Evaluation of scheduling techniques for solving flowshop problems with no intermediate storage

Abstract

The flowshop scheduling problem with no intermediate storage (NIS problem) was studied in this research. This problem, a modification of the classical flowshop scheduling problem, arises when a set of jobs, once started, must be processed with no wait between consecutive machines. By eliminating the need for intermediate storage, reduction of capital investment in work-in-process inventory can be achieved. This approach can be practically applied to a steel mill, in which the metal should be continuously processed in order to maintain high temperature, as well as many other similar processes. To provide insight into selecting an appropriate scheduling technique for solving the NIS problem, six methods were compared in terms of the quality and efficiency of the scheduling solutions they produced. The quality of solution was measured by makespan and the efficiency of solution was measured by the computational time requirements. The six methods examined in this study included: the Gupta algorithm, the Szwarc algorithm, an integer linear programming method, the Campbell et al. algorithm, the Dannenbring rapid access with extensive search algorithm, and a mixed integer linear programming procedure. The problem factors considered in this study were number of jobs, number of machines, and range of processing times. Relatively small-sized problems were tested with up to ten jobs, five machines, and 1–100 processing time units. Six solution techniques were selected and compared, with respect to makespan and computational time requirements, for multiple combinations of the three problem variables. The resulting test data were investigated using graphical procedures and formal statistical analyses. Initially, plots of mean values were used to graphically compare the six solution methods for the two performance criteria. Next, a multivariate analysis of variance study was conducted to investigate the quality and efficiency of the algorithms with respect to the problem factors. Then, a multiple comparison procedure was employed to analyze treatment mean differences among the six solution techniques. Results from the statistical analyses are summarized in this article. It was concluded that the two mathematical programming methods, the integer linear programming procedure and the mixed integer linear programming methods, produced the best performance in terms of makespan. These two methods, however, used a far greater amount of computational time than the other four solution techniques. Producing moderately good results as far as quality of performance, the Gupta and the Szwarc algorithms were comparable with the Campbell et al. and the Dannenbring algorithms in terms of computational efficiency. By comparison, the Campbell et al. and the Dannenbring algorithms produced the poorest performance with respect to the quality of solutions. Certain limitations were imposed for this study. The problem size considered was relatively small and the sample size was also limited to ten problems per cell. In addition, a uniform distribution function was used for generating processing times within certain ranges. These limitations were necessary in order to allow the various scheduling problems to be solved within a reasonable amount of computer time. Finally, some suggestions were provided for future research in the NIS problem area. The integer linear programming method was recommended as a standard of evaluation, owing to its best overall performance. A possible area for future research would involve the improvement of the Gupta and the Szwarc algorithms through the use of backtracking procedures within the branch-and-bound technique, so that they might be competitive with the mathematical programming methods with respect to quality of performance. Other distribution functions could be investigated in terms of the influence of the distribution of processing times on the performance measures.