A Tactical Planning Model for a Job Shop

We propose and develop a discrete-time, continuous-flow model for studying the operation of a job shop that sees a stationary input mix of job types. We are not concerned with issues of detailed scheduling, but rather hope to develop a tactical planning tool for a job-shop operation. With the model, we are able to characterize the operational behavior of each work center in the job shop for a given control policy. The control rule sets the production rate at a work center as a fixed proportion of its queue level in each time period, and is consistent with the assignment of a planned lead time to each work center. For these control rules, the model gives the steady-state distribution of the production levels at each work center, as well as the distribution of queue lengths. We show how to use the model not only to evaluate a choice of the controls but also to find a good specification that results in acceptable shop behavior. An example for a factory that produces grinding machines illustrates the use of the model.