Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers

This paper deals with the problem of optimally controlling the service rates for the perishable inventory system at service facilities with impatient customers. We consider a finite capacity inventory system with Poisson demands and exponentially distributed service times. The maximum inventory level is fixed at $$S$$S. The ordering policy is $$(s,Q)$$(s,Q) policy, that is, whenever the inventory level drops to $$s$$s, an order for $$Q(=S-s)$$Q(=S-s) items is placed. The ordered items are received after a random time which is also distributed as exponential. The waiting customer independently reneges the system after an exponentially distributed amount of time. The items in the inventory have shelf life times that are assumed to follow an exponential distribution. Here we determine the service rates to be employed at each instant of time so that the long run total expected cost rate is minimized. The problem is modelled as a semi-Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically.