Constrained Optimal Control of a Two-Stage Queueing Inventory System with Production Delay

Fong-Fan Wang

《International Journal of Information and Management Sciences》 23:4 (2012/12) Pp. 371-394

https://doi.org/10.6186/IJIMS.2012.23.4.3

並列摘要

In this paper we investigate a make to stock two-stage queueing-inventory system with production delay. Under such production policy, the manufacturing facility may be shut down whenever it is idle and there is a non-negligible setup cost involved each time the facility reactivates its production. We also allow a non-negligible setup time for each reactivation process. Quasi-birth-and-death (QBD) models are employed to model the studied queueing-inventory system. We obtain the performance measures for the whole system using a convolution approach after the variation of inter-departure time of the first stage is obtained. A convexity-based searching scheme is developed to find the joint thresholds of production delay and target inventory levels for minimizing inventory holding and setup costs under a time-based service level constraint. Numerical examples are provided with discussions.

並列關鍵字

Queueing-inventory ； production delay ； setup ； departure ； QBD

參考文獻

Altiok, T.(1985).On the phase-type approximation of general distributions.IIE Transactions.17,110-116.

Bai, L.,Fralix, B.,Liu, L.,Shang, W.(2004).Inter-departure times in base-stock inventory-queues.Queueing Systems.47,345-361.

Buzacott, J. A.,Shanthikumar, J. G.(1993).Stochastic Models of Manufacturing Systems.New Jersey, USA:Prentice Hall.

Ching, W. K.(2001).Optimal (s, S) policies with delivery time guarantees for manufacturing systems with early set-up.Computers & Industrial Engineering.40,249-257.

Curry, G. L.,Deuermeyer, B. L.(2002).Renewal approximations for the departure processes of batch systems.IIE Transactions.34,95-104.