A Hybrid Forward/backward Approach for Single Batch Scheduling Problems with Non-identical Job Sizes

This paper considers the single batch scheduling problem with different release times and non-identical job sizes and the objective is to minimize the makespan. A mixed integer programming (MIP) model is developed to describe the complexity of the problem and then a hybrid forward/backward algorithm (HFBA) is developed by moving blocks within an initial schedule to improve the solution quality. Changing the initial schedule at each iteration, HFBA could decrease the influence of the initial schedule and reach the best solution efficiently in the final runs. Extensive experiments show that HFBA can obtain optimal solutions for small-job instances, and have good performances on solution quality for large instances with a modest CPU times.