Solving coupled task assignment and capacity planning problems for a job shop by using a concurrent genetic algorithm

Abstract

The problems of task assignment and capacity planning of manufacturing systems have been researched for many years. However, in the existing literature, these two types of problems are researched independently. Namely, when solving the task assignment problem, it is usually assumed that the production capacity of the manufacturing systems has been determined. On the other hand, when solving the capacity planning problem, the production tasks assigned to the workstations in the manufacturing system have also been determined. Actually, the task assignment problem and the capacity planning problem are coupled with each other. When we assign production tasks to workstations, production capacities of these workstations should be regulated so that they are enough for completing the tasks. At the same time, when planning the production capacity, we must know what production tasks are assigned to what workstations. This research focuses on the coupling relations between the two problems for a closed job shop, in which the total work-in-process (WIP) is assumed to be constant. The objective of the task assignment problem is to balance the workloads of the workstations and the objectives of the capacity planning problem are maximising the throughput and minimising total costs of machine purchasing and WIP inventory. We construct the fundamental system architecture for controlling the two coupled optimisation processes, and propose a concurrent genetic algorithm (CGA) to solve the two coupled optimisation problems. The influences of the decision variables of one problem on the objective function of the other problem are taken into consideration when the fitness functions of the CGA are constructed. Numerical experiments are done to verify the effectiveness of the algorithm.

Keywords:

• job shop
• task assignment
• capacity planning
• closed Jackson queueing networks
• coupled optimisation problems
• concurrent genetic algorithm

Acknowledgements

This research is partially supported by the National Natural Science Foundation of China under grant 50505006, and by the Financial Support Project for the Teaching of Research of the Young Faculty Members of Southeast University.