parallel-machine scheduling

Nowadays, in production environments where the production system is parallel machines, the reliability of the machines is important and the uncertainty of scheduling parameters is common. In this paper, unrelated parallel machine scheduling problem using a fuzzy approach with machines maintenance activities and process constraints is of concern. An important application of this problem is in the production of products that the due dates are defined as a time window and the best due date is close to the middle of the time window and the jobs processing times depend on other factors such as operator and their value is not specified and are announced as interval under uncertainty. In this study, first, a fuzzy mathematical model is proposed in which changing between a fuzzy approach and a deterministic model is described. Then, since the problem is NP-hard, a fuzzy-based genetic algorithm to solve large instances is developed. In this algorithm, a greedy decoding approach according to fuzzy parameters is developed. Numerical experiments are used to evaluate the performance of the developed algorithm. It is concluded that the proposed algorithm shows great performance in large instances and is superior to the proposed mathematical model in small instances too.

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.