2007
DOI: 10.1287/mnsc.1070.0701
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A Single-Product Inventory Model for Multiple Demand Classes

Abstract: We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service level requirements. We assume a critical-level control policy, and show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization, under the assumptions of Poisson demand, deterministic replenishment lead-time, and a continuous-review (Q, R) policy with rationing. We propose a comp… Show more

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Cited by 114 publications
(79 citation statements)
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“…In addition, our approach requires calculation of only x * 0 = l * k service levels (in step k the service levelγ cl k is computed l * k times), while an exhaustive search requires the calculation of O(n x 0 * +1 ) service levels (all n service levels are calculated for each configuration that is tested, and there are O (n x 0 * ) configurations that are tested prior to halting the algorithm). Note that the inductive approach from Corollary 3.18 also works if a multi-period continuous-review (Q, R) model is being used, as Arslan et al (2007) show in Section 5.1 of their paper. However, there are some differences between the algorithms presented in Arslan et al and in the present paper that go beyond using a single period and multiple periods, respectively.…”
Section: Proposition 317 (Uniqueness and The Separation Property)mentioning
confidence: 98%
See 2 more Smart Citations
“…In addition, our approach requires calculation of only x * 0 = l * k service levels (in step k the service levelγ cl k is computed l * k times), while an exhaustive search requires the calculation of O(n x 0 * +1 ) service levels (all n service levels are calculated for each configuration that is tested, and there are O (n x 0 * ) configurations that are tested prior to halting the algorithm). Note that the inductive approach from Corollary 3.18 also works if a multi-period continuous-review (Q, R) model is being used, as Arslan et al (2007) show in Section 5.1 of their paper. However, there are some differences between the algorithms presented in Arslan et al and in the present paper that go beyond using a single period and multiple periods, respectively.…”
Section: Proposition 317 (Uniqueness and The Separation Property)mentioning
confidence: 98%
“…However, when incorporating these expressions into an algorithm to derive the system parameters, they must either employ exhaustive searches or resort to a heuristic approach, while we gain structural insights into the problem that enable us to formulate an efficient algorithm exploiting the special structure of critical-level policies. Arslan et al (2007) study a multi-period, n-class, continuous review (Q,R) model with deterministic lead times in which the average inventory is minimized subject to a service-level constraint. To compute the system parameters, they provide an algorithm that yields close to optimal solutions.…”
Section: Literature Reviewmentioning
confidence: 99%
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“…Keeping a single generic item to serve multiple customer classes is a commonly made assumption especially in spare parts management literature (Dekker et al 1998); however, there are studies that make this assumption in other problem contexts as well (Bulut and Fadiloglu 2011;Ha 1997a, b;Arslan et al 2007). In our problem we assume that the generic item can be differentiated into a specific end-product in a negligible amount of time (Vericourt et al 2002;Benjaafar and ElHafsi 2006).…”
Section: The Modelmentioning
confidence: 99%
“…Arnold et al [8] presents a deterministic optimal control approach optimizing the procurement and inventory policy of an enterprise that is processing a raw material when the purchasing price, holding cost, and the demand rate fluctuate over time. Arsla et al [9] developed a model for cost evaluation and optimization under the assumptions of Poisson demand, deterministic replenishment lead time, and a continuous-review (Q, R) policy with rationing.…”
Section: Introductionmentioning
confidence: 99%