Algorithms for Minimizing Resource Consumption Over Multiple Machines With a Common Due Window

Scheduling on multiple machines has attracted considerable attention recently. However, most of traditional studies focused only on commercial cost and customer satisfaction. In fact, we are able to alleviate environmental damages via proper scheduling. This study explores a multi-machine scheduling problem with a due window. The objective is to minimize the total cost (including environmental cost). We develop a branch-and-bound algorithm (B&B) and two complementary lower bounds for optimally solving the problem when n <; 16. Moreover, we propose an imperialist competitive algorithm (ICA) to obtain near-optimal schedules for large problem instances. Experimental results are provided to show the performance of the proposed algorithms.