Setting Basestock Levels in Multi-product Systems with Setups and Random Yield

This paper provides procedures for setting optimal, or near-optimal, basestock levels in a multi-product system with setups and random yield. The procedures are derived using a novel polling system model of the system that contains both queues for production orders and queues for temporary storage of rework orders with routing occurring between these two types of queues. Both systems with backlogging and lost sales are analyzed using existing work on polling models with routing and possibly finite buffers. For a system with backlogging, we provide a cost function that is minimized by solving a set of single-item newsvendor problems. In systems with lost sales, each queue is given a finite buffer equal to the basestock level and excess demand is lost. We provide a cost function and show that finding optimal solutions for large problems is not tractable; thus, we provide a heuristic for finding the basestock levels and demonstrate the effectiveness of the heuristic and accuracy of the cost approximation through numerical tests