Minimizing range of job completion times with general position-dependent processing times and job-rejection

We study the scheduling measure of minimum range of job completion times, i.e., the difference between the minimal and the maximal completion times. This measure is relevant, e.g., when the pricing of deliveries to customers is a function of the delivery time interval. We extend this problem by (i) assuming general position-dependent job processing times (implying that the well-known settings of job-deterioration and learning effect are special cases), and (ii) allowing job rejection (when the scheduler may process only a subset of the jobs and is penalized for each of the rejected jobs). For the problem of minimizing range plus total rejection cost, a polynomial-time solution algorithm based on non-standard sequential solution of linear assignment problems is introduced. When an upper bound on the total permitted rejection cost is assumed and the objective function is minimum range, the problem becomes NP-hard, and an efficient pseudo-polynomial dynamic programming algorithm is introduced and tested numerically.