciences, and the Proceedings of the Fourth Annual Simulation Symposium, as well as in the proceedings of a number of regional and national conferences. He is a member of TIMS and AIDS.

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236 J. N. D. GUPTA and L. J. KRAJEWSKI

This paper surveys the operations research applications (potential and actual) to analyze and resolve decision problems faced by postal managers in various countries. The studies described in the paper and referenced at the end do not comprise an exhaustive list of all such studies performed or in progress. It is only a subset of and representation of the problem areas addressed and the methodologies used.* It is our hope that this paper will stimulate enough interest for several significant studies not yet reported to be openly communicated and that further developments will create a cooperative spirit of mutual benefits.

OPERATIONS RESEARCH APPLICATIONS

The schematic representation in Fig. 1 outlines the problem areas for operations research applications to postal decisions. The postal system is not self-governing; it is governed by the customers and is initiated by the availability of a mail-volume forecast. The outputs from the mail-volume forecast become inputs to the decisions related to facility location, facility layout, and vehicle routing (called network design in our analysis). This, in turn, provides inputs for the aggregate employment plans which are subsequently disaggregated into tour assignments, employee schedules, and maintenance schedules. All these decisions are dictated by two conflicting goals: minimum cost operations and maximum service characteristics. Therefore, cost and revenue analysis and the service characteristics measurements become an integral part of the framework in applying operations research and analytical thinking to postal problems. We describe studies in each of these problem areas.

(a) Forecasting Perhaps one of the most common inputs to postal decision models is a forecast of mail

volumes. The USPS utilizes most standard forms of forecasting methodology such as multiple regression, correlation analysis, time series analysis and good judgment to generate national and regional level forecasts by major postal product line.? Household income and population have been found to be major determinants of postal activity and are used as explanatory variables in the national and regional level models.

The Postal Service in Israel is developing a forecast of postal activity requirements for a particular area so that the size of the new branch office to be located there can be determined.S First attempts included (1) a multiple linear regression model with such independent variables as population growth, level of education, number of cars per family and number of bank accounts and their level, and (2) a nonlinear regression (parabola) model, but resultant correlations for either approach were not acceptable. Presently, analysts are breaking down the aggregate measure of total postal activity into its specific components (such as stamp sales and postal bank activities) and attempting to develop a forecasting equation for each one.

FACILITY LOCATION I I

FACILITY VEHICLE

LAYOUT ROUTING

w EMPLOYMENT

PLANNING I

TOUR ASSIGNMENT

0 LL EMP- MAINTENANCE

SCHEDULING SCHEDULING

Fig. 1. Schematic representation of problem areas.

*A number of the models discussed in this paper are the sole property of USPS and as such specific details on methodology are omitted. These models will be referenced by [4] which contains brief descriptions of all ADP models available to USPS as of 1973.

tSee [6] for a detailed description of the basis for USPS mail volume forecasts made in 1973. tThe authors wish to thank Mr. Ran Gonen of the Ministry of Communications, Jerusalem, Israel, for the information

on the use of operations research for the analysis of postal problems in Israel.

Operations research in postal services-a survey

(b) Cost and revenue analysis

237

The analysis of costs and revenues in postal systems is a necessary activity if efficient operations are to be maintained. This section highlights several studies in the areas of cost estimation, returns to scale, and capital budgeting.

Cost estimation. Mandel[9] describes a Work Sampling system for estimating the in-office cost of handling the various classes of mail and providing special postal services. The sampling universe consists of all post offices in the United States, all employees in these offices (except custodial and motor vehicle employees), and all the worktime they spend. Thus the sampling procedure has three levels: first select a random sample of post offices; then select a random sample of employees within these offices; and finally select a random sample of instants of time. Once the estimated percentages of time that each occupational group spends on each activity are determined, they are multiplied by the total wage bill (broken down by occupational group and specific post office) and summed to arrive at estimated total costs. About 4.5 million observations are made per year and over 200,000 employees participate annually which probably makes this application of Work Sampling the largest in the world.

Two other examples of cost estimation models are the Analysis of Loading Methods System (ALMS) and the Network Cost Model, both used by USPS.* The objective of ALMS is to analyze and compare three alternative methods of truck loading: manual, stacker and com- bination. Given specific inputs relating to stacker investment costs, maintenance, labor wage rates, loading rates, mail volumes and truck data, the program estimates the total costs per truck and per sack for each of the three alternatives.

The Network Cost Model[l2] was used in the development of the Bulk Mail System. Given a proposed postal network, the model simulates the volume of mail to be processed at each facility in the system and estimates the daily operating cost at each facility and ;or the entire system for various sorting, packing and transportation policies.

As a third example of applying a cost model to postal operations, White [ 161 used regression analysis to evaluate sorting cost variations as a function of numerous characteristics (explana- tory variables) in a post office. For the aggregate of all operations in the post office, the two major factors associated with differences in mail processing cost were: depth of sort required (number of handlings) and type of mail (metered, stamped, etc.). In the disaggregate case, where the cost model was applied to individual operations, no single characteristic was found to be dominant to explain the cost variation.

Returns to scale. In a theoretical study, Merewitz [ 101 analyzed costs and returns to scale in U.S. post offices with the intent of determining an optimal post office size. Under the assumptions of a Cobb-Douglas model for intra-post office activity, it was shown that there are diminishing returns to scale based upon a total sample of 156 offices. In order to determine if the degree of returns to scale is dependent upon the level of output, the post offices in the sample were stratified according to the authorized employee complements. This resulted in three groupings: small (2X-630), medium (636-1422), and large (lSll-38,360). Using a regres- sion analysis to estimate the parameters of the CobbDouglas cost function, it was found that increasing returns to scale persisted up through the medium sized offices while the larger offices exhibited decreasing returns to scale. Based upon these results it was recommended that an optimum size office should be about 1400 employees. Thus, the post offices in smaller communities should be amalgamated whereas the offices in the larger cities should be decen- tralized. Of course, no consideration was made for the costs of inter-post office activity which would be greatly affected by the recommendation.

Capital budgeting. The processing of mail in this day and age requires substantial capital input. The USPS has several computer programs capable of evaluating equipment a1ternatives.t Output consists of net salvage value, total cash inflow per year, cash outflow per year, net cash inflow, cumulative net cash inflow and internal rate of return. Such an analysis was used to evaluate main processing alternatives, such as manual systems, Letter Sorting Machine sys- tems, Zip Mail Translator systems, Optical Character Reading systems, Encoder systems and combinations of the above.

*See [4], pp. 9 and 11, for a brief description of these two models. tSee [4], p. 12. for a description of the programs for economic evaluation of mail processing alternatives. Also see [I)].

238 J. N. D. C&PTA and L. J. ~R~EWSKI

The British Post Oflice prefers to use the Discounted Cash Flow and Present Value of Annual Charges methods for capital budgeting.* it should be noted that the scope of the capital budgeting problem is larger in Britain because the British Post Office has responsibility for the capital intensive telecommunications business as well as the postal business.

Revenue analysis. The accounting records reveal the revenues collected by the postal service. However, all this revenue may not be earned by the postal service since customers may still hold stamps and other such devices. Further, the accounting records do not reveal the revenues by each mail category. Therefore, additional analytical studies are required to estimate the revenues in each mail category. The U.S. and Canadian postal services employ similar probabilistic and judgemen~l sampling systems for this purpose. The frame of post offices used for samples is as the one for cost estimates described earlier. Instead of sampling the employees, mail is sampled to determine (i) mail category, (ii) revenue, (iii) volume of mail, and (iv) weight of mail handled. Probabilistic estimates are then derived to provide measures of revenue earned by each mail class and the influence of weight distribution on revenue. For details, see references [2,7].

(c) Postal networks There has been considerable work expended in the analysis of postal networks. In this

sense, a postal network consists of a set of nodes, or processing facilities, connected by transportation links. Designing such a network is no easy task, since, for example, there are over 30,000 nodes in the postal transportation network in the continental United States. This section will review some of the work devoted to facility location, vehicle routing, network evaluation and facility layout.

~ac~~~ty location. In order to improve customer service, the USPS has decided to categorize mail into two basic types: preferential and bulk. Each basic type of mail is to have its own processing and distribution network revolving around the concepts of the Preferential Mail Center (PMC) and the Bulk Mail Center (BMC). PMCs are to process all airmail, first class and time preferential second class mail whereas the BMC’s are to process the nonpreferential second class, third class and fourth class (parcel post) mail. The contention is that by separating the mail on the basis of its physical characteristics, certain economics can be achieved in processing and distribution. Of course, two of the most critical decisions in the designing of these two networks are the determination of the number of facilities and the choice of location for them.

Herring and Horowitz~23] describe the models used by the USPS to design the PMC network. The models determine the number and location of facilities, select the equipment configuration at each location, and estimate the cost and service characteristics for a given equipment configuration.

At the heart of the Detailed Network Model (DNM), which determines the number of facilities and selects their location in the PMC network, is a Mixed Integer Program (MIP) module with the objective of minimizing intra-PMC transportation, platform, and distribution costs within general service constraints on the total network. Since the costs are non-linear, it is necessary to use separable programming and approximate the costs as piece-wise linear. Input to the MIP formulation consists of a list of candidates for PMCs constructed from user input and a heuristic process of checking each potential candidate for its ability to interface with the available transportation network. The output from the model consists of the selected PMCs and the Transfer Post Offices assigned to them for support. Other modules of DNM estimate the service characteristics and the detailed costs of the proposed network. The model was used to select a proposed network of 180 PMCs, although the PMC concept has not yet been initiated by USPS.

The Equipment Configuration Model (ECM) was used to select the optima1 equipment requirements for each PMC once the location and mail volume input of each PMC was determined. The objective function of this MIP model is to minimize total operating and investment costs subject to service constraints and certain technical constraints. Finally, a GPSS simulation model, called the Facility Processing Model, was used to analyze the

*See 181 for the details of how these are used in the British Post Oflice.

Operations research in postal services-a survey 239

dynamics of mail flows through the facility designed by ECM and to adjust the specified equipment requirements to achieve the overall objectives of minimal cost and desired service.

Unlike the proposed PMC network, the BMC network has been authorized and is presently in operation. Cave11 and Edgerton[l9] describe the heuristic model that was used to select the locations for 21 BMCs. Input to the model consists of a population of 600 existing Sectional Center Facilities (SCF) to be considered as BMC candidates, originating and destinating average daily mail flows between these 600 SCFs, processing costs for BMC operation as a function of volume, processing and handling costs at the SCFs and regional transportation rates throughout the country. Given this input, the problem is to assign SCFs to BMCs in such a way that the costs of transportation, handling and processing are minimized subject to service constraints. In the BMC network, mail is routed from an originating SCF to a BMC, to another BMC and finally to a destinating SCF for delivery to the customer.

The heuristic consists of two phases. In the first phase, candidate SCFs are assigned to BMCs in such a way that the sum of the SCF processing cost plus transportation cost to the BMC is minimized. Once all the SCFs have been assigned, the SCF with the largest processing plus transportation cost is selected as the next BMC candidate and all SCFs are reassigned to the new network of BMCs. The procedure continues until an arbitrary number of BMCs have been assigned.

The second phase reduces the number of BMC candidates determined in the first phase by deleting the BMC with the lowest intra-BMC transportation and volume-related costs. When a BMC is deleted all the SCFs are reassigned to BMCs as in the first phase. The process is repeated until an arbitrary lower limit of candidates is achieved.

Once the BMC network was defined it became apparent that transportation costs could be further reduced by considering transshipments for certain routes. The Transshipment Mode1[35] employs a heuristic methodology to select candidate BMCs for transfer points. Routes are candidates for transshipment when they exceed a certain cost level or are below a minimum volume level. These candidates are ranked by cost or volume as chosen by the user. The BMC candidates for transfer points are ranked by priority determined by the user. The heuristic selects the top priority route and transfer point candidate and assigns the route to the BMC candidate if the added volume can be processed and truck capacity is available. If not, the next candidate is selected and the check is repeated. The process terminates when all candidate routes have been assigned to a transfer point.

Vehicle routing. The vehicle routing and scheduling problem in postal systems has drawn considerable research attention in the past. This is primarily due to the magnitude of the problem (many nodes in the network and many links between them) as well as the complication that the scheduling of transportation determines dispatch schedules at the processing facilities which in turn affect operating decisions within those facilities. This research has resulted in a number of different approaches to solving various aspects of this problem.

In a theoretical study, Oliver[30] used the concepts of calculus of variations to derive a solution to the problem of setting optimal dispatch times at one post office in a simple two post office network. The object is to maximize mail making next-day delivery at the second post office, which is equivalent to choosing the dispatch times at the first post office such that the delay of mail in the system is minimized. Further research is required to extend these results to the more general network with transfer points.

The USPS has used the Transportation Model to analyze intra-BMC transportation prob- lems.* The program translates originating mail volume into truckloads given specifications on the use of containers, mail characteristics and shipping priorities. The output consists of an outbound time table for truck departures (dispatches) from sectional centers and associate offices as well as a schedule of arrival times at the BMC.

The Vehicle Scheduling Program (VSPX), purchased from IBM by the USPS, has been successfully implemented in Boston to determine the intra-city routing and scheduling of postal vehicles. The model will minimize cost, number of trucks, number of miles travelled or time on the road depending upon the user’s desire. The result is a routing given the number of nodes in the network. Extensions to the original model enable a maximum of three scheduled trips per

*See [4], p. 2, for a brief description of this model.

240 J. N. D. GUPTA and L. J. KRAIEWSKI

period from the terminal specification of priority ratings for mail classes, and constraints on truck size and dock capabilities.

The Postal Service in Israel is presentfy analyzing route structures for such vehicles as mobile postal units and mail box collection vans. The object is to minimize the total kilometrage of the vehicles. The VSPX program, Eifon-Christophides’ Afgorithm[l] and modifications of the traveffing salesman approaches are being studied for their applicability.

Another model which may prove applicable to the transshipment problem of the bulk and/or preferential mail systems as it relates to vehicle scheduling is the Linehauf Computer Simufa- tar.* The model develops schedules for pickups and deliveries, determines fleetsizes and the number of drivers, and provides the most economical domiciling of drivers and equipment. Unlike VSPX, the model identifies economical transfer points.

Finally, the USPS has an optimizing model for the assignment of postal vehicles for long hau1s.t The problem is to perform the mail transportation from a terminal to a number of postal facilities with the available fleet at minimum cost, subject to the requirement that the schedule be carried out within certain hours of the day. The model specifies the optimal number of trips to each facility, expected number of emergency trips, costs of the trips, total expected costs and the truck time consumed by the scheduled trips.

Network evaluation. Once a network has been designed using methodologies such as those described above, computer simulation has been used to evaluate the network from the standpoint of costs and service. The Network Bulk Mail Simufator[28] has been used by USPS to analyze such activities as input yard queuing of trailers, processing of bulk mail, output dock queuing and the transportation from one point to another. Such design issues as transportation mode selection, dispatch schedules and processing policies have been analyzed with the model.

Tuan and Nee [38] describe MASS, a mail service simulation model developed for the USPS by the Stanford Research Institute. The basic purpose of the model is to evaluate given network designs. The model is quite flexible, in that the specification of the nodes in the network can range from post offices to individual work stations within a post office, enabling the use of the model for analyzing inter-post office problems as well as intra-post office problems. The model was used to evaluate a containerization program between Chicago and New York.

Facility layout. Since large volumes of mail pass through postal facilities in a given day, the arrangement of processing stations within those facilities greatly affects their capability to process the mail in an economical and timely fashion. Postal facilities in the U.S.A. have access to CRAFT which makes use of a paired-tradeoff heuristic to generate relative location patterns for departments such that the cost of the flow of materials throu@r the facility is minimized. The USPS has developed an interesting refinement to CRAFT in that the paired-tradeoff heuristic is used to generate the feast cost material flow patterns as before, but then a location preference matrix (similar to ALDEP) is applied to the five best solutions with respect to material flow costs4 The user then selects the solution with the best tradeoff between the materials flow cost and work center location preference ratings.

(d) Manpower planning and scheduling Since postal systems these days are stiff very fabor intensive, an area worthy of research is

manpower planning and schedufing at individual post o&es. This topic presents many interesting operations research questions since mail volumes are dynamic and postal clerks can be assigned to various different duties on short notice. This section addresses some of the research that has been devoted to the analysis of aggregate manpower planning, disaggregation of manpower plans and short-term employee scheduling.

Aggregate ~uupower piun~ing. It is a well known fact that mail volumes are seasonal, peaking in the vicinity of national holidays and bottoming out in other periods of the year. This presents a problem of manpower planning: determine cost effective employee complement levels for individual post offices subject to acceptable levels of service. Aggregate manpower planning analysis seeks to determine optimal employee complement sizes, hiring schedules, vacation schedules and overtime usage for each accounting period of the year, subject to the

*The Linehaul Computer Simulator was developed by Logistics Systems Incorporated, Wellesigy, Mass. Wee [4], p. IO, for a brief description of this model. $See 141, p. 4, for a brief description of ALDARE, a combination of CRAIT and ALDEP for workfloor layout analysis.

Operations research in postal services-a survey 241

condition that no seasonal backlogs are permitted.* Such an analysis provides the basis for sound annual employment budgets and effective manpower usage.

Vitt and Krajewski[52] have developed a linear programming mode1 which could be used to determine optima1 aggregate employment plans for individual post offices. The mode1 plans for career employees, postal assistants, summer aides, temporary assistants, hires and overtime given productivity factors, attrition rates, vacation schedules and mail volumes. The model could also be used to analyze the desirability of seasonal employee complements, reductions in the number of allowed new hires and changes to the overtime budget.

L&aggregation. The results of the aggregate employment planning analysis are employee complement levels for each planning period in the year. These aggregates must be broken down to arrive at specific manpower assignments to tours and work centers. Such an analysis might be called disaggregation or tour assignment.

The USPS uses the Interactive Postal Simulator (IPSIM) to arrive at tour assignments.t IPSIM is a man-machine interactive computer mode1 for scheduling manpower by work center, operation; tour and hour. Given a trial manpower assignment by the user, IPSIM performs a deterministic simulation of mail flow, sorting and distribution and provides feedback as to the volume of mail processed versus dispatch times. In a trial-and-error fashion, the user can develop an effective staffing plan.

IPSIM relies quite heavily upon present USPS information systems to provide data on mail volumes, productivities and mail flows. When analyzing manpower assignments for dock operations, the information system has proved inadequate for IPSIM. Chlosta[39] describes a study whereby a functional relationship between work activity on the dock and work activity in processing the mail was developed using regression techniques. The motivation for the study surfaced when it became apparent that manually collecting the necessary data for IPSIM would be too time consuming. Thus, once the manpower assignments for mail processing have been determined using IPSIM, the regression equation could be used to determine manpower requirements on the dock.

Ritzman et al.[49] suggest an alternative methodology for the postal tour assignment problem. In this study a tour is defined as a 5 consecutive day, 8 hr per day block of time. Employees are assigned to tours such that minima1 average work-in-process inventory (tan- tamount to maximizing service for a given volume of mail input), administrative costs and Sunday and night premiums are achieved. The methodology consists of a heuristic program, which works primarily on minimizing work-in-process inventories, and a simulation mode1 which determines the operating characteristics of the resultant solution. The heuristic consists of a biased sampling routine whereby each time a tour assignment for a group of employees is to be made, the routine r&domly selects one of N possible assignment decision rules. Certain rules can be selected more often than others depending upon a weighting vector supplied by the user. Thus, replication of the solution procedure makes it possible to generate different solutions to choose from even if the same weighting vector is used.

The simulation output provides information on average work-in-process inventories, administrative costs (as evidenced by the number of different tour starting times) and the number of premium hours paid. The user can then select the solution which provides the best tradeoff between these costs. The methodology can be put in the man-machine interface mode, however, unlike IPSIM, this procedure results in a prescribed tour assignmentA

Short-term scheduling. The tour assignments specify a workforce availability at each work center for each hour of the day. These assignments are made on the basis of average mail arrivals throughout the day, however, above average mail surges occur frequently and short- term reassignment of postal clerks and mail handlers is necessary. Reassignment is a feasible alternative for short-term adjustment of capacity since many clerks and mail handlers have proficiency at more than one work center.

*In the USPS, an accounting period is 4 weeks. Thus the planning horizon would be 13 periods. tSee [4], p. 17, for a description of IPSIM, and [40] for its application to a post office. $Showalter[SO[ has recently expanded the concepts discussed above to accommodate a larger number of work centers.

He has developed two heuristic approaches: one called the building heuristic, is patterned after the concepts above while the other, called the modifying heuristic, is intended to fine tune a given tour assignment supplied as input. The models are patterned after a sectional center facility, although the statistical data is for the most part hypothetical.

242 J. N. D. G~P~A and L. J. K~~EWSKI

Oliver and Samuel]461 applied the concepts of the calculus of variations to the postal scheduling problem. Analytic and graphical procedures were developed to determine the processing rate at each work center such that average mail delay is minimized. Both serial and parallel processing stage configurations were analyzed and constraints on storage and process- ing rates at each stage were incorporated. The resultant decision rules were tested at the Roosevelt Park Annex Post Office in Detroit where the delay reduction in first class mail was estimated to be 25 per cent.

Ritzman and Krajewski[48] proposed a linear programming model for determining the processing rate at each work center over an eight hour (one tour) planning horizon given the tour assignments for the work centers. The objective is to minimize transit time costs and overtime costs, however since transit time costs involve social costs which are di~cult to quantify, inventory holding costs are used as a surrogate. The procedure for determining the holding cost parameters involves a resolution of multiple objectives.

Soares and Hotta[Sl], two senior students in Electronic Engineering at the Air Force Technological Institute of Brazil, tried to adapt the Ritzman-Krajewski model to the Sao Paulo Post Office System.* Several modifications were made to the model in the areas of mail classification, determination of the inventory holding cost parameters and the objective func- tion. Due to a lack of readily available statistical data, the model was not actually applied.

One advantage that Oliver and Samuel’s approach has over linear programming is that an analytic solution is possible which results in useful decision rules, whereas a linear program- ming model is only capable of numerical solutions and must be resolved each time a decision must be made. Krajewski and Ritzman[41] attempted to develop heuristic r&es which closely mimic the responses of the linear programming model in [48]. The linear programming model was used to create a “target” response surface and a nonlinear least squares regression routine determined parameter values for hypothesized decision rules. The resultant regression analysis explained about 90% of the total variation in the target response surface.t

Another approach to the problem of employee scheduling is to formulate it as a queuing problem. The Postal Service in Israel has undertaken a window service analysis to determine the number of windows needed and the corresponding level of employment given the level of service desired as decided by the Postmaster General in terms of average waiting line lengths. Poisson arrival times and exponential service times were assumed, although these assumptions later proved to be somewhat inaccurate. The model is being used to study the effects of changing service levels. The next step will be to get more accurate arrival and service time distributions.

(e) ~ajntenance

Even though postal systems today are still labor intensive, there is a lot of capita1 equipment that must be kept in good operating order. Items such as mechanical sorting machines, conveyor systems and postal vehicles must receive periodic maintenance attention if the postal system is to provide the best possible service. The USPS has undertaken a project to develop a National Maintenance Information and Control System.S It is intended that the information and control system governing the maintenance of postal plant and mail processing equipment will be automated. Among other things, the system issues preventive maintenance work orders, measures manpower utilization and provides management with various support data to make effective maintenance decisions.

Hardy and Krajewski[56] have used a postal truck facility as a setting to demonstrate the interactive nature of maintenance policy decisions. Broadly defined, maintenance policies fall into two categories: those that reduce the frequency of failure (such as preventive maintenance and early replacement) and those that reduce the severity of failures (such as increased repair crews and equipment redundancy). A simulation model was used to assess the degree that these various policies are interdependent.

*The authors would like to thank Dr. Wilson C. D. Delfino, Coordenator Adjunto, Engerharia de Sistemas, Instituto de Pesouisas Espaciais for this information on operations research activities in Brazil.

t’Mabert [&I extended the results of the above initial efforts to incorporate different forms for the decision rules. The rules were tested via simulation and the ones which performed the best were subjected to a blocked fractional factorial design test to determine the best one for a preselected set of operating characteristics,

*See [4] for details of the proposed project as of 1 January 1973.

Operations research in postal services-a survey

(f) Service characteristics measurement

243

The effectiveness of the postal system depends on how fast it delivers the mail from origin to destination. Thus, the measure of service effectiveness is the time differential between a defined point-of-mailing and a defined point-of-receipt. Essentially, there are two approaches to measure service characteristics. The first approach is to sample statistically live mail flowing through the postal network. An explanation of such a system, which is presently operational at U.S. Postal Service is found in [7,59]. This system provides an objective measure of the true service characteristic of the postal network and its related modes.

An alternative method of meas~ng service characte~stics is to su~eptitiously mail, under controlled conditions, test items (letters, parcels, etc.) through the postal network and then observe the resultant service times. This technique is constrained, however, in that inferences about the service characteristics are limited to the domain in which the test is performed. Chlosta[57] uses this method in a factorial experimental design to a subset of a postal network, in order to evaluate service differentials for various customer mailing and receiving options with parcel post. Major uses of the postal delivery system also monitor service characteristics through the use of controlled tests. A typical example of such a test is presented by Chlosta[%].

OPERATIONS RESEARCH TRAINING FOR POSTAL MANAGERS

From the foregoing discussions, it is apparent that a considerable amount of effort has been devoted to the application of operations research to postal problems. However, managerial acceptance of these models and recommendations to a large extent is dependent upon postal management’s understanding of the quantitative techniques that are used. The Postal Service Training and Development Institute (PST&DI) has undertaken a program for postal managers aimed at developing an awareness of the power and potential of quantitative methods as well as an ability to apply the techniques. The program consists of three courses: Analytical Methods for Postal Managers, Quantitative Management and Operations Research Management.

The first course in the sequence, Analytical Methods for Postal Managers&O], is a 5 day seminar addressing topics in statistics such as sampling theory, data collection, measures of central tendency, measures of variability, moving averages, least squares and correlation analysis. All topics are reinforced by using postal cases as the setting for class assignments. An interactive simulation model is used on the last day to allow the students to conduct their own sampling study.

Following the Analytical Methods course, postal managers take Quantitative Managementj621, a 10 day seminar which introduces the participants to basic quantitative methods. Such techniques as the simplex method, transportation method of linear program- ming, queueing, PERT, dynamic programming, inventory control, exponential smoothing and multiple regression are discussed and applied to postal case settings. The students make use of the computer by applying canned routines for multiple linear regression, the transportation method and the simplex method and working with an unloading dock simulation model to analyze a queueing problem. The course concludes with a problem recognition assignment based upon a large postal case which actually provides the setting for the last course in the sequence, aerations Research Management [$I].

Operations Research Management is a 10 day seminar which is problem oriented as opposed to technique oriented. The problem areas addressed are capacity planning, layout, maintenance, aggregate manpower planning, tour assignment, scheduling and facility location.

The course draws upon the basic knowledge acquired in the previous two courses and applies it to realistic postal problems. To assist in this process, a number of man-machine interactive decision models were designed which make it easy for the students to apply quantitative techniques to complex problems. In capacity planning, the students use the computer and previous knowledge of sampling theory to develop a histogram useful for assessing the desireability of various capacity alternatives. In the second lesson, a modified version of CRAFT, which allows student interface with the model through computer terminals, is used to analyze a specific postal layout problem. In the lesson on mainte~nce, a maintenance simulation of a truck pool enables the study of the interactive effects of maintenance policies, In another lesson, a parametric planning model was developed for a postal aggregate planning

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244 J. N. D. GUPTA and L. J. KRAJEWSKI

problem which allows the students to adjust the workforce levels of the career employees, postal assistants or casual clerks to arrive at an economic manpower plan. In the area of tour assignment, an interactive form of the model used in [49J is used. Finally, a model which enables the student to apply the technique of steepest descent is used to analyze a facility location problem. The participants enjoy the computer models and often develop a competition to see which team can arrive at the “best” solution for a given problem area. In many cases a heuristic problem solving approach is necessary, thus many different solutions are generated for class discussion.

Participant interest and enthusiasm was very high for the course offerings so far. The real question, however, is how these courses have changed behavior in the field, It might be expected that behavior has not been changed much to date primarily because the proper atmosphere has not yet been created in the field. Not every post office has a computer or the capability to interact with one on a frequent basis. Most daily computer usage is devoted to information processing as opposed to the application of decision models. Full utilization of operations research technology will not be realized until the appropriate computer hardware and decision models are available to all post offices of reasonable size and these offices employ personnel knowledgeable in operations research and interested in applying it. Herein lies the challenge to postal systems throughout the world and to the operations researchers interested in helping them to become more efficient.

BIBLIOGRAPHY AND REFERENCES The following references provide a broad spectrum of studies relating to operations research applications to postal_

problems. Not all references are cited in the text. Further, several of those listed here are not readily available. Interested readers may correspond with the authors regarding their availability.

General I. N. Christophides and S. Eilon, An algorithm for the vehicle dispatching problem, Op. Res. Q. 20, 309-318 (1%9). 2. J. N. D. Gupta, Framework for statistical information systems design, Paper presented at the ORSA/TIMS meeting.

San Juan, Puerto (November 1974). 3, J. A. Rayner, United Kingdom-computers in British Post Office, P.O. Telecommun. J. 30.691-694 (1969). 4. The Missiue, News of the U.S. postal service management information systems department, issue No. I (1973). 5. Towards postal excellence, report of the President’s Commission on Postal Reorganizational (F. Kappel-chairman).

GAO, Washington, D.C.

6. Postal economic forecast, Economic Analysis Division, U.S. Postal Service, Washington, D.C. (1972).

Cost and revenue analysis 7. J. N. D. Gupta, Statistical information systems at U.S. postal service, Paper presented at the ORSA/TIMS meeting,

Philadelphia, PA. (March/April 1976). 8. D. C. Holmes and K. E. Parish, Engineering cost-study methods in the British Post Office and their financial

background, P.O. elect. Engrs’ 3. 65, 76-79 (1972). 9. B. J. Mandel, Work sampling in financial management-cost determination in Post Office department, Mgmt Sci. 17,

8324-8338 (1971). 10. L. Merewitz, Cost and returns to scale in U.S. post o&es, J. Am. statist. Ass. 66, 504-508 (1971). Il. L. Merewitz, Pricing of Postal Resources, Paper presented at the 44th National Meeting of ORSA, San Diego,

California (November 1973). 12. rational bulk mail system, Network Cost Model, Functional Specifications, User’s Guide and Addenda, IBM

Co~ration under contract No. REI37-70 to the U.S. Postal Service (~ptem~r 1971). 13. Retant on Investment Analysis of Alte~ative Systems for recessing Mail. report to United States Postal Service,

Computer Sciences Coloration (June 1972). 14. J. T. Walter, Price Elasticity of Demand for First-Class Mail, Paper presented at 134th Annual Meeting of American

Statistical Association with Biometric Scoeity, St. Louis, MO (August, 1974). 15. G. M. Wattles, The rates and costs of the United States Postal Service, 1. Law .&on. 89-117 (1973). 16. T. W. White et al., Productivity Variations and Normalized Cost Comparisons of Letter Mail Sorting, report (2

volumes) to U.S. Postal Service, Institute for Defense Analysis (Nn., 1971). 17. An approach to post ojice operations research, Advanced Technology Department, Military Development, The

National Cash Register Company, Dayton, Ohio (1’88). 18. Brigham and Burgess, Generalized simulation of post office systems, J. Ass. Comput. Mach. 252-259 (April, l%l). 19. G. R. Cavell and J. A. Edgerton, National Bulk Mail Processing, Bulk Mail Systems United States Postal Service,

Washington, D.C. 20. R. Cohen, Sorting Mechanization Requirements for Large, Medium, and Small Post O&es, paper presented at the

44th National Meeting of Operations Research Society of America, San Diego, California (November, 1973). 21. Economic an~~y~~ of advanced t~n~po~ation systems, Weste~ Region Logistics Division, United States Postal

Service, San Francisco, CA. (January, 1973). 22. J. Edmonds and E. Johnson, Matching, EULER tours, and the Chinese postman, ~uthemutical P~grammi~g

$88-124 ($973).

Operations research in postal services-a survey 245

23. G. P. Herring and H. M. Horowitz, Preferential Mail Network Modelling for the United States Postal Service, paper presented at the TIMS International Meeting (April, 1972).

24. J. W. Lazur, Improving Postal Systems and It’s Impact on National Economy, paper presented at IFAC-IFORS Conference on System Approaches to Developing Countries, Algiers, Algeria (May. 1973).

25. J. W. Male and J. C. Liebman, A Heuristic Solution to the M-POSTMAN’S Problem, paper presented at ORSA/TIMS National Meeting, Boston. Mass. (April, 1974).

26. S. Mitric, Design of Postal Networks with Centralized Sorting Function, paper presented at the ORSA~IMS National Meeting, Chicago, IL (April, 1975).

21. National bulk mail system facility simulation model system user’s guide, IBM Corporation under contract No. 72-I-01853 to the United States Postal Service (October, 1972).

28. National bulk mail system network simulation mode/ user’s guide, IBM Corporation under contract NO. 72-I-01853 to the United States Postal Service (January, 1973).

29. D. S. Nee and P. L. Tuan, A mail service simulation (MASS), SRI Research Memorandum ORDRM6748-5 (January, 1369).

30. R. M. Oliver, Optimal dispatches between two post o&es, PRX 3rd Int. Conf. on Operations Research, Oslo, 1%3. Dunod (Paris) and English Universities Press (London). 394-403 (1964).

31. Preferential mail model network analysis, IBM Corporation under contract No. ERI 37-70 to the United States Postal Service (October, 1971).

32. J. R. Rao, National bulk mail system network operation simulator, paper presented at 5th Annual Pittsburgh Conference on Modelling and Simulation, Pittsburgh, PA (April, 1974).

33. A. J. Roark and J. Payet, Scheduling of postal truck drivers, paper presented at ORSAlTlMS National Meeting. Chicago, IL (April, 1975).

34. S. Sultan and G. Ferret, Bulk mail containerization within the matrix sorter concept, paper presented at the ORSAlTIMS National Meeting, Boston, Mass. (April, 1972).

35. Transshipment model functional requirements specifications and user’s guide, prepared under contract No. REI 37-70 to the United States Postal Service by International Business Machines Corporation (1971).

36. P. L. Tuan, A Postal Network Simulation, SRI Research Memorandum ORD-RM 6748-I (July, iW8). 37. P. L. Tuan, Parcel post time test and evaluation, Appendix C of SRI Interim Technical Report 6748-i (August, 1968). 38. P. L. Tuan and D. S. Nee, MASS-a mail service simulation, Third Conference on Application of Si~~l~tio~

(December, i%9).

Manpower planning and scheduling 39. N. W. Chlosta, Modelling secondary manpower requirements (dock facilities) at selected post offices, paper presented

at ORST/TIMS National Meeting, Chicago, IL (April, 1975). 40. N. W. Chlosta, Staffing and manpower utilization study of the state college, PA. Post Office, Postal Engineering

Systems Office, U.S. Postal Service, Washington, DC. (July, 1974). 4I. L. J. Krajewski and L. P. Ritzman, Man~wer scheduling decision rules for a single post o&e, ~uision of Reseurch

Waking Paper Series, College of Administrative Science, Ohio State University (May, 1974). 42. L. J. Krajewski and L. P. Ritzman, Tour assignments in a service organization, Diuision of Research Working Paper

Series, Ohio State University (May, 1974). 43. L. J. Krajewski, L. P. Ritzman and S. T. Hardy, Manpower decision rules in a single post office: a simulation of mail

flows, Fruc. 4th Ann. Simulation Symp., Gordon Breach, New York (March, 1971). 44. V. A. Mabert, A methodology for work scheduling and labor assignment within a single postal facility, Ph.D.

dissertation, The Ohio State University (1973). 45. E. H. Mantell, Factors affecting labor productivity in post offices, L Am. sratisr. Ass. 69,303-309 (1974). 46. R. M. Oliver and A. H. Samuel, Reducing letter delays in post o&es, Op. Res. 10.839-892 (1962). 47. L. P. Ritzman and L. J. Krajewski, A linear programming model for scheduling postal resources, unpublished paper.

College of Administrative Science, Ohio State University (September, 1971). 48. L. P. Ritzman and L. J. Krajewski, Multiple objectives in linear programming-an example in scheduling postal

resources, Decision Sci. 4, 364-378 (1973). 49. L. P. Ritzman, L. I. Krajewski and M. J. Showalter, The.disaggregation of aggregate manpower plans, Mgmt Sci. 22,

120&1214 (1976). 50. M. J. Showalter, A meth~ology for man~wer tour assignment within a U.S. Postal Service processing center facility,

Ph.D. dissertation, The Ohio State University (1976). 51. F. R. Soares and L. K. Hotta, Introduao Ao Estudo da Efficiencia da Mao-de-Obra no Sistema de Classificacao

Tecnico Aeroespacial, Instituto Technologico Do Aeronautica (1974). 52. L. D. Vitt and L. J. Krajewski, Employment planning for a major U.S. post office, Proceedings of the Mid-west

Regional AIDS Meetings, Bowling Green, Ohio (April, 1971). 53. T. White, Productivity variations of letter mail sorting, paper presented at 44th National Meeting of Operations

Research Society of America, San Diego, CA (Novem~r, 1973).

Maintenance 54. B. J. Garrick, Reliability and maintainability of automated bulk mail systems, paper presented at 1974 Annual

Reliability and Maintainability Symposium, Los Angeles, CA (January, 1974). 55. S. T. Hardy and L. J. Krajewski, Multipolicy maintenance decisions, Academy of Management Proceedings, 33rd

Annual Meeting: Boston, Mass. (August, 1973). 56. S. T. Hardy and L. J. Krajewski, A simulation of interaction maintenance decision, Decision Sci. 6,92-105 (1974).

Service characteristics measurements 57. N. W. Chlosta, A statistical examination of customer mailing options for parcel post, paper presented at ORSA/TIMS

national meeting, Boston, Mass. (April, 1974). 58. N. W. Chlosta, A customer tests our service: a compilation of the results. Office of Consumer Affairs, U.S. Postal

Service, Washington, D.C. (March, 1973). 59. OLhlS Wlrar Zr is, What It Does, U.S. Postal Service, Publication 195 (October, 1972).

246 Operations research in postgl services-a survey

l’rainhg in operaiions mearch

60. ~~&~yf~&a~ methods ~~~pos~ul smnagers, Postal Service Training and Deveiopment institute, Bethesda, MD. 61. ~~pfjed ~pe~a~ju~~ research ~a~ag~~e~~, The Ohio State University (L. J. Krajewski, principal investigator) under

contract No. NC-PSMI-72-32 to Postal Service Training and Development Institute (1973). 62. ~~pfjed ~~~~~a~ju~ mu~u~me~, The Ohio State Uo~vers~y (L. J. Krajewski, principal investigator) under contract

No. NC-PSNI-72-32 to Postal Service Training and Development Institute (1973). 63. R. Latz and J. Seabey, A cost-effectiveness study of first level supervisory training in the U.S. postal service, paper

presented at the 41st National Meeting of ORSA, New Orleans, LA (April, 1972).