An Inventory Problem with Two Randomly Available Suppliers

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 Es1[Es2]/G1[G2] 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 E2[E2]/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.

Disruption‐management strategies for short life‐cycle products

“…To the best of our knowledge, [13,19], and [25] are the only disruption papers that consider multiple suppliers. Long-run average cost expressions for an economic-order-quantity (EOQ) problem with two identical (cost and reliability) suppliers are developed in [19] and [13]. A firm with two suppliers, one subject to disruptions and the other perfectly reliable, but more expensive and capacity-constrained, is studied in [25].…”

“…The marginal expected values of epoch-3 inventories 13 are given by 13 One can prove that E X [π(z, X)] is jointly concave in z and that, therefore, it is optimal to split the order (equally among both suppliers) in the common dual source structure. …”

A tight approximation for an EOQ model with supply disruptions

“…The suppliers are non-identical with respect to reliability but identical with respect to price, so as long as at least one supplier is active, the retailer does not care which one it orders from. Gürler and Parlar (1997) generalize the two-supplier model by allowing more general failure and repair processes. They present asymptotic results for large order quantities.…”

Inventory and pricing decisions in a single-period problem involving risky supply

“…Papers in this category include models in which supply uncertainty is specified as random capacity (Erdem et al, 2006), all-or-none supply availability (Dada et al, 2007;Babich et al, 2007), on and off times with random durations (Gurler and Parlar, 1997), and random yield (Agrawal and Nahmias, 1997;Yang et al, 2007). Minner (2003) reviews the research in multiple-supplier inventory models.…”