Scheduling a single batch-processing machine with disagreeable ready times and due dates

Batch processing is defined as processing several jobs simultaneously. Ikura and Gimple (IG) presented a procedure for optimal scheduling of a single batch processing machine with the objective of minimizing makespan assuming that ready times and due dates of jobs are agreeable (i.e., ri < rj ⩾ di ⩽ dj). In many real world applications, the agreeable property assumption does not hold. Therefore, in this paper, the agreeable property assumption is relaxed and the resulting problem is formulated as a mixed integer nonlinear optimization problem. The optimization problem is solved using a developed Hybrid Genetic Algorithm (HGA). At the heart of this algorithm resides a modified version of the IG procedure used to initialize the population set. The performance of the HGA is evaluated and the results indicate that it is effective in finding feasible solutions.