A perishable inventory system with service facilities, <Emphasis Type="Italic">MAP</Emphasis> arrivals and <Emphasis Type="Italic">PH</Emphasis> — Service times

We consider a continuous review perishable (s, S) inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process (MAP). An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE (removal of a customer from the end). The individual customer’s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically. This work was supported in part by National Board for Higher Mathematics, INDIA under Grant No. 48/3/2004/R&D-II/2114. Paul Manuel graduated PhD (1981–1986, Applied Mathematics) from Indian Institute of Technology India, MS (1991–1992, Computer Science) from University of Saskatchewan, Canada, and PhD (1992–1996, Computer Science) from University of Newcastle, Australia. He is an Associate Professor in Information Science, Kuwait University, Kuwait. While in the industries, he was working in various projects related to supply chain management. He is an ABET consultant to several institutions. His research interests are Knowledge Management and Algorithmic Graph Theory. He has published several papers in various journals of mathematics and computer science. B. Sivakumar is carrying out his Ph.D. programme in the study of Inventory Systems with Service Facilities in the Department of Applied Mathematics and Statistics, Madurai Kamaraj University, Madurai. In 2002 he received his M.Sc (Mathematics) from School of Mathematics, Madurai Kamaraj University, INDIA. His areas of research interest are Inventory Management and Queueing theory. G. Arivarignan received M.Sc(Statistics) from Annamalai University and his Ph.D. from Indian Institute of Technology, Madras. Since 1974, he worked as Assistant Professor of Statistics in Tamilnadu Collegiate Educational service and has joined Madurai Kamaraj University in 1990. His research interests are Stochastic Modelling and Applied Statistics. He has numerous publications in various journals of Statistics, Mathematics and Operations Research.