A New Machine Scheduling Problem with Temperature Loss

This paper considers a new problem of scheduling hot jobs with nonlinear temperature drop curve which is more approximate to the real situation than linear temperature drop curve to minimize the total temperature drop loss. In the problem, all jobs have the same temperature drop curve and different processing times. In this paper, two cases of problems are studied. (1) For the case of jobs without release dates, we prove that the shortest processing time first rule is optimal to the single-machine problem. And we extend the result to the parallel-machine problem. (2) For the case of jobs with release dates, the single-machine problem is strongly NP-hard. And a heuristic, modified shortest processing time first, is proposed to deal with the problem. In order to verify the performance of the heuristic, a lower bound based on release times delaying is presented. Computational results show the effectiveness of the heuristic on a set of random test problems.