Using GRASP Approach and Path Relinking to Minimize Total Number of Tardy Jobs on a Single Batch Processing Machine

Abstract

This paper considers the problem of scheduling a single batch processing machine such that the total number of tardy jobs is minimized. The machine can simultaneously process several jobs as a batch as long as the machine capacity is not violated. The batch processing time is equal to the largest processing time among those jobs in the batch. Two decisions are made to schedule jobs on the batch processing machine, namely grouping jobs to form batches and sequencing the batches on the machines. Both the decisions are interdependent as the composition of the batch affects the processing time of the batch. The problem under study is NP-hard. Consequently, solving a mathematical formulation to find an optimal solution is computationally intensive. A Greedy Randomized Adaptive Search Procedure (GRASP) is proposed to solve the problem under study with the assumption of arbitrary job sizes, arbitrary processing times and arbitrary due dates. A novel construction phase for the GRASP approach is proposed to improve the solution quality. In addition, a path relinking procedure is proposed for solving large-sized problems effectively. The performance of the proposed GRASP approach is evaluated by comparing its results to a commercial solver (which was used to solve the mathematical model) and a construction heuristic. Experimental studies suggest that the solution obtained from the GRASP approach is superior compared to the commercial solver and the construction heuristic.