Simultaneous Determination of Lot Sizes and Routing Mix in Job Shops

Flexibility and versatility of batch production job shops has increased in the last 25 years through the use of multi-purpose numerically controlled (NC) machine tools; these computer controlled machines can perform a wide variety of different operations. In recent years, even greater flexibility has been achieved by flexible manufacturing systems, where groups of NC machines are linked by automated material handling devices and controlled by computer. In such shops, a batch of product may have several possible alternative routes that it may follow through the shop. A number of researchers have shown that determining the proper mix of routes for each product can have a significant effect on shop throughput and work-in-process inventory. Other researchers have found that the lot sizing decision also affects these performance measures. The primary thrust of this paper is to develop a model to explore the interaction between routing and lot sizing decisions in a multi-machine, multi-work center job shop. A heuristic is developed for simultaneously determining lot sizes and routing mix in problems of practical size, and numerical examples are provided in order to illustrate the solution method. The examples show that there can be considerable potential for performance improvement by simultaneous consideration of routing and lot sizing.