Inventory policies for an assemble-to-order system with joint discount incentives

Abstract

We consider an assemble-to-order system to meet all of the stationary stochastic demand of a finished product in a periodic review setting. The finished product is assembled using two subassemblies (components). The demand must be met either by regular production or by using a faster but more expensive expedited mode. Components have independent setup, production, holding and expediting costs. However when both components fall short of demand they use the same expediting resource (same plane, same supplier channel, same overtime shift in a factory, etc.) causing a joint discount in unit expediting costs. This joint cost factor prevents solving of inventory control problem of each component independently and increases the time and space complexity of solving optimal inventory policy. We analyze models with and without setup costs. We prove that the optimal policy of the model without setup cost is a modified base stock policy, where target inventory for a component is a function of the other component's inventory level, both for a finite and an infinite horizon model. Similarly the optimal policy of the single and two period model with positive setup cost is a modified state dependent (s,S) policy, where (s,S) values of a component is a function of the other component's inventory level. Based on these results we develop an algorithm, which decreases time complexity, for solving finite and infinite horizon models in models without setup-costs optimally and in models with setup costs very close to optimal results.