Optimizing batch-processing operations with batch-position-based learning effects

Abstract

Motivated by applications in porcelain-making companies, we consider a type of optimization problems for batch-processing operations. In production, a single batch-processing machine with a fixed capacity is used to process jobs. Several jobs can be processed together if their total size is no more than the machine capacity. Batch-position-based learning effects are considered because workers become skillful gradually after they perform the processing task repeatedly. The actual processing time of a batch is a decreasing function of its position in production. The objective is to minimize makespan and we consider three different problems. In the first problem, jobs have identical sizes and we present an algorithm which can find optimal solutions in polynomial time. In the second problem, jobs have identical processing times and we show the problem is NP-hard in the strong sense. We propose an approximation algorithm with an absolute performance guarantee of 1.5 and asymptotic performance guarantee of 1.223. In the third problem, jobs have non-identical sizes and processing times simultaneously. We propose an algorithm with an absolute and asymptotic performance guarantee of 2. Besides, we present the evolution of the performance guarantee and provide managerial insights for decision makers of manufacturing companies.