Minimizing Total Weighted Tardiness on Single Batch Process Machine with Incompatible Job Families

Abstract

The focus of this research is minimization of the total weighted tardiness on a single batch-processing machine with incompatible job families, a problem very pertinent to scheduling semiconductor wafer fabrication facilities, especially in the diffusion process. Ideally, we would like to form the batches and schedule them simultaneously, but since this problem is NP-hard, the problem is decomposed into two sub-problems: forming the batches, which includes initial assignment of jobs to batches and modifying the batches after they have been sequenced; and sequencing the batches. After assigning the batches to the jobs initially, the two procedures are employed iteratively on these subproblems until no improvement in the solution is obtained. A good solution can be obtained by this procedure. The best sequencing of the batches is obtained by using dynamic programming, but a decomposition heuristic based on it yields a good solution in a reasonable amount of time. The batches are modified using a swapping algorithm, which moves jobs between batches.

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corresponding author