A Single-Product Inventory Model for Multiple Demand Classes

Arslan, Hasan; Graves, Stephen C.; Roemer, Thomas

doi:10.1287/mnsc.1070.0701

Cited by 114 publications

(79 citation statements)

References 19 publications

(27 reference 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%

“…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%

“…This is in line with the literature (cf. Arslan et al 2007;Deshpande et al 2003;Dekker et al 2002;Nahmias and Demmy 1981), and there is no reason to expect different results for α service levels. To ensure a dispersed distribution of the weighted average service-level guarantees across the entire range between 0.75 and 0.95, we use stratification (Appendix 2 provides more details on the stratification procedure).…”

Section: Numerical Analysismentioning

confidence: 99%

See 2 more Smart Citations

Service differentiation in a single-period inventory model with numerous customer classes

Schulte

Pibernik²

2016

OR Spectrum

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We study critical-level inventory-management policies as means to provide differentiated (α and β) service levels to more than two classes of customers. First, we derive closed-form expressions for the service levels of a single-period critical-level policy with an arbitrary number of customer classes (with Poisson demand). Based on the service-level expressions, we derive additional structural insights and provide an efficient algorithm with which to compute the essential system parameters, that is, the minimum required starting inventory and the associated critical levels. Based on these results, we conduct numerical experiments and develop structural insights into the system's behavior.

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Section: Proposition 317 (Uniqueness and The Separation Property)mentioning

confidence: 98%

Section: Literature Reviewmentioning

confidence: 99%

Section: Numerical Analysismentioning

confidence: 99%

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Service differentiation in a single-period inventory model with numerous customer classes

Schulte

Pibernik²

2016

OR Spectrum

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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%

Dynamic lead time quotation under responsive inventory and multiple customer classes

Savaşaneril

Sayin

2016

OR Spectrum

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We address the lead time quotation problem of a manufacturer serving multiple customer classes. Customers are sensitive to the quoted lead times and the manufacturer has the flexibility to keep inventory to improve responsiveness. We model the problem as a Markov decision process and characterize the optimal lead time quotation, rationing, and production policies. We then define internal and external service level measures and analyze the impact of inventory keeping decision on these measures. Before analyzing the impact, we first derive the relation between inventory level and lead time quotes. We then show that the effect of inventory level on the service levels may not follow the intuition. We also study alternative lead time quotation and production schemes. We contrast the performance of these alternative policies with that of the optimal policy. Specifically, through a numerical study, we quantify the value of controlled arrivals and customer rejection, the value of information on customer status, and the value of a far-sighted policy. Through the numerical study, we also identify the effect of revenue mix and demand mix on the inventory keeping decisions and the performance measures. Finally, we measure the impact of lead time quotation on resource pooling (i.e., inventory and capacity pooling). We show that the value of resource pooling is limited under the optimal policy, since lead time quotation is already effective in balancing the demand with capacity, and in allocating the resources among different customer classes.

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“…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%

Acquisition and production management with two inventories under fluctuating prices and demand

Cao

Huang

Wen

2009

Wuhan Univ. J. Nat. Sci.

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We propose a continuously deterministic procurementproduction-inventory model to optimize the raw material procurement and production problem with raw material inventory and finished products inventory when the raw material purchasing price, the production cost, the raw material inventory holding cost, the finished products holding cost, and the demand rate fluctuate over time. We use Hamilton-Lagrange function and Pontryagin's maximum principle in optimal control theory to analyze the model, and we obtain the necessary and sufficiency conditions of the optimal solution to the model. We find some optimal policies regarding the procurement and production under some special circumstances.With the great development of the worldwide market economy, the competitions among manufacturing corporations are becoming sharper. The raw material procurement prices can impose a high influence on tied-up capital and therefore the total cost of final products and company's profit. On the other hand, fluctuations of production costs are commonly faced by many manufacturing firms. If the production policy were not properly managed, the fluctuations could also inflict damages to the firm.Several contributions address the raw material procurement, production, and related inventory policy problems. Khmelnitsky et al [1] state a stationary capacitated inventory and production problem, analyze it in both discrete and continuous time, and give guidelines under which circumstances the models yield similar results, whereas Luhmer [2] formulates a nonstationary control problem considering ordering cost in three settings, backlogging, nonbacklogging, and limited warehouse space. Silver et al [3] and Grubbstrom et al [4] analyze EOQ models to solve the procurement problems. Toktay et al [5] considered a production stage that produces a single item in a make-to-stock manner, in which demand for finished products is stationary. He et al [6] dealt with several inventory replenishment policies for a make-to-order inventory-production problem that consists of a production workshop and a warehouse and Poisson demands. Golabi [7] considered a problem with an independent price process, negligible setup cost, and deterministic but

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A Single-Product Inventory Model for Multiple Demand Classes

Cited by 114 publications

References 19 publications

Service differentiation in a single-period inventory model with numerous customer classes

Service differentiation in a single-period inventory model with numerous customer classes

Dynamic lead time quotation under responsive inventory and multiple customer classes

Acquisition and production management with two inventories under fluctuating prices and demand

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