Algorithms for job scheduling problems with distinct time windows and general earliness/tardiness penalties

This paper addresses the single machine scheduling problem with distinct time windows and sequence-dependent setup times. The objective is to minimize the total weighted earliness and tardiness. The problem involves determining the job execution sequence and the starting time for each job in the sequence. An implicit enumeration algorithm denoted IE and a general variable neighborhood search algorithm denoted GVNS are proposed to determine the job scheduling. IE is an exact algorithm, whereas GVNS is a heuristic algorithm. In order to define the starting times, an O(n²) idle time insertion algorithm (ITIA) is proposed. IE and GVNS use the ITIA algorithm to determine the starting time for each job. However, the IE algorithm is only valid for instances with sequence-independent setup times, and takes advantage of theoretical results generated for this problem. Computational experiments show that the ITIA algorithm is more efficient than the only other equivalent algorithm found in the literature. The IE algorithm allows the optimal solutions of all instances with up to 15 jobs to be determined within a feasible computational time. For larger instances, GVNS produces better-quality solutions requiring less computational time compared with the other algorithm from the literature.