Allocating work in process in a multiple-product CONWIP system with lost sales

To operate a multiple-product manufacturing system under a constant-work-in-progress control policy, one must decide how to assign kanbans to products. With a fixed total number of kanbans in a competitive environment, the goal is to determine their allocation to product types in order to minimize lost sales equitably. In particular, we consider systems in which the products may make multiple visits to the same station with a different processing time distribution on each repeat visit. With a fixed number of kanbans dedicated to each product, the system is modeled as a multiple-chain multiple-class closed queuing network. A nonlinear program simultaneously provides an approximate performance evaluation and optimizes the allocation of kanbans to product types. In numerical examples, the allocations identified are similar to those obtained by exhaustive enumeration with simulation, but frequently differ significantly from a naïve allocation according to demand rates. A variant of the model that minimizes the total work-in-process to achieve specified throughput targets yields results similar to a previous heuristic method.