Simple computational methods for the analysis of (s, s) type inventory models

A simple computational method (SCM) to analyze a class of (s, S) type inventory problem is developed. Under this (s, S) policy, (i) the number of units demanded where d = 1, 2… a (£ s) at successive demand epochs form a Markov chain (MC) with one step transition probability matrix (TPM) P and (ii) the replenishments are instantaneous. This method gives the algorithm for computation of stationary probabilities of inventory process, joint probability function of number of transitions and quantities of replenishments per cycle, conditional and unconditional average costs. Illustrative example for a few special cases are provided, which strengthen the applicability of the SCM to practical problems.