An Inventory Problem with Two Randomly Available Suppliers

Ülkü Gürler and Mahmut Parlar
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Ülkü Gürler: Bilkent University, Bilkent/Ankara, Turkey
Mahmut Parlar: McMaster University, Hamilton, Ontario, Canada

Operations Research, 1997, vol. 45, issue 6, 904-918

Abstract: This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is modeled 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 general distribution. In analogy with queuing notation, we call this an E s 1 [ E s 2 ]/ G 1 [ G 2 ] system. Since the resulting stochastic process is non-Markovian, we employ the “method of stages” to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition functions for the semi-Markov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detailed numerical example is presented for the E 2 [ E 2 ]/ M [ M ] case. Analytic solutions are obtained for the particular case of “large” (asymptotic) order quantity, in which case the objective function assumes a very simple form that can be used to analyze the optimality conditions. The paper concludes with the discussion of an alternative inventory policy for modeling the random supply availability problem.

Keywords: inventory/production; supplier uncertainty; probability; stochastic model applications (search for similar items in EconPapers)
Date: 1997
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