Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements

We study an inventory control problem with two storage facilities: a primary warehouse (PW) of limited capacity M, and a subsidiary one (SW) of sufficiently large capacity. Two types of customers are considered: individual customers arriving at (positive and negative) linear rates governed by a Markov chain, and retailers arriving according to a Markov arrival process and bringing a (positive and negative) random number of items. The PW is managed according to a triple-parameter band policy (Formula presented.) (Formula presented.) under a lost sales assumption. Under this policy, as soon as the stock level at the PW falls below s, a refilling to S is performed by a distributor after a random lead-time. However, if the stock exceeds level S when the distributor arrives, no refilling is carried out, and only maintenance services are performed. Items that exceed level M are transferred to the SW at a negligible amount of time for those used in related products. Our cost structure includes a fixed order cost, a variable cost for each item supplied by the distributor, a cost for the additional maintenance, a salvage payment for each transferred item from the PW to the SW, and a loss cost for each unsatisfied item due to demands. We seek to determine the optimal thresholds that minimize the expected overall cost under the discounted criterion. Applying first-passage time results, we present a simple set of equations that provide managers with a useful and an efficient tool to derive the optimal thresholds. Sensitivity analysis and fruitful conclusions along with future scope of research directions are provided.