International Journal of Engineering Research in Electronics and Communication Engineering

Stochastic Perishable Inventory Control in a Service Facility System Maintaining Inventory for Service: Semi Markov Decision Problem

Author : R.Mugesh ¹ S.Krishnakumar ² C.Elango ³

PDF

Date of Publication :20th April 2017

Abstract: In this article we address the problem of optimally controlling the service rate in a service facility system maintaining perishable inventory for service completion. We consider a finite service facility system having finite waiting space with Poisson arrivals and exponentially distributed service times and lif e time of items. For the given values of maximum inventory and waiting space capacity, we determine the order quantities at various instance of time so that the long run expected cost rate is minimized. The problem is modeled as a semiâ€“Markov Decision Problem. We prove the existence of a stationary optimal policy and solve it by employing value iteration technique. Numerical example is provided to get insight into the system behavior.

Reference :

1. Berman, O. and Sapna, K.P., “Optimal Control of Service for facilities holding inventory”, Computers and operations Research (2001), 28, 429-441.
2. Berman, O. and Sapna, K.P., “Inventory management at service facilities for systems with arbitrarily distributed service times”, Stochastic Models 16 (384), (2000), 343 – 360.
3. Berman, O. “Stochastic inventory policies for inventory management at service facilities”, Stochastic Models, 1999, 15, 695 – 718.
4. Cinlar, C., Introduction to Stochastic Processes, Englewood Cliffs, N. J., Prentice – Hall, 1975.
5. Elango, C., Inventory system at service facilities, Ph. D Thesis, (2002), Madurai Kamaraj University, India.
6. Hilal Mohamed Al Hamadi, Sangeetha, N., and Sivakumar, B., “Optimal control of service parameter for a perishable inventory system maintained in service facility with impatient customers”.
7. Mine, H. and Osaki S., Markov Decision Processes, American Elsevier Publishing Company Inc, New York (1970).
8. Puterman, M.L., Markov Decision Processes: Discrete Stochastic Dynamic Programming, Wiley Interscience Publications Inc., (2005).
9. Henk C. Tijms, A First Course in Stochastic Models, John Wiley & Sons Inc., (2003).