Waiting Time Distribution of Demand Requiring Multiple Items under a Base Stock Policy

Naoaki Morita, Koichi Nakade

Department of Industrial Engineering and Systems Management, Nagoya Institute of Technology, Nagoya, Japan..

DOI: 10.4236/jssm.2013.64030                

Abstract

In demanding for repair items or standard products, customers sometimes require multiple common items. In this study, the waiting time of demand which requires multiple items under base stock policy is analyzed theoretically and numerically. It is assumed that the production time has an exponential distribution and the demand is satisfied under a FCFS rule. Each demand waits until all of its requirements are satisfied. An arriving process of demand is assumed to follow a Poisson process and the numbers of required items are independent and generally distributed. A method for deriving waiting time distribution of demand is shown by using methods for computing M^X/M/1 waiting time distribution and for deriving the distribution on the order corresponding to the last item the current customer requires. By using the analytical results, properties of waiting time distribution of demand and optimal numbers of base stocks are discussed through numerical experiments.

Keywords

Base Stock Policy; MX/M/1 Queue, Waiting Time Distribution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. H. Zipkin, “Foundations of Inventory Management,” McGraw-Hill Companies, New York, 2000.
[2]	G. J. Feeney and C. C. Sherbrooke, “The (s-1,s) Inventory Policy under Compound Poisson Demand,” Management Science, Vol. 12, No. 5, 1966, pp. 391-411. http://dx.doi.org/10.1287/mnsc.12.5.391
[3]	Y. Zhao, “Evaluation and Optimization of Installation Base-Stock Policies in Supply Chains with Compound Poisson Demand,” Operations Research, Vol. 56, No. 2, 2008, pp. 437-452. http://dx.doi.org/10.1287/opre.1070.0461
[4]	I. Higa, A. M. Feyerherm and A. L. Machado, “Waiting Time in an (s-1,s) Inventory System,” Operations Research, Vol. 23, No. 4, 1975, pp. 674-680. http://dx.doi.org/10.1287/opre.23.4.674
[5]	S.-S. Ko, J. Young Choi, D.-W. Seo, “Approximations of Lead-Time Distribution in an Assemble-to-Order System under a Base-Stock Policy,” Computers and Operations Research, Vol. 38, No. 2, 2011, pp. 582-590. http://dx.doi.org/10.1016/j.cor.2010.07.020
[6]	M. L. Chaudhiry and U. C. Gupta, “Exact Compound Analysis of Waiting-Time Distributions of Single-Server Bulk-Arrival Queues: MX/G/1,” European Journal of Operations Research, Vol. 63, No. 3, 1992, pp. 445-462. http://dx.doi.org/10.1016/0377-2217(92)90161-2