The Minmax Regret Scheduling-Location Problem on Trees with Interval-Data Edge Lengths

Abstract

We address in this paper a variant of the scheduling-location (ScheLoc) problem on tree networks with interval edge lengths where the total deviation of the uncertain data cannot exceed a threshold. We further use the minmax regret concept to deal with the corresponding uncertainty. In order to solve the problem, we investigate the structure of the schedule which leads to the maximum regret value at a fixed point. Then we consider the machine location belonging to a specific edge of the tree and partition the underlying edge into regions with linear maximum regret function. Finally, we develop a combinatorial algorithm that solves the minmax regret ScheLoc problem in polynomial time based on a finite dominating set approach.