Single machine due window assignment and resource allocation scheduling problems with learning and general positional effects

This paper considers single machine scheduling problems which determine the optimal job schedule, due window location and resource allocation simultaneously. The optimized criteria consist of makespan, earliness, tardiness, due window starting time and size, and the allocated resource cost, to conform with just-in-time (JIT) manufacturing. The job's actual processing time is a general function of its position, starting time, and the resource quantity allocated for the job. Specifically, both the linear and convex resource consumption scenarios are considered. In the context of the linear and convex resource consumption, we present four research problems and prove that all of them are polynomially solvable under CON due window (all jobs share a common due window), SLK due window (each job is assigned an individual due window based on a common flow allowance) and DIF due window (each job has a different due window with no restrictions) assignment assumptions, respectively.