×

A partial replenishment model for an inventory with constant demand. (English) Zbl 1145.90303

Summary: An inventory with constant demand is considered. The inventory is checked according to a Poisson process and replenished either fully or partially when the stock is below a threshold. We obtained the stationary distribution of the level of the inventory. After assigning several costs to the inventory, we also derived the long-run average cost per unit time. A numerical example is studied to find the optimal values of the checking rate and threshold, which minimize the long-run average cost.

MSC:

90B05 Inventory, storage, reservoirs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baxter, L. A.; Lee, E. Y., An inventory with constant demand and Poisson restocking, Probab. Eng. Inform. Sci., 1, 203-210 (1987) · Zbl 1133.90301
[2] Beckmann, M. J.; Srinivasan, S. K., An \((s,S)\) inventory system with Poisson demands and exponential lead time, OR Spektrum, 9, 213-217 (1987) · Zbl 0637.90029
[3] Boylan, E. S., Multiple \((s,S)\) policies, Econometrica, 32, 399-409 (1964)
[4] Brill, P. H.; Posner, M. J.M., Level crossings in point process applied to queues: single-server case, Oper. Res., 25, 662-673 (1977) · Zbl 0373.60114
[5] Dirickx, Y. M.I.; Koevoets, D., A continuous review inventory model with compound Poisson demand process and stochastic lead time, Naval Res. Logist. Quart., 24, 577-585 (1977) · Zbl 0372.90044
[6] Dvoretzky, A.; Kiefer, J.; Wolfowitz, J., On the optimal character of the \((s,S)\) policy in inventory theory, Econometrica, 21, 586-596 (1953) · Zbl 0053.27904
[7] Federgruen, A.; Zipkin, P., An efficient algorithm for computing optimal \((s,S)\) policies, Oper. Res., 32, 1268-1285 (1984) · Zbl 0553.90031
[8] Hohjo, H.; Teraoka, Y., The replenishment policy for an inventory system with Poisson arrival demands, Sci. Math. Jpn., 58, 33-38 (2003) · Zbl 1046.90007
[9] Hordijk, A.; van der Duyn Schouten, F. A., On the optimality of \((s,S)\)-policies in continuous review inventory models, SIAM J. Appl. Math., 46, 912-929 (1986) · Zbl 0648.90021
[10] Ross, S. M., Stochastic Processes (1996), Wiley: Wiley New York · Zbl 0888.60002
[11] Schäl, M., On the optimality of \((s,S)\)-policies in dynamic inventory models with finite horizon, SIAM J. Appl. Math., 30, 528-537 (1976) · Zbl 0333.90015
[12] Sethi, S. P.; Cheng, F., Optimality of \((s,S)\) policies in inventory models with Markovian demand, Oper. Res., 45, 931-939 (1997) · Zbl 0895.90079
[13] Tijms, H. C., The optimality of \((s,S)\) inventory policies in the infinite period model, Stat. Neerl., 25, 29-43 (1971) · Zbl 0217.26902
[14] Veinott, A. F., On the optimality of \((s,S)\) inventory policies: New conditions and a new proof, SIAM J. Appl. Math., 14, 1067-1083 (1966) · Zbl 0173.47603
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.