Exact and matheuristic methods for the parallel machine scheduling and location problem with delivery time and due date

The scheduling and location (ScheLoc) problem is a new and important research topic with a wide range of practical applications. It jointly optimizes machine locations, job assignments, and sequence decisions to yield a globally optimal solution. Current studies on the ScheLoc problem are limited, and most have focused on makespan minimization. This paper investigates a new variant of the parallel-machine ScheLoc problem with job delivery time and due date considerations. This is motivated by practical situations where jobs must be transported back to their original locations upon completion of processing, and a specific due date is associated with each job. The objective is to minimize the total weighted sum of location, transportation, and tardiness penalty costs incurred if a job is delivered after its due date. We propose three models adapted from classic ones for scheduling problems. We then develop an exact logic-based Benders decomposition method, which decomposes the problem into a master problem (MP) for determining machine locations and job assignments, and a subproblem (SP) for determining job sequences on each machine. The MP is augmented by dynamically adding optimality cuts generated by solving the SP. We also develop a matheuristic (MH) and its variant to achieve near-optimal solutions. An approximate model with predetermined job processing sequences on each machine is formulated and solved to determine the machine locations and job assignments. The obtained solutions are further improved by solving a series of single-machine scheduling problems. The variant combines a kernel search framework to make MH more efficient. Computational experiments on 720 randomly generated instances show the effectiveness and efficiency of both the exact and matheuristic methods.