Predicting the Performance of a Two-Stage Flowshop: Lower Bounds and Heuristics for Single and Bicriteria Measures

Abstract

This study examines the scheduling problem for a two-stage flowshop. All jobs are immediately available for processing and job characteristics including the processing times and due dates are known and certain. The goals of the scheduling problem are (1) to minimize the total flowtime for all jobs, (2) to minimize the total number of tardy jobs, and (3) to minimize both the total flowtime and the total number of tardy jobs simultaneously. Lower bound performances with respect to the total flowtime and the total number of tardy jobs are presented. Subsequently, this study identifies the special structure of schedules with minimum flowtime and minimum number of tardy jobs and develops three sets of heuristics which generate a Pareto set of bicriteria schedules. For each heuristic procedure, there are four options available for schedule generation. In addition, we provide enhancements to a variety of lower bounds with respect to flowtime and number of tardy jobs in a flowshop environment. Proofs and discussions to lower bound results are also included.