Customer Order Scheduling on Unrelated Parallel Machines to Minimize Total Completion Time

This paper considers a customer order scheduling problem with product type splitting property in the unrelated parallel machine environment. Product type splitting property refers to the case where each customer order consists of several product types and the workload of all associated product types can be arbitrarily split among machines. The objective is to minimize the total completion time of the orders. Several optimality properties of the general problem are derived. Based on these properties, an easily computable lower bound of the objective function is established. Two important special cases are further explored. Three heuristics are proposed to solve the general problem. It is shown that the worst case performances of all the three heuristics are bounded by simple functions of makespan related measures. Numerical studies are carried out to demonstrate the effectiveness of the lower bound and heuristics. Additional insights are offered by comparison studies focusing on the computational efficiency of the heuristics proposed.