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Identifying Opportunities for Improving Teradyne’s Service-Parts Logistics System Morris A. Cohen
Operations and Information Management The Wharton School University of Pennsylvania Philadelphia, Pennsylvania 19104
Yu-Sheng Zheng
Operations and Information Management The Wharton School University of Pennsylvania
Yunzeng Wang
School of Business Administration University of Mississippi University, Mississippi 38677
Teradyne is a major manufacturer of electronic testing equipment used in semiconductor and electronics assembly plants throughout the world. In a recent project, we evaluated opportunities for improving Teradyne’s global service-parts repair and logistics network. This system is complex because of the large number and variety of parts, the geographic dispersion of the installed base of customers’ machines, the use of multiple classes of service, and stringent requirements for prompt response to customer requirements. We used basic inventory models to capture key characteristics of the system. These models provided insight into the relative value of several improvement opportunities. Teradyne used these insights to prioritize change options and has successfully implemented several of them. The project’s success was, in part, based on the role of a company-academic team that combined understanding of relevant inventory models with in-depth knowledge of logistics processes.
T
oward the end of 1994, Teradyne, a major electronic-equipment manufacturer, asked faculty members of Wharton’s Fishman-Davidson Center for Service and
Operations Management to identify and prioritize improvement opportunities for its service-parts logistics system. The project was inspired by the company’s partici-
Copyright 䉷 1999, Institute for Operations Research and the Management Sciences 0092-2102/99/2904/0001/$5.00 This paper was refereed.
INVENTORY/PRODUCTION—APPLICATIONS INDUSTRIES—ELECTRONICS
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COHEN, ZHENG, WANG pation in our recent benchmark studies of service-parts logistics systems [Cohen and Zhang 1998; Cohen, Zheng, and Agrawal 1997]. Despite the company’s high ranking with respect to the service standards identified in the study, it realized that it could reduce costs and improve service. Within the limit of its managerial resources, Teradyne wanted to identify the most promising opportunities for improving its operations performance. Teradyne manufactures electronic testers, which semiconductor and other hightechnology electronic manufacturers use in their capital-intensive production lines. The testers are often bottlenecks in such lines [Ou and Wein 1996], and therefore their reliability is essential. It has been estimated, for example, that one hour of tester downtime can cost a typical semiconductor fabrication plant user as much as $50,000. The testers are complex electronic devices, composed of many parts and circuit boards. The boards, though quite reliable, are subject to random failures. Therefore, customers demand prompt and reliable parts service, and providing it is critical to Teradyne’s long-term success. The Replacement-Parts-Service (RPS) Division of the company provides and repairs service parts for customers. It manages over 10,000 parts and distributes them through a global, multisite logistics network. Many of these parts have a high unit cost (as much as $10,000) and a low usage rate (as low as a few pieces a year worldwide). RPS must therefore allocate its inventory investment efficiently across its stocking locations to achieve a high level of service, which is measured in terms of parts availability.
Two key RPS planning managers, who initiated the project and specified the project objectives, and the authors made up the team. We carried out the work in two phases. The first phase was a short-term effort, lasting several months. Our goal was to review the company’s current inventory-management processes and to identify and prioritize improvement opportunities. The second phase was to support implementation of those improvements and to develop a comprehensive, multiechelon inventory model to help the company to enhance its inventoryplanning and control system. We completed Phase 1 successfully on time, and it is the subject of this paper. The Phase 1 findings have been well received by the company and many have been implemented. Phase 2 of the project has just been completed, and it is described in a doctoral thesis [Wang 1998]. We will describe the analytical results based on this phase in follow-up papers.
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One hour of tester downtime can cost $50,000. Although Teradyne’s system is complex and has several features not covered by standard inventory models, we decided to use existing inventory models as much as possible in the initial phase. We developed an approach based on Palm’s [1938] theorem and the METRIC model used to support military logistics systems [Sherbrooke 1968]. We used this approach because we needed to carry out the analysis quickly and in a manner that would maximize the likelihood that Teradyne would implement our recommendations. We discov-
TERADYNE ered, however, that application of even a simple model can be challenging in the face of real-world-system complexity. The lessons we learned through this project include the following: (1) For complex logistic systems, basic models can be very effective for both operational control and strategic analysis, that is, the policies these models recommend can dominate the decision rules used in practice. (2) Applying a basic model successfully is often difficult. One needs a thorough understanding of both model theory and the underlying logistics processes, and one must pay attention to choosing the correct model, validating its assumptions, collecting data, and estimating parameter values. (3) The simplicity of the basic models and the policies they generate enhance the likelihood of implementation. One can communicate effectively both quantitative and qualitative insights based on a basic model to managers. As a consequence, managers at all levels in the company can understand and embrace the policies generated. The Service-Parts Logistics System At the end of 1994, RPS managed over 10,000 different part numbers throughout the world. Parts fall into two categories, consumables and repairables. A customer who orders a repairable item must return a corresponding defective unit, which the company then repairs at the repair depot. Consumables, where defectives are not returned, typically have higher usage rates and lower unit costs. RPS tries to maintain the uptime of its tester equipment at all customer sites. To do so, it must replace and repair parts rapidly, relying on its extensive multiechelon service-parts logistics and repair network.
Eight inventory locations worldwide are organized into two echelons: a single US central depot (CD) at the top and seven local centers (LCs) outside the US (in Europe and Asia) at the lower echelon. The CD ships parts to all North American customers directly and replenishes the LCs’ inventory. The CD also operates a repair center for repairable parts and replenishes its inventory from outside vendors or from the company’s manufacturing facilities (Figure 1). The repair center repairs the defective parts returned from both US and non-US customers. Multiple repair lines share equipment within the repair center. The repair process consists of such stages as diagnosis, replacement of failed components, and testing and can involve random rework. As a consequence, the process takes a random lead time with large variance. In spite of this variability, the probability distribution of lead times is not significantly different for different types of parts. RPS offers emergency service (ES) and regular replacement service (RR). ES is faster and more expensive. ES orders must be filled on the same day the order arrives. The customer is expected to return corresponding defectives later. The time between the order arrival and the receipt of the corresponding defective part is called the D1 (delay of defective return) time. RR orders can be filled within 12 days for US customers and within 20 days for non-US customers, only after RPS receives the defective unit from the customer. Many customers maintain inventories of frequently used service parts to replace defective parts within minutes when their
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Figure 1: Teradyne’s service-parts logistics network has a two-echelon structure with a single parts-repair and inventory-stocking depot (CD) located in Boston and seven non-US inventorystocking centers (LCs) located in Asia and Europe. The CD ships parts to North American customers directly and to LCs. An LC ships parts to non-US customers.
testers fail. Customers usually place emergency orders when they need a part for an on-line repair, and they place regular replacement orders to replenish their inventories. In 1994, about 47 percent of orders were ES orders. The two-class service allows customers to choose between fast service at a high price and slower service at a lower cost. RPS does not need to hold parts inventory to satisfy RR demand, making its logistics costs lower for this service class. Because tester products have a short life cycle, depreciation and obsolescence costs can be significant. The price incentives this twotier service policy provides allow the company to achieve a high level of customer satisfaction at a cost lower than that associated with a single class of service. The repair and replacement processes for repairable parts give rise to two
streams of material flow: good parts move out to satisfy customer demands, and defective parts move in to be repaired at the depot. When a US (non-US) customer places an ES order, the CD (the local center) ships a good part immediately, if available, to the customer. If a good part is not available, RPS records a late ES demand. As noted above, customers must first send their defective part to the CD (or to the appropriate LC if the customer is not in the US) in order to place an RR order. Upon receipt of the defective, the CD (LC) is allowed 12 (20) days before it is required to ship out a good replacement part to the customer. RR demands are counted late only if this due date is missed. When an LC receives an ES customer order, it places a replenishment order with the CD, which fills the order immediately if parts are available. Otherwise,
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TERADYNE the CD back-orders this replenishment order. For an RR order, the CD must ship a good part, if available, to the LC just in time, that is, to reach the LC just before the LC’s due date (thereby maximizing the potential for CD inventory to satisfy ES demand). LCs send the returned defectives to the CD repair center, which repairs parts within an estimated mean time of eight days and puts them into good-part inventory.
Each location in the system follows a one-for-one replenishment policy [Nahmias 1981]. Orders are filled on a first-come, first-served basis. The planned level (the base or order-up-to stock level) for each part at each location is calculated to attain a target service level of 95 percent, assuming a Poisson distribution of the replenishment-lead-time demand. The mean replenishment lead times have been conservatively estimated by the company to be four weeks for all locations. The demand rate for each part is updated every quarter based on a weighted moving average of the latest four quarters of demand data. Transportation time between the CD and LCs takes an average of five days. To save on transportation costs, LCs and the CD consolidate returns of defectives and replenishment orders and ship them once a week (each way). The average D1 (defective delay) time is 15 days, most of which is the customers’ delay in shipping. A major performance metric of customer
service is the percentage of demand met on time. Teradyne averaged about 12-percent lateness in 1994, which it considered to be too high. RPS management wanted to reduce lateness to six percent without increasing its investment in parts inventory. To understand the operations of the system, the project team interviewed various RPS managers. Throughout this process, academic and management team members communicated intensely. The managers gained many new insights concerning the RPS system and the value of performance data. The interviews helped them to organize their process knowledge systematically. This project stage was equally useful to the academic team members. We were challenged to link abstract models to the real-world processes. We realized that the RPS environment was far richer and more complex than the environments described in the literature. We used our knowledge of multiechelon inventory theory and our understanding of the RPS logistics process gained through the interviews to formulate two basic models: one for consumable parts and the other for repairables. These models captured key characteristics of the system, were well known in the inventory literature, and could be communicated to the corporate team members. Analysis supported by these models shed light on specific management problems of interest to the company. We communicated our findings to company logistics managers at all levels. Data Collection and a Pareto Analysis We collected information about parts that caused customer lateness in 1994 to
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RPS managed over 10,000 different part numbers throughout the world.
COHEN, ZHENG, WANG find out why they were in short supply. Of the more than 10,000 part numbers, only 707 were late (539 repairables and 168 consumables). Using the demand-andservice data for the identified parts, we conducted a Pareto analysis by ranking them according to the quantity that were late. Only a small number caused most of the lateness problems. To our surprise, more than 80 percent of the lateness occurred in consumables. Although consumables are usually less critical than repairables, such a high rate of lateness can decrease customers’ satisfaction with service. We found that the main cause of the problem with consumables was the company’s inventory-control method. Most of the parts stocked are repairables, and they are far more expensive than consumables. As a result, managers focus on them. Planning responsibility for consumables is not as well defined. We were told that consumables in the system “were managed like repairables, but their planning was more ad hoc.” Consumables are different from repairables, however, in several ways: (1) Their demand rates are much higher, and their demands often come in batches. (2) Their replenishment lead times are longer because they are replenished by shipments from external vendors or from the company’s manufacturing facilities. Replenishment order lead times for consumables are 13 weeks on average. Defective repair cycle times are much shorter. (3) Unit costs for consumables are lower— the average unit cost of a repairable part is 22 times the cost of a consumable part. The investment in inventory for consumables experiencing shortage was about one
percent of that for the repairable parts that also experienced a shortage. These differences suggested that the company should manage inventory for consumables quite differently from that for repairables. Although inexpensive, consumables should not be neglected. A delay in supplying a $1 part can cause as much downtime as a delay in supplying a $10,000 part. Improving service on consumables, however, requires a relatively small increase in parts-inventory investment and can reduce or eliminate shortages of consumables. Because their cost is low, the company should use a routine material-control scheme, requiring little management attention for consumables. Policy Recommendations for Controlling Consumables To construct inventory control policies for consumables, we need to understand the relationship between the CD and the LCs. The CD ships to US customers and to LCs, which ship to non-US customers. Therefore, the CD supplies all of the system-wide demands. While the LCs replenish their inventory from the CD, the CD replenishes its inventory from outside vendors. Consequently, the replenishment lead time for the CD is much longer than that for the LCs. Currently, the CD lead time averages 13 weeks and the LC lead time averages eight days (if the CD has no stock out). Because the CD and LCs differed in their characteristics, we recommended a periodic-review, base-stock control system for the CD and a continuous-review, onefor-one replenishment system for the LCs for consumables. The periodic-review, base-stock system, also called a periodic,
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TERADYNE order-up-to policy, has been studied extensively. Although less accurate than a continuous-review system, it is suitable for inexpensive high-demand items. Since Teradyne’s management resources were limited, we decided that monthly review would be adequate for consumables. Company managers thought they could not quantify the cost of a back order, and thus they chose to use the order fill rate as the service-performance metric. We recommended that every month the company should bring its inventory position (onhand plus on-order inventory) to a level such that it could fill the desired fraction of demand. We determined this order-upto level based on the probability distribution of total demand over the time period of lead time plus inventory-review time. We analyzed historical usage data for a large sample of part numbers to estimate the distribution. In all the cases we considered, the empirical data fit the normal distribution reasonably well. This approach is based on a standard, single-location model perspective. Hence, the service level predicted is accurate only for service provided to US customers, who order directly from the CD. Service levels for non-US customers will be affected by the LCs inventory policies, and thus we would need a multiechelon model to predict their service levels. The historical demand data indicated that demand rates at each of the LCs for most consumable part numbers are low. On average, an LC receives only one customer order every three to five months for most of the parts. For the most frequently used parts, an LC receives one order every three to five weeks. On the other hand, a
single order often requests a batch (multiple units) of a part, ranging from one to five units for most cases and five to 20 units for a very few cases.
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Managing repairables is much more challenging than managing consumables. A continuous-review, one-for-one policy is appropriate for consumables at the LCs due to their low demand rate. We used the compound Poisson distribution for modeling the batch arrival process. We applied a variant form of Palm’s theorem extended to compound Poisson arrivals [Feeney and Sherbrooke 1966] to determine the planned inventory-target levels at the LCs. To do this, we needed to compute the expected delay at the CD, due to a stock out, for filling randomly arriving replenishment orders from LCs. Expressing this expected delay exactly is complicated because the CD uses a periodicreview system in the model. Thus, we computed an upper bound for it (appendix). We used this upper bound in the LC model to generate a conservative inventory stocking level for a prespecified service level at a LC. We used simulation to check the effectiveness of the proposed models for consumables. Specifically, for a sample of parts that were often late, we used a rolling-horizon method to generate transactions that would have occurred under the proposed policies in response to the historical demand data. We used the most recent nine months’ data to estimate demand-distribution parameters for the next month and to update the order-up-to
COHEN, ZHENG, WANG level based on a prespecified service level. The simulation indicated that the company could reduce the total number of late customers in supplying consumables by over 90 percent with less than a threepercent increase in inventory investment if it applied the policies the team suggested consistently. The company decided to implement an order policy for consumables based on our model. Improvement Analysis for Repairables Managing repairables is much more challenging than managing consumables. The company uses a one-for-one replenishment policy, which is appropriate for these low-demand, high-cost items. Our goal was to improve the operation of this system. Even a small improvement in its performance could lower inventory investment or enhance service or both. Based on our knowledge of the logistic process, we realized that we would need a large-scale, multi-item, multiechelon model to capture all of its distinctive features. We decided, however, not to construct this type of a model for this phase of the project for several reasons. First, it would take a long time and a large quantity of data to formulate, solve, validate, and implement a faithful model of the system. Second, it would be difficult to communicate the logic and insights of a complex model to RPS managers. They would see such a model as a black box. Finally, no published models could deal with the two-tier service policy and the global complexities we observed in the RPS environment. Indeed, development of a more realistic multiechelon model took two years of doctoral research [Wang 1998] and led to fundamental contributions to the
literature. The team thus chose to develop a simplified model based on published models. The model applied Palm’s [1938] theorem to a single-location repairable inventory system. This approach is very close to the methodology that the company was in fact using. We also adopted the METRIC [Sherbrooke 1968] multiechelon approach to deal with linkages between the CD and the LCs. Our model captured many of the key characteristics of the system and yet was simple enough that the managers could readily understand its results. In applying Palm’s theorem to a stocking location with one-for-one replenishment policy, we treat outstanding replenishment orders as customers in an M/G/⬁ queuing system. The theorem states that the steady-state probability distribution for the number of orders outstanding in such a system is Poisson, with a mean value equal to the mean demand-arrival rate multiplied by the average service time. Service time here is equal to the replenishment lead time, which is the elapsed time between placement and receipt of an order. Special care was required in estimating parameters to be used in applying Palm’s theorem. We discovered that the approach RPS was using in computing values for the base stock level (in RPS’s terminology, the planned inventory levels) was problematic for this reason. The equations RPS used to generate a planned level to achieve a fill-rate target indeed conformed to the general Palm’s theorem approach. The values it used to estimate input parameters, however, were based on an overly simplified and inaccurate assess-
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TERADYNE ment of delays and lead times. We found that the cause of this problem was the absence of a multiechelon perspective in RPS’s methodology and its inability to deal with interactions between ES and RR demands. We noted that two distinguishing features of the RPS environment are not addressed in the multiechelon inventory literature: (1) Demands of the ES type are filled immediately, but defectives arrive after a return delay (D1). (2) Demands of the RR service type are not filled until a demand lead time has elapsed [Hariharan and Zipkin 1995]. The demand lead time is the time between RPS’s receipt of the defective part and the demand due date. For US customers, this interval is 12 days, and, for non-US customers, it is 20 days. Our challenge was to deal with these nonstandard system features in the context of our basic model. The first issue was easy to deal with (in an approximate manner). For ES demands, the repair process does not start until the defective unit arrives at the CD (assuming no stockpile of defective items). Thus, we can set mean replenishment lead time at the CD to be equal to the sum of the repair lead time and the return delay D1. For non-US ES demands, we need to add the defective consolidation and transportation times (from LCs to the depot) as well. Dealing with feature (2) is more involved. In the standard repairable model, we use the probability distribution of outstanding orders (obtained from Palm’s theorem) to compute the distribution of the good-part inventory level. This is straightforward because the good-part inventory level plus the number of out-
standing orders equals the selected basestock level. This equality, however, is based on the assumption that inventory is depleted as soon as a demand occurs. For RR demands, the inventory level does not go down until a demand lead time after the demand occurrence. Therefore, the above equality is not true in the RPS system. To deal with this issue, we modified the definition of replenishment lead time to equal the time between when a demand is filled and when a corresponding replenishment unit is received. By doing so, we shift the RR replenishment order placement by a demand lead time, that is, from when the RR demand arrives to when the RR demand is filled. This reinstates the relationship between inventory level and outstanding orders.
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The simplicity of basic models and policies improves communication with managers. Based on this definition, replenishment lead time for an RR order may be negative—when the replenishment order arrives before the time when the demand is to be filled. RR demand at the CD has a demand lead time of 12 days, and the average repair lead time at the CD is only eight days. Thus, the average replenishment lead time, based on our modified definition, is equal to four days (8 ⳮ 12 ⳱ ⳮ4). Defectives brought into the system by an RR demand can be repaired and be available as good parts, on average, four days before their required shipment date. A negative replenishment lead time thus
COHEN, ZHENG, WANG can improve service because the repaired good parts can be shipped out to satisfy (higher priority) ES demands during the days they are waiting for their required ship date. Our treatment of negative replenishment lead times is an approximation (appendix). The approach was adequate, however, for the strategic analyses required in Phase 1. We carried out an exact analysis of the two-tiered service with negative lead time in the follow-on Phase 2 of the project [Wang 1998]. The values used for replenishment lead times in our model will vary with the location (origin) and type of demand. In general, the replenishment lead time can contain one or more of the following components. RT: the repair lead time, D1: the defective return delay for ES demands, CT: the consolidation time for weekly international transportation, TT: the international transportation time (between an LC and the CD), DLT: the demand lead time for an RR demand, RD: the random delay, caused by a stockout at the CD, experienced by a replenishment order placed by an LC. Each of these components can affect logistics system performance. Teradyne was especially interested in quantifying the benefits of reducing lead time by improving the processes associated with each factor. Therefore, we needed to account for each component correctly in our model to support sensitivity analysis of performance to such changes. In our system, an LC has two demand
streams (the two classes of customer demands), and the CD has four demand streams (the two classes of US customer demands and the two classes of LC replenishment orders). From our analysis of the logistics processes, we developed the following definitions for the replenishment lead times, corresponding to each of the demand streams. Let RLT [x] denote the replenishment lead time corresponding to demand stream x. At the CD: (1) RLT [US ES] ⳱ D1 Ⳮ RT, (2) RLT [US RR] ⳱ RT ⳮ DLT[US], (3) RLT [LC ES] ⳱ D1 Ⳮ CT Ⳮ TT Ⳮ RT, and (4) RLT [LC RR] ⳱ 2[CT Ⳮ TT] Ⳮ RT ⳮ DLT [LC] and at the LCs: (5) RLT [LC ES] ⳱ CT Ⳮ TT Ⳮ RD, (6) RLT [LC RR] ⳱ RD. The mean replenishment lead time at the CD (LCs) is the weighted average of components 1 through 4 (5 and 6). A key assumption in using Palm’s theorem is that replenishment lead times are independent and identically distributed (iid) random variables. Since the repair center at the depot repairs thousands of part numbers, adoption of iid repair lead times is reasonable. Researchers commonly make this assumption and refer to it as the ample capacity assumption. For most other lead time components, iid is also a good assumption. It is plausible, however, that the consolidation time and the random delay of two adjacent orders for the same part number may be dependent. In that case, the iid assumption becomes an approximation. The correlation between these components, however,
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TERADYNE is usually insignificant (because orders occur infrequently with a large time gap between successive orders). In summary, our model of the company’s two-echelon logistics system for repairables includes the following assumptions: (1) Poisson demand arrivals for each demand stream, (2) one-for-one inventory policy at each inventory location, (3) independent and identically distributed replenishment lead times at each inventory location, and (4) first-come, first-served rule in satisfying all demands. We describe the mathematical model in detail in the appendix. Our model differs from the standard METRIC formulation [Sherbrooke 1968] in several ways. First, in addition to performing repairs and holding replenishment inventory for LCs, the CD in our system serves local customers directly. Second, there are two types of customer demands in our system. Third, we use the service level (fill rate) as a performance measure at various locations, whereas METRIC uses expected back order (cost). We used 1994 data for a group of sample part numbers to check the validity of the model. The input data included actual planned inventory levels, observed demand rates, and estimated lead times. The outputs of the model included service levels at the various inventory locations throughout the system. One minus these service levels multiplied by the corresponding demand rates at various locations gives us a prediction of the expected number of late demands. We compared the predicted number to actual data during 1994 and found that our model is reasonably accurate. The system-wide error
for lateness was about six percent. We used the model to support the Phase 1 policy analysis to quantify system-wide benefits of alternative improvement policies. Equipped with the validated repairable model, we considered how much the company could gain by reducing the repair time (RT), the defective delay time (D1), or the consolidation time (CT). Since the company’s goal was to improve customer service, we quantified the benefits of reducing lead time in terms of the systemwide service level (Table 1). A one-day reduction in either D1 or CT may improve the service level by about five percent, while a one-day reduction in RT would improve the service level by about 8.5 percent. This is not surprising since RT contributes to the RLT of all demand types. Although the benefits show diminishing returns, this effect is insignificant within the range of interest. Managers used these results to support their allocation of scarce resources for system improvement. They did so by comparing predicted benefits to estimated costs for implementing the various lead-time reductions. RPS’s methodology for computing the planned inventory levels for repairables used approximations of replenishment lead times. Furthermore, planners periodically reviewed and revised the planned levels based on recent performance. For example, if a part number experienced late delivery in the last month, the planner might increase its planned level in the next stocking cycle. Since the total inventory investment is constrained by a budget, increasing one part number’s inventory ultimately meant reducing inven-
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tories of other parts, resulting in an inappropriate allocation of inventory among all of the parts. Based upon our model, we first recalculated the planned levels needed to achieve the desired service levels. Our computations showed that the overall service level could have been higher and the total inventory investment could have been lower if the company had used our model in 1993-1994. We computed three sets of planned inventory levels using uniform target service levels of 90, 93, and 95 percent, respectively (Figure 2). We recommended that Teradyne use our model as a starting point for developing a new inventory control system. The company agreed and as a result supported research to extend the basic model in the second phase of the project. So far we have focused on individual part numbers, assuming that all part numbers have the same (uniform) target service level and that the service levels set for the CD and LCs would be equal. At RPS, all part numbers compete for a limited in-
ventory budget and for managerial attention. Part numbers differ greatly in cost and demand rate, however. The manager members of our team readily agreed that there was no reason to use the same service level for all part numbers and locations. This suggests that the company should use a system-wide, multipart optimization model to maximize overall service, subject to an inventory budget constraint [Cohen, Kleindorfer, and Lee 1986; Cohen et al. 1990; Cohen et al. 1998]. Such a model would require the solution of a large-scale, nonlinear program and was beyond the scope of Phase 1. We therefore used the basic model to explore the impact of service-level differentiation based on part-parameter differences. The analysis indicated that high-cost parts require larger investments in inventory to achieve a fixed service level and that it is more economical to service highdemand parts (rather than low-demand parts). For example, if an LC has an annual demand rate of 31 for a part number, it must plan to stock five parts to achieve a 96.6 percent service level. At a demand rate of 14, the same service level requires a planned level of three. At a demand rate of less than one, this service level requires a stock level of one unit. Using the same level of service for all parts leads to lowusage parts consuming a disproportional amount of the parts-inventory investment. A Pareto analysis indicated that about 19 percent of the parts investment was tied up in 1,305 part numbers, whose system-wide 1994 average demand rate was less than one unit. About 14 percent of the investment was for 263 part numbers whose 1994 usage was between one
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Lead/time component
\
Lead-time 1 reduction Day
D1 Repair cycle time Consolidation delay time All three components
2 3 Days Days
4.82% 9.24% 13.24% 8.45% 15.69% 21.72% 5.21% 10.07% 14.69% 17.46% 31.32% 42.13%
Table 1: The benefits of lead-time reductions are quantified through model sensitivity analysis. A one-day reduction in defective return delay (D1) or transportation consolidation delay can improve the system-wide service level by about five percent, and a one-day reduction in defective repair time can improve it by 8.5 percent.
TERADYNE and 2.25 units. Finally, 17 percent of the investment was for 181 part numbers whose 1994 usage was between 2.25 and 5.2 units. Thus, low-usage items accounted for 50 percent of the inventory investment. Also, there was a strong negative correlation between part demand rate and cost [Cohen and Zhang 1997], that is, lowusage items are more expensive. We demonstrated the benefits of differentiating service level by applying a simple stocking rule for setting service targets for different part numbers and inventory locations. The basic idea behind the rule is to allocate high service to the depot and high service to part numbers with high usage rates and lower unit cost (Table 2).
Comparison runs of the model indicated that such nonuniform service-level assignments dominate uniform service policies by reducing inventory investment and increasing system-wide service level (Figure 2). Our analysis also suggested that LCs should not stock some very expensive low-usage part numbers. To achieve any nonzero service level, these locations need to keep at least one unit in stock. A $10,000 part with an annual usage rate of 0.25 unit would sit on the shelf for an average of four years. If we assume the annual holding cost is 15 percent of the purchase cost, RPS would incur an inventory holding cost of $6,000 in meeting this de-
Figure 2: Uniform service is to provide the same service level for all part numbers at all inventory-stocking locations; differentiated service is to provide high service levels for part numbers with high usage rates and low cost and for inventory locations with high demand. Compared with the current planned level, the planned inventory recommended by our model with a uniform target service of 93 percent could increase the system-wide service level from 92 percent to 96 percent, while reducing inventory investment in the part sample set by 35.5 percent. Differentiated service dominates uniform service. A normalized index is used to measure inventory investment.
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mand, a cost that could be greater than the profit margin of service. We recommended that RPS consider stocking low-demand, high-cost parts only at the CD. It could fill orders for these parts using express delivery. This would increase the delivery time for emergency service from one day to three or four days for parts the LCs do not stock. It was noted that customers may resist this change even if their overall service level increases and system costs decline. Accordingly, we carried out further analysis of redeployment through a central stocking policy and regional pooling (where some LCs stock the parts and others do not) in Phase 2. Conclusions We applied two basic inventory models to identify opportunities for improving a complex service-parts logistics system. The consumable model showed that the company could reduce late shipments to customers by over 90 percent, with a less than three-percent increase in inventory investment. The repairable model indicated that it could reduce inventory investment by as much as 37 percent, while improving customer service level by around four per-
cent. These results showed that basic inventory models could be used effectively to improve system performance and to analyze logistics policies. Applying basic models successfully is not easy, however. One must have a deep level of understanding of both the models and the logistics processes. Although the models we used were well known, their appropriateness for analyzing this particular logistics system was not obvious. Initially, we found the complexity of the system suggested that basic models would be inappropriate. As the manager members of the team explained their logistics management system to us, however, we discovered that with appropriate interpretation and estimation of input parameters, we could apply the basic models to provide managerially useful insight. The approach was successful since model selection and application were based on a thorough understanding of the underlying processes and of the limitations of the models. The simplicity of basic models and policies improves communication with managers and enhances their applicability. Indeed, we were able to improve managers’ understanding of their own process through modeling insight by using the models to explain policy trade-offs. Instead of talking about a multiechelon inventory model, we focused on models for individual locations. We demonstrated that each part at each location could be represented by a queuing system in which outstanding orders could be viewed as the customers. We then showed how customer service was driven by the various leadtime components that the managers con-
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Usage rate per quarter
\
Unit cost
Low
High
CD: 0 ⳮ 15 ⬎15
94% 97%
90% 95%
LC: 0 ⳮ 0.25 ⬎0.25
90% 95%
0% 90%
Table 2: A simple service differentiation rule is to allocate a high service level to parts numbers with high usage rates and low unit costs and to allocate a high service level at the central depot for a given part number.
TERADYNE trolled. These model insights reinforced managers’ intuition and quantified the effect of specific improvements. Once the manager team members understood how part service-level differentiation could improve system effectiveness, they conveyed the idea to the entire RPS planning group. RPS managers now classify parts based on usage rate and cost. They routinely use this information to guide stocking decisions. When a problem occurs in managing a specific part number, they now immediately ask for its usage-cost category and treat the problem accordingly. New parts with high demand rates and low costs now receive priority for approval in quarterly budget allocations. The success of the Phase 1 project owes much to the contributions of the manager team members. At the outset of the project, the team outlined how members would cooperate, what each group’s goals were, and how we would achieve those goals. With manager members providing process knowledge and data and academic members providing modeling knowledge, we used basic models effectively to improve performance for a complex logistics system. The Phase 1 project led us to identify new research opportunities in modeling repairable systems. These include the following: (1) The depot replenishment lead times may vary for local centers as times for shipping defectives to the repair center vary. (2) The system has two classes of customer service (ES and RR). We approximated these features in Phase 1. An extended multiechelon model has been developed to address these features
explicitly [Wang 1998]. Acknowledgments We thank the referees for their careful reading of the previous version of this paper and for their constructive suggestions. We also acknowledge the contributions and participation of the company team members, Jason Anton, John Leutjen, and Ted Miller of the Teradyne Corporation. Finally, we thank Randy Stone and Brian Amero who, as senior managers, supported the project and the implementation of its recommendations. APPENDIX The Continuous Review One-for-One Model for Inventory Control of Consumables at LCs We compute an upper bound for the expected random delay at the CD experienced by the replenishment orders from LCs as follows: Let L be the replenishment lead times [number of review periods] of the CD. Let S be the order-up-to inventory position of the CD at each review period. Let D[i, j] denote the cumulative demand from period i to period j at the CD. Let Rt, 0 ⱕ Rt ⱕ L Ⳮ 1, denote the random delay (number of CD’s review periods) at the CD by an LC replenishment order placed in period t. We have the following relation of events:
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15
{Rt ⱕ k} 傶 {D[t ⳮ L Ⳮ k, t] ⱕ S}, 0 ⱕ k ⱕ L.
(A1)
This implies that Pr {Rt ⱕ k} ⭓ Pr {D[t ⳮ L Ⳮ k, t] ⱕ S}, 0 ⱕ k ⱕ L. (A2) Now, consider the system in steady state. Let D[n] denote the cumulative demand of n periods at the CD. Let R denote the random delay (number of CD’s review periods) at the CD of a typical LC replenishment order. We can then write (A1) and (A2), respectively, as
COHEN, ZHENG, WANG {R ⱕ k} 債 {D[L ⳮ k Ⳮ 1] ⱕ S}, 0ⱕkⱕL
(A3)
h(x) ⳱ p(x|kT), 0 ⱕ x ⬍ ⬁.
and Pr{R ⱕ k} ⭓ Pr{D[L ⳮ k Ⳮ 1] ⱕ S}, 0 ⱕ k ⱕ L.
(A4)
Define the integer valued random variable K on [0, L Ⳮ 1] by
冦
ders of the LC in steady state will have the probability distribution of
{Pr{K ⱕ k} ⳱ Pr{D[L ⳮ k Ⳮ 1]
(A7)
If the planned stocking level at the LC is S¯, the service level (that is, the probability of not stocking out) at the LC can then be calculated as ¯ Sⳮ1
b⳱
兺
h(x).
(A8)
x⳱0
ⱕ S} for 0 ⱕ k ⱕ L,
where, f k* (x) is the k fold convolution of { fj}. Assume (1) the replenishment orders are always filled in full batches at the CD; (2) the replenishment lead times are independent and identically distributed with a mean value of T as defined above. Then, by the result of Feeney and Sherbrooke [1966], the outstanding replenishment or-
An Example of Negative Replenishment Lead Time We used the weighted average, regardless of sign, of the replenishment lead times corresponding to different demand streams, and this is in fact an approximation. To see this, consider a simple single location system with the following two demand streams: stream 1 has a Poisson arrival rate of k1 and (positive) service time of L1; stream 2 has a Poisson arrival rate of k2 and negative replenishment lead time of ⳮL2. In other words, while an occurrence of a stream-1 demand will decrease the inventory level in the system by one unit for a time period of L1, an occurrence of a stream-2 demand will increase the inventory by one unit for a time period of L2. Let P(l) denote a Poisson random variable with the mean value of l. In steady state, the number of outstanding orders corresponding to stream-1 demand is P(k1L1) and the number of negative outstanding orders (extra inventory) corresponding to stream 2 is P(k2L2). Thus, the overall outstanding orders can actually be written as [P(k1L1) ⳮ P(k2L2)], that is, the difference of two Poisson random variables. Our model approach approximates [P(k1L1) ⳮ P(k2L2)] by the single Poisson random variable of P(k1L1 ⳮ k2L2). The Two-Echelon Model for Repairables We use the following notation and assumptions: N ⳱ the number of international local centers (LCs) in the system.
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Pr{K ⳱ L Ⳮ 1}⳱ 1 ⳮ Pr{D[1] ⱕ S}.
(A5)
The expected value of K, that is, E[K], can then be computed. However, due to the relationship of (A4), we have E[R] ⱕ E[K], that is, E[K] is an upper bound of E[R]. We calculate the outstanding replenishment orders and service level at an LC as follows: Let T be the total average replenishment lead time, that is, the transportation time from CD to LC plus E[K] (T is actually an upper bound of the average replenishment lead time since E[K] is an upper bound for the average waiting time at CD). Customers arrive at the LC according to a Poisson process with a rate of k. The total demand of each arrival customer is, independent of all others, a discrete random number with pmf of {fj}. Then, the compound Poisson probability of x demands during a unit time period is x
p(x|k) ⳱
兺 k⳱0
kk exp(ⳮk) k* . f (x), k!
(A6)
TERADYNE k0,j ⳱ the Poisson arrival rate of type j US customers, j ⳱ 1 for ES, and j ⳱ 2 for RR. We assume that the two demand streams of customer arrivals are independent, since they usually come from two different customer groups, one with its own inventory of spares and the other not. ki,j ⳱ the Poisson arrival rate of type j customers at local location (LC) i, i ⳱ 1, 2, . . . , N, j ⳱ 1 for ES, and j ⳱ 2 for RR. We assume that all the demand streams of customer arrivals are mutually independent. i,j 2 k0 ⳱ 兺N i⳱0 兺j⳱1k ⳱ the total demand rate at the CD, which is the total systemwide customer demand rate. L0,j ⳱ CD average replenishment lead time of type j US customer demand. L1,j ⳱ CD average replenishment lead time of type j international demand. We assume that L1,j is the same across all the LCs. L2,j ⳱ LC average replenishment lead time of its type j demand, excluding the waiting time at CD due to stock out. We assume that L2,j is the same for all the LCs. li ⳱ the mean value of the Poisson random variable representing the steady-state outstanding orders at location i, i ⳱ 0 for CD, and i ⳱ 1, 2, . . . , N for LC i. Si ⳱ the planned inventory level at location i, i ⳱ 0 for CD, and i ⳱ 1, 2, . . . , N for LC i. bi ⳱ the service level (that is, fill rate) at location i, i ⳱ 0 for CD, and i ⳱ 1, 2, . . . , N for LC i. B0 ⳱ the random number of back orders at CD. Note that B0 includes all the back orders of both US customer orders and LC’s replenishment orders and of both ES and RR types of demands. W0 ⳱ the random waiting time of orders at CD due to stock out. First, consider the central depot. Its total number of outstanding orders (that is, total number of units on order) is Poisson distributed with the mean value of
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2
l0 ⳱
2
兺
k0,jL0,j Ⳮ
j⳱1
兺
j⳱1
N
L1,j
兺
i⳱1
ki,j
(A9)
Our first quantity of interest about the CD is its service level or fill rate, which is the probability of not stocking out. The CD will not stock out as long as its outstanding orders are less than S0—its planned inventory level. Thus, we have S0ⳮ1
b0 ⳱
兺 k⳱0
lk0 exp(ⳮl0). k!
(A10)
On the other hand, back orders occur whenever its outstanding orders exceed S0. As a result, we can compute the expected back orders at CD as ⬁
E[B0] ⳱
兺
k⳱S0Ⳮ1
(k ⳮ S0)
lk0 exp(ⳮl0). k!
(A11)
Now, E[B0] can be considered as the expected queue length of customer orders at CD. By Little’s law, the expected waiting time is given by E[W0] ⳱
E[B0 . k0
(A12)
Consider any international local location LC i, i ⳱ 1, 2, . . . , N. The total expected replenishment lead time for its demand type j, j ⳱ 1 for ES, and j ⳱ 2 for RR, is equal to L2,j Ⳮ E[W0]. By assuming that the replenishment lead times are independent and identically distributed, we know that the total number of outstanding orders at LC i is a Poisson random variable with a mean value of 2
li ⳱
兺 ki,j(L2,j Ⳮ E[W0]). j⳱1
(A13)
Thus, with a planned inventory level of Si, the service level at LC i can be calculated as Siⳮ1
bi ⳱
17
兺 k⳱0
lki exp(ⳮli). k!
(A14)
COHEN, ZHENG, WANG In the above model, the various demand rates and replenishment lead times are exogenous parameters. For a given set of planned inventory levels {Si}, i ⳱ 0, 1, . . . , N, we can compute the service levels at each location in the system, that is, {bi}, i ⳱ 0, 1, . . . , N, and hence predict the system performance. Or, alternatively, for prespecified service levels {bi}, i ⳱ 0, 1, . . . , N, we can determine the required minimum inventory levels {Si}, i ⳱ 0, 1, . . . , N. References
Production/Inventory Control Systems, ed. L. B. Schwarz, TIMS Studies in Management Science, Vol. 16, North-Holland, Amsterdam, pp. 253–277. Ou, J. and Wein, L. M. 1996, “Sequential screening in semiconductor manufacturing, II: Exploiting variability,” Operations Research, Vol. 44, No. 1, pp. 196–205. Palm, C. 1938, “Analysis of the Erlang traffic formulae for busy-signal arrangements,” Ericsson Technics, Vol. 4, No. 1, pp. 39–58. Sherbrooke, C. C. 1968, “METRIC: A multiechelon technique for recoverable item control,” Operations Research, Vol. 16, No. 1, pp. 122–141. Wang, Y. 1998, “Service-parts logistics: Modeling, analysis and applications,” PhD dissertation, The Wharton School, University of Pennsylvania.
Cohen, M. A.; Kleindorfer, P.; and Lee, H. 1986, “Optimal stocking policies for low usage items in multi-echelon inventory systems,” Naval Research Logistics, Vol. 33, No. 1, pp. 17–38. Cohen, M. A.; Kleindorfer, P.; Lee, H.; and Tekerian, A. 1990, “OPTIMIZER: A multiechelon inventory system for service logistics management,” Interfaces, Vol. 20, No. 1, pp. 65–82. Cohen, M. A.; Zheng, Y.-S.; and Agrawal, V. 1997, “Service-parts logistics: A benchmark analysis,” IIE Transactions, Vol. 29, No. 8, pp. 627–639 (Special issue of scheduling and logistics on supply chain integration and coordination). Cohen, M. A. and Zhang, S. 1997, “Determinants of performance metric variation in service-parts logistics systems: An empirical assessment,” Working paper, The Wharton School, University of Pennsylvania. Cohen, M. A.; Donohue, K.; and Deshpande, V. 1998, “Supply chain coordination study: US Navy/Defense Logistics Agency,” FishmanDavidson Center for Service and Operations Management, The Wharton School, University of Pennsylvania. Feeney, G. J. and Sherbrooke, C. C. 1966, “The [S-1, S] inventory policy under compound Poisson demand,” Management Science, Vol. 12, No. 5, pp. 391–411. Hariharan, R. and Zipkin, P. 1995, “Customerorder information, lead-times, and inventory,” Management Science, Vol. 41, No. 10, pp. 1599–1607. Nahmias, S. 1981, “Managing repairable item inventory systems: A review,” in Multi-Level
Brian D. Amero, Director of Parts Services, Teradyne, Inc., 321 Harrison Avenue, Boston, Massachusetts 02118, writes: “The benefit to Teradyne has been significant. The project has allowed Teradyne to expand services offered to customers through use of the ‘optimizer’ software model, a direct result of the joint work. It facilitated a better understanding of the complexities that exist between our service offerings to customers and its relation to the logistical network. “The results of both phases of the project are in use by the Global Customer Services organization. The project is one of the means used to accomplish a set of business goals established by the organization. Additional steps remain to fully institutionalize the concepts and tools allowing the full benefit to be realized.”
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