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 nphard, thus the under investigation problem, which is more complicated, is np-hard too. in this study, a mixedinteger 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.