Rescheduling on a single machine with part-type dependent setup times and deadlines

Abstract

We consider the problem of rescheduling a facility modeled as a single machine in the face of newly arrived jobs with part-type dependent setup times. The facility contains a number of jobs that have been assigned due dates and scheduled so as to meet them. We wish to insert the new jobs into the existing schedule in a manner that will minimize the disruption of the jobs in the system and minimize the total weighted completion time or the maximum completion time of the new jobs. We provide a polynomial-time algorithm for the maximum completion time problem, prove that the total weighted completion time problem is NP-hard in the strong sense and study several of its special cases. In particular, we show that the case with reverse-agreeable weights (of which the unit weight problem is a special case) can be solved in polynomial time when the number of part types is fixed. We also present two heuristics for the problem with arbitrary weights and develop data-dependent worst-case error bounds. Extensive computational experiments show that the heuristics consistently obtain near-optimal solutions in very reasonable CPU times.