A Tactical Planning Model for a Job Shop

TLDR

The authors develop a discrete‑time, continuous‑flow model to serve as a tactical planning tool for job shops with stationary input mixes, aiming to evaluate and design control policies that achieve acceptable shop behavior. The model employs a control rule that sets each work center’s production rate as a fixed proportion of its queue level per period, consistent with planned lead times, and is used to assess and optimize control specifications. Using the model, the authors characterize each work center’s operational behavior, producing steady‑state distributions of production levels and queue lengths, and demonstrate its application with a grinding‑machine factory example.

Abstract

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.