Discounted costs and obsolescence with the Joint replenishment problem

Real life inventory lot sizing problems are frequently challenged with the need to order different types of items within same batch. The Joint Replenishment Problem (JRP) addresses this setting coordinated ordering by minimizing total cost, composed (or setup) costs and holding costs, while satisfying demand. complexity problem increases when some or all item prone obsolescence. In fact, may experience an abrupt decline in demand because they no longer needed, due rapid advancements technology, going out fashion, ceasing be economically viable. This article proposes extension where suddenly become obsolete at time future. model assumes constant items’ lifetimes follow independent negative exponential distributions. optimization process considers value money using expected discounted cost as minimization criterion. proposed was applied test cases, sensitivity analyses were performed, assess impact obsolescence on policy. increase risk, through progressive rates types, determines smaller sizes discount rate causes quantities ordered well.