×

Inventory policies with quantized ordering. (English) Zbl 0749.90023

Authors’ summary: “The article studies \((nQ,r)\) inventory policies, under which the order quantity is restricted to be an integer multiple of a base lot size \(Q\). Both \(Q\) and \(r\) are decision variables. Assuming the one-period expected holding and backorder cost function is unimodal, an efficient algorithm is developed to compute the optimal \(Q\) and \(r\). The algorithm is facilitated by simple observations about the cost function and by tight upper bounds on the optimal \(Q\). The total number of elementary operations required by the algorithm is linear in these upper bounds. By using the algorithm, the performance of the optimal \((nQ,r)\) policy is compared with that of the optimal \((s,S)\) policy through a numerical study, and results show that the difference between them is small. Further analysis of the model shows that the cost performance of an \((nQ,r)\) policy is insensitive to the choice of \(Q\). These results establish that \((nQ,r)\) models are potentially useful in many settings where quantized ordering is beneficial”.
Reviewer: S.Goyal (Montreal)

MSC:

90B05 Inventory, storage, reservoirs
90-08 Computational methods for problems pertaining to operations research and mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] and , ”Some Inequalities in (s, S) Inventory Models with Exponential Demands,” Department of Decision Sciences, The Wharton School, University of Pennsylvania, Working Paper (1989).
[2] and , ”Inventory Models with General Backorder Costs,” European Journal of Operational Research, to be published. · Zbl 0792.90022
[3] Clark, Management Science 6 pp 475– (1960)
[4] and , ”Approximate Solutions to a Simple Multi-Echelon Inventory Problem,” in Studies in Applied Probability and Management Science, , and (Eds.), Stanford University Press, Stanford, CA, 1962, pp. 88–100.
[5] Federgruen, Operations Research 31 pp 957– (1983)
[6] and , ”An Efficient Algorithm for Computing an Optimal (r,Q)policy in Continuous-Review Stochastic Inventory Systems,” Operations Research, to be published. · Zbl 0758.90021
[7] Hadley, Management Science 7 pp 351– (1961)
[8] and , Analysis of Inventory Systems. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1963.
[9] and , ”A Stationary Inventory Model with Markovian Demand,” in Mathematical Methods in the Social Sciences, , and (Eds.), Stanford University Press, Stanford, CA, 1963.
[10] Morse, Operations Research 7 pp 67– (1959) · Zbl 0105.12803
[11] Naddor, Management Science 21 pp 1234– (1975)
[12] Richards, Operations Research 23 pp 366– (1975)
[13] Applied Probability Models with Optimization Applications, Holden-Day, San Francisco. 1970. · Zbl 0213.19101
[14] Roundy, Management Science 31 pp 1416– (1985)
[15] Roundy, Mathematics of Operations Research 11 pp 699– (1986)
[16] ”The Uniform Distribution of Inventory Position for Continuous Review (s, Q) Policies.” RAND Corporation Report No. P-3938, Santa Monica, CA (1968).
[17] Stochastic Modelling and Analysis: A Compirtational Approach, Wiley, New York, 1986.
[18] Veinott, Operations Research. 13 pp 424– (1965)
[19] Veinott, Management Science 11 pp 525– (1965)
[20] Wagner, Management Science 11 pp 690– (1965)
[21] ”On Properties of Stochastic Inventory Systems,” Management Science, to be published.
[22] Zheng, Operations Research 39 pp 654– (1991)
[23] Zipkin, Naval Research Logistics Quarterly 33 pp 763– (1986)
[24] ”Lecture Notes in Inventory Theory,” Graduate School of Business. Columbia University, New York (1988).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.