An Integrated Markovian Queueing-Inventory Model in a Single Retailer- Single Supplier Problem with Imperfect Quality and Destructive Testing Acceptance Sampling

This paper proposes a retailer-supplier queueing-inventory problem (RSQIP) in which the imperfect lots are investigated using a single sampling inspection plan. We integrate an M/M/m response queueing system for handling and responding to customers’ demands with a classical retailer-supplier inventory model considering defective items and inspection process for the first time. Customers whose demand is met leave the retailer system with exactly one item unless the inventory shortage occurs. The retailer places an order once the inventory level reaches an economic reorder point. The lead time is assumed exponential, and due to the imperfect incoming items, the retailer conducts a destructive acceptance sampling plan. The rate of inspection depends on the sample size. Provided that a lot is rejected, the supplier is required to provide a defect-free shipment. We present the stationary distribution of the number of demands in the response system. Then the joint stationary distribution of the order status and inventory level of the retailer is derived. Several performance measures and the expected total cost are presented steady-state, and a non-linear integer programming model is proposed to minimize the expected total cost. The results are numerically illustrated and reveal the convexity of the expected total cost. The optimal reorder point, order quantity, and the number of servers is computed for some numerical examples. A comprehensive sensitivity analysis is conducted to examine the effect of defective items, response system, and some important parameters on the entire developed model. Finally, useful managerial insights are presented.