EOQ model with defective products, batch shipment and partial backorders

The existing literature on the economic order quantity (EOQ) problem with backordering does not address the impact of batch shipments on backordering behavior in a business to customer (B2C) environment. This study develops inventory models for a retailer receiving batch shipments and managing inventory through backorders. In this scenario, a large quantity of items is received, some of which are found to be defective. To identify defective items, the retailer conducts a 100% inspection of the goods received. Once inspected, the saleable products are added to the warehouse inventory in batches, rather than individually. The retailer follows a policy of receiving equal-sized batches at regular time intervals, deciding on the number of batches, as well as the ordering and backordering quantities. The analysis explores two approaches for handling defective products, incorporating time-proportioning for the backordering cost and a penalty cost for each lost unit. The classical optimization technique is applied to determine the optimal policy. A numerical example demonstrates the theory, with results showing that partial recovery of customer loyalty and product repair are more profitable approaches.