A Transfer Line Design Problem with Setup Times and Costs

Abstract

A paced transfer line has to be designed for the mass production of parts of several types. Each part requires a specific set of operations. The superset of all required operations has to be distributed between stations of the line. No operation re-distribution is allowed when switching between types. A station is set up if at least one operation is executed on it. This incurs setup time and cost. Each operation has a size and a processing time. Operations on the same part assigned to the same station are performed sequentially. Precedence relations are given on the superset of all operations. There are upper bounds on the total size of operations assigned to the same station and on the total setup and operation processing time for a part on the same station for all types. The primary objective is to minimize the number of stations and the secondary objective is to minimize the total setup cost. We establish computational complexity of various special cases and present heuristics and integer linear programming formulations.