A perishable EOQ model subject to distinct demands for conforming and non-conforming items

Abstract

ABSTRACTThis paper presents an Economic Order Quantity model with imperfect quality subject to distinct demands for conforming and non-conforming items where holding cost is a nonlinear function of time an item is held in inventory. We assume that the vendor operates a process that is in statistical control. The purchaser applies a 100% quality inspection policy and accepts all conforming items to satisfy demand in a primary market and rejects all non-conforming items and sends them to a warehouse to satisfy demand in a secondary market. Inspection cost per lot is a linear function of lot size. Shortage costs for the conforming units are assumed to be high. Hence, shortages are not allowed in the primary market while permitted in the secondary market. Non-conforming shortage costs are levied based on the number of units short, irrespective of the duration of shortage. All non-conforming leftover units at the end of each cycle, if any, are sold (or disposed of) for a fixed price (or disposal cost) per non-conforming unit. For the scenario described above, this paper develops explicit expressions for the optimal lot size and optimal total inventory cost incurred by the purchaser in both markets for two separate cases of shortages or excess units of non-conforming items. A simple numerical example is also given.