AN INVENTORY PROBLEM WITH 2 RANDOMLY AVAILABLE SUPPLIERS

This paper considers a stochastic inventory model in which supply avai lability is subject to random fluctuations that may arise due to machi ne breakdowns, strikes, embargoes, etc. It is assumed that the invento ry manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is mode led as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a gene ral distribution. In analogy with queuing notation, we call this an E- s1[E-s2]/G(1)[G(2)] system. Since the resulting stochastic process is non-Markovian, we employ the ''method of stages'' to transform the pro cess into a Markovian one, albeit at the cost of enlarging the state s pace. We identify the regenerative cycles of the inventory level proce ss and use the renewal reward theorem to form the long-run average cos t objective function. Finite time transition functions for the semi-Ma rkov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detail ed numerical example is presented for the E-2[E-2]/M[M] case. Analytic solutions are obtained for the particular case of ''large'' (asymptot ic) order quantity, in which case the objective function assumes a ver y simple form that can be used to analyze the optimality conditions. T he paper concludes with the discussion of an alternative inventory pol icy for modeling the random supply availability problem.