Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in a multi-layer ceramic capacitor production line, we study a scheduling problem of batch processing machine in which a number of jobs are processed simultaneously as a batch. The performance measures considered include makespan, total completion time, and total weighted completion time. We first present a new simple integer programming formulation for the problem, and using this formulation, one can easily find the optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is very large, we propose a number of heuristic algorithms and design a hybrid genetic algorithm to solve practical big-size problems in a reasonable computational time. To verify performance of the algorithms, we compare them with lower bounds for the problems. From the results of these computational experiments the heuristic algorithms including the genetic algorithm show different performances for the three problems.