The Batch Loading and Scheduling Problem

This paper discusses a problem that commonly occurs in the batching and schedulingof certainkinds of batch processors. Examplesof these processors include heat treatment facilities, particularly in the steeland ceramicindustries as well as a varietyof operations in the manufacture of integratedcircuits. There are a set of jobs waiting to be processed. The processing time for a batchdependsonly on the family and not on the number or the volume of jobs in the batch. Each job is associated with a given family. The schedule must organize jobs into batches where each batchconsists of jobs from a single family. The batchesmust be sequencedon the facility. Each job has a weight or delay cost and a volume. The facility can handle a set of jobs from the same family as a batchonly if, the total volume of thejobs is less than the capacityof the facility and all the jobs belong to the samefamily. The objective is minimizing themean weightedflow time. The paper presents an integer programming formulation for this problem. A partial LP relaxation provides a lower bound. In addition, we present several heuristics based on various subproblems. These include a greedy heuristic, a successive knapsack heuristicand a generalized assignment heuristic. The conclusions of the computational study show that the successive knapsack and generalized assignment heuristic perform better than the greedy. The generalized assignment heuristic does slightly better than the successive knapsackheuristic but is substantially slower. The study also shows that the size of the job relative to the capacity of the facility affects the performance of the heuristics. Finally a worst-case analysis of the greedy heuristic is presented.