Design of a Hybrid Genetic Algorithm for Parallel Machines Scheduling to Minimize Job Tardiness and Machine Deteriorating Costs with Deteriorating Jobs in a Batched Delivery System

This paper studies the parallel machine scheduling problem subject to machine and job deterioration in a batched delivery system. By the machine deterioration effect, we mean that each machine deteriorates over time, at a different rate. Moreover, job processing times are increasing functions of their starting times and follow a simple linear deterioration. The objective functions are minimizing total tardiness, delivery, holding and machine deteriorating costs. The problem of total tardiness on identical parallel machines is NP-hard, thus the under investigation problem, which is more complicated, is NP-hard too. In this study, a mixed-integer programming (MILP) model is presented and an efficient hybrid genetic algorithm (HGA) is proposed to solve the concerned problem. A new crossover and mutation operator and a heuristic algorithm have also been proposed depending on the type of problem. In order to evaluate the performance of the proposed model and solution procedure, a set of small to large test problems are generated and results are discussed. The related results show the effectiveness of the proposed model and GA for test problems.