Exact and heuristic algorithms for the just-in-time scheduling problem in a batch processing system

•A just-in-time scheduling problem on a batch processing machine is considered.•A mixed integer linear programming model is developed.•A DP algorithm to find the optimal schedule for a given set of batches is presented.•Several heuristics, a lower bounding method, and a B&B algorithm are proposed. Batch processing systems are commonly used in many different environments such as chemical and semiconductor industries. In this research, a just-in-time scheduling problem in a batch processing system is investigated. Minimization of total earliness and tardiness of the jobs with respect to a common due date is considered as the objective function. First, the research problem is formulated as a mixed integer linear programming model. Then, to find the optimal schedule for a predetermined set of batches, a dynamic programming algorithm is proposed. Based on the proposed dynamic programming algorithm, several heuristics are also developed. A lower bounding method is presented, and then a branch and bound algorithm is proposed to solve the problem optimally. To demonstrate the performance of the proposed algorithms, several computational experiments are conducted.