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Copyright � 2001 INFORMS 0092-2102/01/3104/0001/$05.00 1526–551X electronic ISSN

INDUSTRIES—TRANSPORTATION—SHIPPING FACILITIES—EQUIPMENT PLANNING—DESIGN

This paper was refereed.

INTERFACES 31: 4 July–August 2001 (pp. 1–14)

Strategic Service Network Design for DHL Hong Kong

Waiman Cheung Department of Decision Sciences and Managerial Economics

The Chinese University of Hong Kong Shatin, N.T., Hong Kong

Lawrence C. Leung Department of Decision Sciences and Managerial Economics

The Chinese University of Hong Kong

Y. M. Wong Propack International Holdings Limited Unit 1006, 10/F Technology Plaza 29-35 Sha Tsui Road Tsuen Wan, N.T., Hong Kong

We developed a two-phase network planning methodology to design a service network for DHL(HK) based on two measures of service performance: service coverage and service reliability. The methodology consists of first using an optimization model to determine a least-cost distribution network, which forms the basis of a simulation model for analyzing the network’s opera- tional characteristics. It takes into consideration such design is- sues as inbound and outbound shipment, equivalent shipment, cutoff time, demand fluctuation, and random behaviors. DHL decision makers can now examine trade-offs between coverage and reliability by adjusting workforce, changing cutoff time, or redesigning the service network.

DHL, an international air expresscompany, serves over 220 countries around the world. Its worldwide opera- tions network consists of over 40,000 employees, 1,900 international service sta- tions, 30 regional gateways, and 28 inter- national sorting hubs. DHL’s fleet of 177 aircraft and 11,000 vehicles transports mil- lions of customers’ packages daily. In ad- dition to the hub-and-spoke routings of

the company’s own aircraft, DHL also uses commercial flights extensively for di- rect point-to-point transport. Established in San Francisco in 1969, DHL’s major markets are in Europe and the Asia Pacific (AP) Region. Within the AP Region, DHL is a leading carrier in terms of total vol- ume, with Japan, Hong Kong, and Singa- pore as its three largest subregions.

In 1998, the Hong Kong international

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airport was relocated. As one of the larg- est air-express couriers in the Asia-Pacific region, DHL had to design a new service network for its Hong Kong operations. The network plan had to provide for stra- tegic and timely installation of depots and service centers to meet future changing customer needs and provide competitive service. DHL(HK) has about 1,200 staff and 160 vehicles. Its main operations cen- ter is in a district three kilometers from the old international airport, and it has other smaller operating facilities within Hong Kong. Hong Kong’s economic develop- ment has been strongly influenced by rapid growth in southern China. Business and social activities between mainland China and Hong Kong have intensified since July 1997 when Hong Kong was reunited with China, with southern China acting as a manufacturing base for Hong Kong businesses because of its cheaper land and labor. There is a growing need for express delivery of documents and packages between the two regions. The New International Airport

The relocation of the international air- port to Chek Lap Kok (CLK) on Lantau Is- land (to the far west of Hong Kong Island) significantly affects the effectiveness of DHL(HK)’s current service network. The new airport is much farther away from the city than the old airport, thus increasing commuting time and operating costs. Also, for safety reasons, the highway linkages between the city and the new airport re- strict the type of truck that can be used. The customs office uses electronic-data- interchange (EDI) technology to shorten the customs-clearance process for those shippers who can provide EDI manifests

before flight arrival. DHL has developed a new operating system, called the Air Cargo Clearance System, to be used at the new airport. Moreover, by setting up an express cargo terminal inside the new air- port, DHL would be able to carry out some shipment registration processes while waiting for customs clearance. In many ways, the new airport has brought both challenges and opportunities to DHL(HK). Competition Among Air Express Companies

DHL(HK) operates in a very competi- tive air-express market. Overnight service within the AP region and next-day service to Europe and North America are the in- dustry standards. For selected sectors, such as banking and finance, same-day in- ternational service to the US is also avail- able. These service standards are much higher than those offered by airfreight for- warders. In addition, air-express compa- nies offer money-back guarantees in case of failure to keep delivery promises.

The factors customers consider in choos- ing an air-express company are —Short transit times and a large global network, —Late cutoff time for package pickups without incurring delay, —Convenient communications and order placement, and —Competitive price.

Increasingly, to remain competitive, companies must reduce delivery times. To respond quickly to customer requests, couriers must stay close to the customers. They must also have the necessary logisti- cal support to transport shipments to planned flights quickly. To continue to

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meet or exceed industry service standards, DHL(HK) must provide superior service at a competitive price. It needs to balance service level with the fixed cost of install- ing facilities and the variable cost of oper- ating the service network. The Service Network

DHL’s service network consists of de- mand zones, satellite depots, service cen- ters, and the airport. Demand zones are service areas determined according to the level of customer demand and geograph- ical characteristics. Zones are smaller within busy commercial areas where or- ders are concentrated than in most out- lying zones where demand is scattered.

Customer requests for pickups are for- warded to couriers responsible for their zone. Couriers are assigned to specific sat- ellite depots, each of which covers pickups

Customer requests peak around the daily cutoff time.

in several zones. The depots consolidate packages and deliver them to the corre- sponding service center. Each service cen- ter, which also functions as a depot, is responsible for several depots. Service cen- ters handle all major processing, such as labeling, X-ray screening, reweighing, sort- ing, documentation, and formality follow- up. The service centers further consolidate shipments into air containers or bags and transport them to the airport for transfer onto the appropriate aircraft.

DHL(HK) must manage this process from pickup to delivery at the airport ef- fectively. The service network is at the heart of this process. The critical decisions in the design of the service network con-

cern the installation of the depots and ser- vice centers: —The locations of depots and what de- mand zones they cover, —The locations of service centers and what depots they cover, —The capacities of these facilities, and —The installation schedule for these facilities. Objectives of the Study

DHL(HK) asked the authors (Cheung and Leung) to perform a study to improve their services. The objective of the research study was to design a service network that would be the most desirable economically and operationally for DHL over a multi- year period. In designing the network, we had to consider long-term goals and short- term operational goals. The design had to include the strategic and timely installa- tion of depots and service centers based on a judicious examination of service per- formance. The study included designing the overall framework, formulating mod- els, collecting and preparing data, inter- preting results, setting operating rules and policies, and making recommendations to the top management. The principal strate- gic recommendations concerned —Installation decisions for depots and ser- vice centers, and —A strategic cutoff time for pickups that balances capturing more customers with providing reliable service. Inbound and Outbound Shipments

DHL(HK) handles both inbound and outbound shipments. For DHL(HK), the inbound-shipment-flow and the outbound- shipment-flow patterns are basically the same. The volume shipped is slightly less for inbound, while the shipment patterns

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are roughly identical. The two flows do not compete for resources because they oc- cur at different times of day. Unlike in- bound shipments, which DHL collects at the airport according to a predetermined schedule, outbound shipments require more processing and must reach the air- port by a specific time. Therefore, out- bound shipments have more stringent time requirements. To simultaneously con- sider inbound and outbound shipments in planning the network would unnecessarily complicate the design task. Also, it is very likely that optimal conditions for out- bound shipments are close to optimal for inbound shipments as well. In our study, we considered only outbound traffic. Multiyear Demand

The businesses located in Hong Kong and the business volume between Hong Kong and mainland China are expected to increase gradually in the years to come. These changes will affect the quantity of shipment demand in the various zones and the characteristics of the shipments. Today’s optimal service network may not be adequate in the future; however, DHL(HK) cannot abandon, relocate, or scale down facilities without penalty. Therefore, we needed to base the network design on a long-term demand forecast. The marketing department of DHL(HK) has the task of preparing the long-term demand profile, examining demand fluc- tuations, such as seasonality, daily varia- tions, and peak loads; types of shipments (volume and weight); potential changes in market structure; regulatory issues; the macroeconomic profile; and the develop- ment of new industrial and residential zones.

Equivalent Shipment The demand profile has to be refined to

reflect the amount of resources consumed by shipments, which depends largely on their weight. In demand zones where the shipments are heavy, requirements for hu- man and material-handling resources are proportionately higher. To capture this weight factor, we used a unit of measure called equivalent shipment, which we de- fined as one shipment whose weight is one kilogram. We consulted ground- service managers, service-center managers, industrial engineers, and couriers on their perceptions of the impact of a range of shipment weights on the amount of re- sources required. We collected these ex- pert opinions and performed a simple re- gression. We concluded that we could correlate the weight and equivalent shipment-weight approximately using a power correlation function (y � axb) with a as 1 and b as 0.5. We suggested the fol- lowing rule of thumb: —The equivalent number of shipments is equal to the square root of the actual ship- ment weight in kilograms.

For example, we could count a ship- ment that weighs four kilograms as two equivalent shipments, implying that this shipment would consume twice the re- sources a one kilogram shipment con- sumed. We used this rule of thumb to transform all shipments with differing weights into corresponding equivalent demands. Cutoff Time and Decentralization

Determining a service cutoff time and the level of decentralization (or centraliza- tion) of services are related policy issues for DHL(HK). The cutoff time is the time

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of day before which a customer’s order is guaranteed to be delivered to the airport on the same day. It is a critical competitive factor among air-express couriers. An un- necessarily early cutoff time would mean a loss of potential customers, whereas an unreasonably late cutoff time would leave DHL little time for shipment processing

Before we implemented this methodology, managers’ decisions were based on intuition.

and transportation, thus increasing the risk of not reaching the airport in time. One way to achieve late cutoff while meet- ing service promises is to decentralize the service network. In the extreme case of de- centralization, this would mean a depot and a service center in each demand zone. Clearly, this would shorten the response time for pickups and delivery times. How- ever, the facility installation cost would be tremendous, and since there would be no consolidation, the total transportation cost would be very high and resource utiliza- tion would be very poor. On the other hand, a centralized service network would mean having a super-service center that doubled as a superdepot. All couriers would originate from this superfacility for pickups and would return to it for pro- cessing and consolidation. This would provide economies of scale, more efficient consolidation, better utilization of re- sources, and better control of shipments, but the response time for pickups would be longer on average and meeting flight schedules for pickups from some outlying zones would be difficult. In determining

the optimal cutoff time, we had to care- fully weigh the trade-off among level of customer coverage, risk of missing flights, and costs of decentralization. Capacities and Costs of Depots and Service Centers

For each potential depot and each po- tential service center, we had to identify what capacity sizes could be installed and the costs. Because of tremendous variation in real estate costs, our analysis had to be specific to location. The elements we in- cluded in cost assessments were physical plants, material-handling systems (trucks, vans, conveyance systems), human re- sources, and information-processing capa- bilities. Other capacity-related factors we had to determine were the utilization rates of the existing facilities and acceptable utilization rates, and overtime costs for fa- cilities and human resources. Fluctuations and Random Behaviors

DHL(HK)’s operating environment con- sists of many dynamic elements that can fluctuate drastically and unpredictably. Typically, customer demand varies ac- cording to the time of day, the day of the week, and the month. Customer requests peak around the daily cutoff time. They are higher on Fridays, on days before holi- days, and during major holiday seasons, such as Christmas. Facilities with enough capacity to handle average demand may not be adequate to cover peak hours and days. Consequently, we needed to con- sider facility utilization. Furthermore, the randomness in transportation times means that some shipment routings that are feasi- ble under normal traffic conditions may not be feasible during peak hours when traffic is congested. To examine the service

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performance of the network, we needed voluminous operational data. We wanted to characterize hourly customer demand by volume and to describe the random- ness in such elements as pickup times, transport times, and processing times. The Planning Methodology

Clearly, the design of a long-term ser- vice network cannot be separated from short-term operational considerations. Within the context of operations research methodology, design of a service network can be approached using facility-location models or variants of such models. The approach is a normative one to determine least-cost locations that meet certain de- mand and logistics requirements. Because of the problem size, such models can use only aggregate information, such as aver- age annual cost, average utilization, and average annual demand. But a service net- work based only on an optimization model is unlikely to be adequate. An opti- mization model is not suitable for han- dling such operational factors as demand uncertainty, randomness in travel and processing times, and dynamic consolida- tion. The model prescribes the overall least-cost network design but lacks specific operational details. An air-express courier cannot use a network design that does not satisfy important daily and weekly opera- tional specifications.

Analysts can use simulation to model uncertainty and fluctuations in large dy- namic systems, allowing decision makers to examine the behaviors of complex sys- tems operating in uncertain environments. However, before we could simulate opera- tional details (product flow, pickup and delivery schedules, disaggregated

product-mix demand patterns, and proba- bilistic behavior of travel times and pro- cessing times), we needed a network de- sign on which to base the simulation.

Our network-planning framework uses an optimization model and a simulation model (Figure 1). The optimization model is an economic network-planning model that determines the macro optimal net- work configuration in an aggregate fash- ion. The simulation model evaluates the daily operational performance of the rec- ommended network configuration. Ana- lysts have used optimization models and simulation models jointly to analyze hos- pital layout [Butler et al. 1992], freight operations [Moore, Warmke, and Gorban 1991], ambulatory health care [Kropp and Carlson 1997], manufacturing [Leung, Maheshwari, and Miller 1993], and de- fense logistics planning [Nolan and Sovergin 1972]. These are situations in which design and operations are closely related. While the air-express industry is unique, it is similar in that a courier’s ser- vice network is also closely tied to its ser- vice operations. We found no published work concerning an air-express network within this design-operations context. The Macro-Network-Planning Model

The multiperiod model, a mixed 0–1 linear program, takes on the following framework (Appendix):

Minimize present value of (fixed cost � variable cost),

Subject to flow distribution � demand, individual flow � capacity, flow time � time window,

Plus only one installation at a location, conjunctive or mutually exclusive installations.

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Figure 1: The network-planning framework consists of an optimization model and a simulation model. The optimization model takes aggregated data as input and generates a network config- uration. The simulation model evaluates the recommended network with considerations of the operation dynamics.

The objective of the model is to minimize the sum of present-value costs of transpor- tation and facility installation. The variable transportation costs depend on the assign- ment decisions of shipments from zones to depots and from depots to service centers. The installation costs depend on installa- tion decisions, the choice of capacity level, and the schedule of the installations.

We need constraints to ensure that the assignments of shipments from zones to depots to centers will meet forecast de- mand. Also, we need capacity constraints

to ensure that decisions to assign ship- ments to particular facilities correspond to facility-installation decisions and appro- priate capacity decisions. Further, the total flow time for any zone-depot-center- airport assignment cannot exceed the maximum time window (elapsed time be- tween cutoff and due time at the airport). We also needed logical constraints to en- sure that only one installation per site was allowed and that certain correlated time-dynamic installation logic is not violated.

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The Micro Operation-Simulation Model Based on the results of the macro plan-

ning model, the simulation model simu- lates daily operational activities to evalu- ate the service performance of the network. We constructed multiple scenar- ios in terms of peak loads and average loads and collected operational statistics including the workloads of couriers, ca- pacities and utilization of facilities, arrival patterns of vehicles to the facilities, pickup requests not honored, and shipments that miss flights. The Simulation Environment

We used the simulation model to exam- ine the dynamics of courier pickups, deliv- eries to depots and service centers, and deliveries to the airport.

The locations of the depots and service centers, as well as shipment assignments from zones to depots to centers, are in ac- cordance with the results of the planning model. DHL(HK) uses three types of vehi- cles: vans to transport shipments from customers in the zones to depots, trucks to carry shipments from depots to service centers, and lorries to carry shipments from the service center to the airport. We simulated the consolidation of shipments from vans to trucks, and from trucks to lorries. The entire operation is applied to two major product types, documents and packages, collectively representing almost

90 percent of the shipments. The workforce includes couriers and

shipment-processing workers. A typical working day starts at 8:00 am, when the couriers leave these depots in vans to de- liver and pick up shipments in zones. The usual cutoff time is 5:15 pm, but it can be adjusted depending on the cutoff policy. Each week has five-and-a-half workdays. We incorporated in the model probabilis- tic behaviors exhibited in three categories of events—shipment arrivals and charac- teristics, travel time, and processing time. The Simulation Model

The simulation model is divided into four modules (Figure 2): (1) simulation ini- tialization, (2) shipment pickups in the zones, (3) shipment consolidations in the depots, and (4) processing in the service centers and transport to airport. Essen- tially, we modeled both zones and service centers as one-line multiple-server queueing resources. The capacity of a re- source is related to either the number of couriers in a zone or the number of pro- cessing workers in a service center. At the end of each day, documents and packages that remain in the queue of each zone are considered to be lost-sale shipments. Doc- uments and packages that remain in the queue of each service center are undeliv- ered shipments and are to be delivered the following day. Since the depots do no pro-

Figure 2: The simulation model is divided into four modules, (1) initialization, (2) shipment pickups in zones, (3) shipment consolidation in the depots, and (4) processing in the service centers and transport to the airport.

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Figure 3: The locations of the recommended five depots and four centers are shown in the map as “D” and “S,” respectively. The black dots indicate centers of the major zones, while the ar- rows are the routing assignments.

cessing except consolidating shipments, we modeled depots as simple storage with a queue and incorporated a time delay for unloading and loading vehicles. We cre- ated three types of transporters (represent- ing vans, trucks, and lorries) to move enti- ties from zone to depot, from depot to service center, and from service center to the airport. In the simulation model, we used one week as a cycle. It is a duration in which the system resets itself, and it typically reflects the real-life behavior of DHL. The Preliminary Service Network

DHL(HK) has established 33 demand zones in Hong Kong, 15 of which are can- didates for depots and nine of which are potential sites for service centers. Using in- puts from the demand profile, fixed and variable cost estimates, travel and process-

ing times, capacity alternatives for facili- ties, and a cutoff time of 5:15 pm, we solved the macro planning model using the PC-based MPSIII [Ketron 1992]. There are 49,500 continuous variables, 1,050 bi- nary variables, and 820 constraints. Solu- tion takes about seven hours of computa- tion time on a Pentium-166 machine.

In the resulting service network, there are five depots and four service centers (Figure 3).

To protect the interests of DHL(HK), we will not show the corresponding costs of this configuration nor the recommended future expansion plan. The distribution network is neither centralized nor decen- tralized and remains somewhere in- between. This network configuration is only a preliminary result; we had not yet scrutinized the network’s service

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performance. Service Performance of a Network: Coverage and Reliability

To evaluate the service performance of a service network, we defined two related performance measures: —Service coverage, the percentage of re- quests that arrive before cutoff time, and —Service reliability, the percentage of pickups that make the same-day flight. These two criteria are central to an air- express firm’s service performance. The former addresses its coverage of requests and the latter its success in keeping prom- ises of same-day delivery. The actual pick- ups may go beyond the cutoff time be- cause same-day delivery applies to all requests as long as they arrive before or on the cutoff time.

In the macro model, service coverage and service reliability are both 100 per- cent, since all shipment requests are met and all assignments are within the maxi-

mum time window. But the parameters of the macro model are merely deterministic averages. The actual daily fluctuations and randomness of activities will likely result in varying levels of coverage and reliabil- ity. We used the simulation model to make a realistic assessment of the net- work’s coverage and reliability.

Based on the preliminary network con- figuration, we simulated the daily activi- ties. We implemented the simulation ex- periment using a SIMAN-based simulation software package, ARENA [System Mod- eling Corporation 1995; Pegden 1995], in a Pentium-166 machine with 128 MB RAM. A simulation run of one week takes ap- proximately 14 minutes. With the simula- tion results, we plotted the levels of ser- vice coverage and service reliability with respect to a range of cutoff times (Figure 4).

For example, if the cutoff time is 5:15 pm, coverage is at 92 percent and reliabil-

Figure 4: Based on the simulation results, the chart shows the trade-off between service reli- ability and coverage. For example, extending cutoff time will result in a higher level of service coverage but a lower level of reliability.

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Figure 5: The chart shows how service reliability can be improved by increasing the workforce by 10 and 20 percent. In other words, DHL can improve service coverage by extending cutoff time and offset the consequential drop of reliability by enlarging its workforce.

ity is at 97 percent. Service coverage and service reliability have an inverse relation- ship. That is, extending cutoff time will re- sult in a higher level of customer coverage but will decrease the level of reliability, as it allows less time for transportation and processing. Low coverage means loss of customers, while low service reliability will eventually lead to the same end.

The simulation results showed that the reliability of the preliminary network was in the acceptable range while coverage was close to acceptable. Realistically, it is impossible to operate at 100 percent for both coverage and reliability. We had to examine the trade-off between service cov- erage and service reliability judiciously. We needed to explore ways of improving service coverage without impairing service reliability. We also tried to ensure that various facilities in the network were nei- ther over- nor underutilized. The simula-

tion experiments provided an accurate pic- ture of the utilization of various facilities and showed whether the capacities the macro model prescribed were genuinely workable. Improving Coverage and Reliability with an Increased Workforce

Service reliability can be improved by increasing the workforce (Figure 5). To im- prove the service coverage of the prelimi- nary design, we could extend the cutoff time, which would cause reliability to drop. DHL could enlarge its workforce to bring reliability back to an acceptable level. Invariably, the decision maker has to judge whether the incremental cost of an increase in the workforce is justified by the improvement in reliability or coverage. Improving Service Reliability via Network Redesign

Another approach to increasing service reliability is to redesign the distribution

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network using a more stringent time win- dow. That is, we could solve the least-cost optimization model again but with a later cutoff time. Because the time constraint is tighter, the resulted network would have a higher cost but would also be more time efficient (or at least as good) since less time is allowed for services. But this more stringent time window is not implemented during actual operation. Instead, we would use the old time window. Conse- quently, service reliability would improve because of the more stringent network that would provide acceptable reliability and coverage with respect to the actual cutoff (use in the simulation). Again, whether the incremental cost of constructing a more time-efficient network justifies the im- provement in reliability will be a decision top management has to make. There are essentially two cutoff times, one for the network model (planning cutoff) and one for the simulation (operational cutoff). The former determines the preliminary net- work, while the latter provides a realistic assessment of the effects of cutoff times in actual operations. In designing the net- work, we had to explore carefully the rela- tionship between planning and opera- tional cutoff times. Recommendations

Based on the current preliminary net- work, we investigated several scenarios to improve service coverage (without affect- ing service reliability). We iteratively used the optimization model and the simulation model to analyze different levels of hu- man resources and different combinations of planning cutoff time and operational cutoff time. Several variants of the prelimi- nary design showed strong potential. In

addition, we determined several alterna- tive network designs that are not least-cost designs but perform satisfactorily in terms of service coverage and reliability. We pre- sented these network designs and their in- dividual merits to DHL(HK)’s top man- agement. Together with the installation decisions and the cutoff time, we de- scribed each candidate design by three at- tributes, cost, coverage, and reliability. The DHL decision makers will select the even- tual design. Iterative Use of Optimization and Simulation Models

In iterating between the macro model and the simulation model, there is no guarantee that a convergence will always take place. Convergence means that we can progressively zero in on a least-cost network that satisfies all the operational objectives. To do this, we emphasize diag- nosing the outputs of both models judi- ciously and the art of revising the inputs. Arbitrary modification of input parame- ters would likely cause divergence or oscillations.

Many variations and scenarios go into implementing the macro-micro iterations to arrive at the most desirable network. In- variably, the number of iterations required depends on the quality of the input- revision process. We have established some basic algorithms and rules in revis- ing the model inputs during the iterative process. Still, many intangibles in evaluat- ing a network require expert opinions. We found valuable inputs from decision mak- ers at DHL highly useful in streamlining the process of determining the most desir- able network and several good alternatives.

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Regarding the simulation exercise, we recommend doing simulations using de- mand profiles for a busy week, an average week, and a slow week. Decision makers can then judge the variations in utilization and service reliability. For each simulation run, we performed 10 replications. The number of replications should be statisti- cally supported. This should be done for each year in the planning horizon open (using the demand profile for that year) or to a point at which the decision makers are comfortable with the current decisions. However, this can be computationally cumbersome, and its extent is also related to the judicious use of the macro-micro iterations. Conclusion

Our methodology helped DHL decision makers to gain insight into many facets of their planning and operations. Before we implemented this methodology at DHL(HK), managers’ decisions about net- work design and network operation were based on intuition. Using our method as a framework, they can now analyze many network-related issues explicitly. Decision makers can now test many what-if scenar- ios and see the impact of certain strategic decisions. DHL(HK) top managers took our work very seriously and adopted most of our recommendations. They have con- tinued to use our methodology to update their network design.

Since DHL(HK) bases its multiyear dis- tribution plan on many elements in the fu- ture, it must continually update the distri- bution network with its expansion plan as it learns of changes in demand and trans- port structure. Essentially, DHL(HK) should perform the network-planning pro-

cess periodically (for example, every six months) while using the micro model reg- ularly to analyze its operational performance. Acknowledgment

This research project is funded in part by the Hong Kong Research Grant Council (CUHK#4037/99H). APPENDIX

The general mixed 0–1 LP formulation in matrix notation is Minimize

�t {cft xt � cvt pt} Subject to

Atpt � dt, pt � (M1x1 �• • •� Mtxt) etxt � 1, G(x1, . . . , xt) � 0, xt � (0,1), pt � 0, ∀t � 1, . . . , n

where xt � decision vector for the facility and ca-

pacity installations in period t, pt � flow assignment vector in period t, cft � vector for the fixed charges of the in-

stallations in period t, cvt � vector for variable cost per unit flow

in period t, At � flow matrix in period t, dt � demand vector, et � logic matrix (0–1) in period t, Mt � capacity matrix of the installations in

period t, and n � planning horizon. All cost factors are in terms of present value. The flow constraints, Atpt � dt, make sure that assignment of shipment meets demand. The capacity constraints, pt � (M1x1 � • • • � Mt xt), ensure that the assignment of shipments to a facility is ac- companied by the decision to install the facility along with the corresponding ca- pacity decision; the shipment assigned must not exceed the accumulated capacity of the facility. Constraint sets et xt � 1 ensure one installation per site, and G(x1, . . . , xt) � 0 is a system of logic con- straints representing additional correlated

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time-dynamic installation logic. All flow decisions pt must not exceed the maximum flow time. References Butler, T.; Karwan, K.; Sweigart, J.; and Reeves,

G. 1992, “An integrative model-based ap- proach to hospital layout,” IIE Transactions, Vol. 24, No. 2, pp. 144–152.

Ketron Management Science 1992, MPSIII Soft- ware Package.

Kropp, D. and Carlson, R. 1997, “Recursive modeling of ambulatory health care set- tings,” Journal of Medical System, Vol. 1, No. 2, pp. 123–135.

Leung, L.; Maheshwari, S.; and Miller, W. A. 1993, “Concurrent part assignment and tool allocation in FMS with materials handling considerations,” International Journal of Pro- duction Research, Vol. 31, No. 1, pp. 117–138.

Moore, E.; Warmke, J.; and Gorban, L. 1991, “The indispensable role of management sci- ence in centralizing freight operations at Rey- nolds Metals Company,” Interfaces, Vol. 21, No. 1, pp. 107–129.

Nolan, R. and Sovergin, M. 1972, “A recursive optimization and simulation approach to analysis with an application to transportation systems,” Management Science, Vol. 18, No. 12, pp. B676–B690.

Pegden, C. 1995, Introduction to Simulation Us- ing SIMAN, McGraw-Hill, New York.

Systems Modeling Corporation 1995, ARENA User’s Guide, Version 2.2.

Gary Wong, Planning and Development Manager, DHL International (HK) Ltd., DHL House, 13 Mok Cheong Street, Tok- wawan, Kowloon, Hong Kong, writes: “As a Planning and Development Manager of DHL (HK), I found their work very useful. We have used it and will continue to use it as an important resource for our future distribution network planning. As a mat- ter of fact, I was very impressed that the study was both scientific and practical, which included a simulation model that reflected the actual courier activities (such as fluctuation and random behavior). I

also recall the important idea of “shipment weight”, which was used to distinguish the different level of resources needed to handle light and heavy shipments. From a bigger picture, the models allowed us to have a better understanding of the rela- tionships among service coverage, reliabil- ity, and costs.”