Timing problems and algorithms: Time decisions for sequences of activities

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, or flexible processing times, among others. Their efficient resolution is critical in branch and bound and neighborhood search methods for vehicle routing, project and machine scheduling, as well as in various applications in network optimization, resource allocation, and statistical inference. Timing-related problems have been studied for years, yet research on this subject suffers from a lack of consensus, and most knowledge is scattered among operations research and applied mathematics domains. This article introduces a classification of 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, the efficient resolution of series of similar timing subproblems is also analyzed. A dedicated formalism of reoptimization "by concatenation" is introduced to that extent. The knowledge developed through this analysis is valuable for modeling and algorithmic design, for a wide range of combinatorial optimization problems with time characteristics, including rich vehicle routing settings and emerging nonregular scheduling applications, among others.

An integrative cooperative search framework for multi-decision-attribute combinatorial optimization: Application to the MDPVRP

“…Such problem extensions might thus require a more involved algorithmic component (Vidal, Crainic, Gendreau, & Prins, 2015, but does not change fundamentally the nature of the problem. Adding more decision sets to the problem, on the other hand, makes it significantly harder to address and, thus, the general approach when addressing such multi-attribute problems is to either simplify them, or to sequentially solve a series of particular cases, where part of the overall problem is fixed or ignored, or both (e.g., Golden et al, 2002;Hadjiconstantinou & Baldacci, 1998;Hartl et al, 2006;Homberger & Gehring, 1999.…”

A concise guide to existing and emerging vehicle routing problem variants

“…Time constraints. A wide range of VRP variants arising from the addition of time restrictions were surveyed in Vidal et al (2015). Time constraints can arise as customer-or self-imposed time windows for deliveries (Solomon 1987, Agatz et al 2011, Bruck et al 2018).…”

Heuristics for vehicle routing problems: Sequence or set optimization?

“…We use the concatenation strategy of Vidal et al (2014aVidal et al ( , 2015b to perform efficient cost-and load-feasibility evaluations. This strategy exploits the fact that any route obtained from a classical move φ(x t ) on an incumbent solution x t corresponds to a recombination of a bounded number of (customer and depot) visit sequences of x t .…”