Analytical determination of optimal TWK due-dates in a job shop

Abstract

The paper studies the operating characteristics of the total-work-content (TWK) due-date assignment method in a dynamic job shop. The due-date for each job is established by adding a multiple of the job's total processing-time to its arrival time at the shop. It is assumed that there will be penalty costs if the shop quotes excessively long due-dates compared with its competitors' and cannot complete the jobs exactly on their assigned due-dates. A cost model composed of these two opportunity cost components is used. The objective is to find the optimal processing-time multiple k ^∗ _p that will minimize the expected total cost per job. An analytical procedure is presented to derive the optimal solution and to show that k ^∗ _p is a unique absolute minimum point of the strictly convex cost functions included in the cost model. It is also shown that determination of the optimal processing-time multiple requires only information readily accessible in the shop. Under certain circumstances, k ^∗ _p can even be exclusively expressed in terms of the shop parameters, such as the number of machines in the shop, mean job arrival rate and processing-time. Moreover, the cost model is general since no specific distributions about the underlying random processes are assumed. As a result the model can be applied to an actual job shop situation and derivation of the optimal processing-time multiple becomes a simple process that can easily be implemented.