Open shop scheduling with makespan and total completion time criteria

Abstract

In this paper we study the two machine open shop scheduling problem with a hierarchical objective: minimize the total completion time subject to minimum makespan. We show that this problem is distinct from the closely related problem of minimizing the total completion time. We develop polynomial-time algorithms for three special cases and an asymptotically optimal polynomial-time heuristic when a machine is dominant. We also extend some of our results to the three machine open shop case. Scope and purpose Hierarchical scheduling objectives are common in many production environments. When there is no predetermined order of job operations, the resulting scheduling problem is an open shop. The main criterion associated with open shop scheduling problems is the minimization of the maximum job completion time (makespan). In a hierarchical environment, we are then interested in minimizing individual job completion times. The objective of this paper is to derive algorithms for minimizing the sum of job completion times subject to minimum makespan for various two machine and three machine open shop problems.