Scheduling a Batch Processing Machine in a Just-in-Time Production System Considering a Tight Due Date

The development and complexity of new markets, on the one hand, and economic constraints, on the other hand, have made it an inevitable necessity to pay attention to the two principles of providing a desirable and reliable level of service to customers and reducing supply and maintenance costs. Therefore, the need to study the methods that enable the production system to deal with these issues is felt more than ever. Just-In-Time production strategy has been mentioned as one of the appropriate approaches to balance between the two principles. On the other hand, the issue of sequencing and scheduling of operations in batch processing systems has been widely considered in the last two decades. A batch processing machine can process a batch of jobs simultaneously, which reduces the machine's set-up time and facilitates material flow management. This study aims to minimize the total weighted earliness and tardiness penalties of jobs with non-identical sizes on the batch processing machine, considering that the due date is tight.

Design/methodology/approach:

 Mathematical programming has been used to model the problem. A mixed integer linear programming model has been proposed for the research problem. Since the problem is shown to be NP-hard, heuristic and meta-heuristic methods have been developed to find near-optimal solutions for industrial-sized instances. Also, a dynamic programming approach has been proposed to find the optimal scheduling of a predetermined batch of jobs.

The dynamic programming algorithm requires a high computational effort, and the solution time by this algorithm increases significantly when the number of jobs increases. However, the obtained results indicated that the proposed heuristic algorithms lead to good performance with less time and in practice, such algorithms can be used for real applications and large-size instances. The average relative deviation of the proposed particle swarm algorithm is less than 1%, and the value of this index for the proposed heuristic algorithm is 1.78%.

Research implications:

 Examining the two investigated methods for batching the jobs, one based on a heuristic algorithm and the other with the help of solving a mathematical model, indicated no significant difference between these two methods. Therefore, if necessary, the heuristic algorithm with less computational effort can be used without losing the quality of the solution.Practical implications: According to the findings, developing efficient heuristic and meta-heuristic algorithms for batch processing machine scheduling in just-in-time production systems can reduce production costs.

Originality/value:

 For the first  the heuristic and meta-heuristic algorithms were proposed for the problem of scheduling a batch processing machine considering a tight due date in a just-in-time production system. A dynamic programming approach was also proposed for the first time to find the optimal scheduling of a predetermined batch of jobs.