A Unifying View on Timing Problems and Algorithms

Abstract

Timing problems involve the choice of task execution dates within a predetermined processing sequence, and under various additional constraints or objectives such as time- windows, time-dependent costs and so on. Their efficient solving is particularly critical in branch and bound and neighborhood search methods for vehicle routing, scheduling with idle time, as well as in various applications in network optimization or statistical inference. However, although timing related problems have been studied for many years, research on it suffers from a lack of common consensus, and most knowledge is scattered among operations research and applied mathematics domains. This article aims to introduce a classification for timing problems and features, as well as a unifying multidisciplinary analysis of timing algorithms. In relation to frequent application cases within branching schemes or neighborhood searches, efficient solving of series of similar timing subproblems is also analyzed. A dedicated formalism of re-optimization “by concatenation" is introduced to that extent, leading sometimes to considerable reductions in the computational burden of timing resolution. The knowledge developed through this analysis is valuable for modeling work and algorithmic design, for foremost problems such as rich vehicle routing variants, and many emerging non-regular scheduling applications.