Towards robustness of response times: minimising the maximum inter-completion time on parallel machines

Motivated by scheduling practices that require a response to unplanned high-priority jobs as soon as possible without preempting any in-processing jobs, this paper considers a deterministic identical parallel machine scheduling problem to achieve robustness with regard to a worst-case response time. To the best of our knowledge, this paper is the first to study the objective of minimising the maximum inter-completion time, i.e. the maximum time difference between any two consecutive completion times of jobs. For this novel scheduling problem, we first show its NP-hardness, and then propose an integer linear programming formulation and three heuristic approaches. Numerical experiments demonstrate the efficiency of our solution methods.