A Heuristic Algorithm for Sequencing on One Machine to Minimize Total Tardiness

Abstract

The problem of minimizing total tardiness assumes that the N jobs to be processed on a single machine are simultaneously available at time zero. Since due dates and sequence-independent processing times are known, the problem is to determine a processing sequence, from the N! possible sequences, which minimizes the sum of tardiness for all the jobs in the set. The powerful dominance theorems of Emmons are exploited with a new heuristic procedure, avoiding enumeration of all possible sequences. For large problems, often any one of many jobs can be processed first with no change in total tardiness; however, the set of jobs which can occupy the last position in an optimal sequence is much more limited, and easily identified by application of special dominance properties. The heuristic uses Net Benefit of Relocation (NBR) analysis to determine which job should come last to reduce total tardiness. The simplicity of the algorithm enables manual solutions to small problems. Experimentation indicates that the NBR heuristic offers vast improvement over the adjacent pairwise interchange (API) heuristic of Fry et al., both in solution quality and computational effort. The NBR heuristic also performs well compared with the optimizing routine of Potts and Van Wassenhove, especially in the case of large problems where a modest growth in total tardiness is accompanied by drastically reduced computer requirements.