An updated annotated bibliography on arc routing problems

Abstract

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post‐disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 144–194 2017

Arc routing problems: A review of the past, present, and future

“…Beyond the type of underlying graph (undirected, directed, mixed, or windy), if the problem is a single or a multivehicle problem, and so on, the classification of ARPs with profits depends on the objective function pursued [20,167]:…”

The mixed capacitated general routing problem with time‐dependent demands

“…In this study a stepwise linear function is used, because in the real life application with the available data, we have a prediction model for each hour [2]. The demand constraints (6) being non-linear, we introduce new binary variables hk ij , hk i in order to replace these constraints by the linear constraints (30)(31)(32)(33)(34)(35)(36)(37)(38). MIN h ij and MAX h ij represent respectively the minimum time value and the maximum time value of period h. Figure 1 illustrates this linearization with an example.…”

“…Constraints (30) are a linear version of (6). Constraints (31) and (32) and (35) and (36) ensure that the serving time is in the right period. Constraints (33) and (37) imply that each required element is served at one unique period.…”

“…In particular, time‐dependent vehicle routing problems have been widely studied in the literature with different variants of time dependency: service time (e.g., Malandraki and Daskin [29], Ichoua et al [21], Donati et al [18]), time windows (e.g., Dabia et al [16], Jung and Haghani [23], Balseiro et al [6], Adamo et al [1], Cacchiani et al [12]), demand (e.g., Victoria et al [46]). For more details we refer the reader to Mourão and Pinto [31] and Gendreau et al [20].…”

Drone arc routing problems

“…The CARP aims to find a set of minimum cost routes that jointly cover all the required edges while each particular route satisfies the capacity of the vehicle. For a comprehensive treatment of this area, see the books edited by Dror and by Corberán and Laporte , as well as the recent annotated bibliography by Mourão and Pinto .…”