Minimizing total tardiness for the order scheduling problem with sequence-dependent setup times using hybrid matheuristics

This paper aims at presenting a customer order scheduling environment in which the setup times are explicit and depend on the production sequence. The considered objective function is the total tardiness minimization. Since the variant under study is NP-hard, we propose a mixed-integer linear programming (MILP) model, an adaptation of the Order-Scheduling Modified Due-Date heuristic (OMDD) (referred to as Order-Scheduling Modified Due-Date Setup (OMMD-S)), an adaptation of the Framinan and Perez-Gonzalez heuristic (FP) (hereinafter referred to as Framinan and Perez-Gonzalez Setup (FP-S)), a matheuristic with Same Permutation in All Machines (SPAM), and the hybrid matheuristic SPAM-SJPO based on Job-Position Oscillation (JPO). The algorithms under comparison have been compared on an extensive benchmark of randomly generated test instances, considering two performance measures: Relative Deviation Index (RDI) and Success Rate (SR). For the small-size evaluated instances, the SPAM is the most efficient algorithm, presenting the better values of RDI and SR. For the large-size evaluated instances, the hybrid matheuristic SPAM-JPO and MILP model are the most efficient methods.

Customer order scheduling with job-based processing on a single-machine to minimize the total completion time

This study considers a customer order scheduling (COS) problem in which each customer requests a variety of products (jobs) processed on a single flexible machine, such as the computer numerical control (CNC) machine. A sequence-independent setup for the machine is needed before processing each product. All products in a customer order are delivered to the customer when they are processed. The product ordered by a customer and completed as the last product in the order defines the customer order’s completion time. We aim to find the optimal schedule of the customer orders and the products to minimize the customer orders’ total completion time. We have studied this customer order scheduling problem with a job-based processing approach in which the same products from different customer orders form a product lot and are processed successively without being intermingled with other products. We have developed two mixed-integer linear programming models capable of solving the small and medium-sized problem instances optimally and a heuristic algorithm for large-sized problem instances. Our empirical study results show that our proposed tabu search algorithm provides optimal or near-optimal solutions in a very short time. We have also compared the job-based and order-based processing approaches for both setup and no-setup cases and observed that the job-based processing approach yields better results when jobs have setup times.