EOQ with independent endogenous supply disruptions

Abstract

We consider an inventory installation, controlled by the periodic review base stock (S, T) policy and facing a fixed-rate deterministic demand which, if unsatisfied, is backordered. The supply process is unreliable, so supply deliveries may fail according to an independent Bernoulli process; we refer to such failures reflecting the supply service quality and being internal to the supply chain, as endogenous disruptions. We seek to jointly determine the two policy variables, so to minimize long-run average cost. While an approximate model for this problem was recently analyzed, we present an exact analysis, valid for two common accounting schemes for inventory cost evaluation: continuous and end-of-cycle costing. After developing a unified (and exact) average cost model for both costing schemes, the cost for each scheme is analyzed. In both cases, the optimal policy variables and cost prevail in closed-form, having an identical structure to those of EOQ (with backorders). In fact, under continuous costing, the optimal solution reduces to EOQ for perfect supply. Analytical properties, demonstrating the impact of deteriorating supply quality on the optimal policy, are established. Moreover, computations reveal the cost impact of deploying heuristics that either ignore supply disruptions or rely on inaccurate costing information.