An Overview of Inventory Systems with Several Demand Classes

Kleijn, Marcel; Dekker, Rommert

doi:10.1007/978-3-642-58568-5_13

Cited by 48 publications

(40 citation statements)

References 18 publications

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“…It may even be suboptimal to always withdraw stock when it is available. In order to keep stock for future, more critical, demands, some stock may be rationed for use in more critical equipment (see Kleijn and Dekker [12] for an introduction to inventory rationing and an overview of relevant literature).…”

Section: Repair Processmentioning

confidence: 99%

Integrating reliability centered maintenance and spare parts stock control

Jaarsveld¹,

Dekker²

2009

Reliability, Risk, and Safety

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In the classical approach to determine how many spare parts to stock, the spare parts shortage costs or the minimum fill rate are a key factor. A difficulty with this approach lies in the estimation of these shortage costs or the determination of appropriate minimum fill rates. In an attempt to overcome this problem, we propose to use the data gathered in reliability centered maintenance studies to determine shortage costs. We discuss benefits of this approach. At the same time, the approach gives rise to complications, as the RCM study determines downtime costs of the underlying equipment, which have a complex relation with the shortage cost for spare parts in case multiple pieces of equipment have different downtime costs. A further complication is redundancy in the equipment. We develop a framework that enables the modelling of these more complicated systems. We propose an approximative, analytic method based on the model that can be used to determine minimum stock quantities in case of redundancy and multiple systems. In a quantitative study we show that the method performs well. Moreover, we show that including redundancy information in the stocking decision gives significant cost benefits.

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Section: Repair Processmentioning

confidence: 99%

Integrating reliability centered maintenance and spare parts stock control

Jaarsveld¹,

Dekker²

2009

Reliability, Risk, and Safety

Self Cite

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“…For example, Cohen, Kleindorfer and Lee (1998) study a service parts application in the computer industry where a retailer could place normal replenishment orders and emergency orders, in case of stockout, at the warehouse. Kleijn and Dekker (1998) provide an overview of inventory systems with several demand classes, including examples ranging from airlines to petrochemical companies.…”

Section: Introductionmentioning

confidence: 99%

“…Very little research exists on how to optimize policy parameters for multiple customer classes, particularly in cases with fixed setup costs, positive lead-times, and backlogged customer demand (Kleijn and Dekker, 1998). This environment is challenging because positive backorders and positive on-hand inventory can coexist at the same point in time, making it difficult to calculate backorder distributions from the inventory level distribution.…”

Section: Introductionmentioning

confidence: 99%

A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes

Deshpande¹,

Cohen

Donohue³

2003

Management Science

230

222

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Motivated by a study of the logistics systems used to manage consumable service parts for the U.S. military, we consider a static threshold-based rationing policy that is useful when pooling inventory across two demand classes characterized by different arrival rates and shortage (stockout and delay) costs. The scheme operates as a (Q, r) policy with the following feature. Demands from both classes are filled on a first-comefirst-serve basis as long as on-hand inventory lies above a threshold level K. Once on-hand inventory falls below this level, low priority (i.e., low shortage cost) demand is backordered while high priority demand continues to be filled. We analyze this static policy first under the assumption that backorders are filled according to a special threshold clearing mechanism. Structural results for the key performance measures are established to enable an efficient solution algorithm for computing stock control and rationing parameters (i.e., Q, r, and K). Numerical results confirm that the solution under this special threshold clearing mechanism closely approximates that of the priority clearing policy. We next highlight conditions where our policy offers significant savings over traditional 'round-up' and 'separate stock' policies encountered in the military and elsewhere. Finally, we develop a lower bound on the cost of the optimal rationing policy. Numerical results show that the performance gap between our static threshold policy and the optimal policy is small in environments typical of the military and high technology industries.

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“…Moon and Kang (1998) extend the research to compound Poisson distributed demand. Kleijn and Dekker (1998) review the studies on inventory models with multiple demand classes. They indicate that one difficulty in deriving optimal solution in a continuous review system is due to the possible existence of multiple outstanding orders.…”

Section: A Brief Literature Reviewmentioning

confidence: 99%

“…Since 1 () F c is assumed to be a non-negative integer. As 1 F is increasing in c, we first need to increase c to satisfy 11 ,, AC Q r c begins to increase.□ Next, we develop lower bound and stop signal for searching Q . As we can observe (see Figure 3), the average cost (with optimal r and c) () AC Q  is not a smooth curve with respect to Q .…”

Section: Heuristicmentioning

confidence: 99%

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

Wang¹,

Tang²,

Huo³

2013

Computers & Operations Research

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, rQ system, we develop a critical level rationing policy in which a threshold mechanism is adopted to allocate backorders when multiple outstanding orders exist. Due to the problem complexity, a heuristic is developed based on the principle that both demand classes are served with respective target service levels. We also introduce bounds so that the search ranges of decision variables become restrictive. The numerical examples indicate an excellent performance of our heuristic. In addition, when ordering cost is medium or high, the threshold clearing mechanism has the same results as the optimal one. When ordering cost is small (set to zero), different clearing mechanisms should be used depending on the priorities of demand classes. Further analysis indicates that transforming the service constraint into a cost parameter and then applying the existing algorithm will not be a good approach for this problem with mixed performance criteria. It either increases the costs or violates the service constraint. This study also shows the importance of applying rationing policy when high priority class has a low demand volume, target service levels between two classes have a large gap, or replenishment lead time is long. The results of this study should enhance our understanding of how to implement rationing policies in practice.

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An Overview of Inventory Systems with Several Demand Classes

Cited by 48 publications

References 18 publications

Integrating reliability centered maintenance and spare parts stock control

Integrating reliability centered maintenance and spare parts stock control

A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

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