Effective league championship algorithm and lower bound procedure for scheduling a single batch-processing machine with non-identical job sizes and job rejection

We address the scheduling problem of a set of non-identical size jobs on a single batch-processing machine (SBPM) wherein the scheduler can make decision whether to schedule a job in batches or not to schedule it with a job-dependent penalty. The processing time of a batch is the greatest job processing time in that batch (parallel batching or p-batching). The scheduler wants to minimize a given objective function f, where f is the total rejection penalties of the rejected jobs (rejection cost) plus the makespan of the scheduled ones. We formulate the aforementioned problem as a 0-1 mixed integer programming model. We also apply an effective dynamic programming algorithm (DPA) to calculate a lower bound (LB) on the optimal cost of the problem. To tackle the problem, we propose a grouping algorithm, based on league championship algorithm (LCA), with new updating equations maintaining the major characteristics of the original updating equations of the LCA and well-suited to the structure of the problem. For small problems, performance of the proposed LCA is compared with GAMS/CPLEX solver. For large-scale instances, a genetic algorithm is adopted as a basis for comparison. Simulated experiments confirm the performance of the proposed methods.