A Mathematical Model for the Periodic Capacitated Arc Routing Problem with Time Windows

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

“…Each vehicle may have a limited capacity and a maximum travel distance (or time). The vehicle fleet can be homogeneous or heterogeneous and time windows may arise, for example, when it is not recommended to perform a service such as waste collection at rush hour [219].…”

“…Benavent et al [30] present a mathematical model and a branch‐and‐cut algorithm for the PRPP‐IS. Other mathematical formulations and exact procedures are proposed in Monroy et al [163], for the PCARP‐IS, Riquelme‐Rodriguez et al [197] for the PCARP with inventory constraints, Laganà et al [135] for the periodic multi‐vehicle ARP, and Thomaz et al [219] for the PARP with time windows.…”

On the periodic hierarchical Chinese postman problem

“…Concurrently, Chu et al (2005) developed an integer formulation for the periodic capacitated arc routing problem and proposed heuristic approaches for its solution. During the following years, a particular attention has been devoted to the introduction of several novel variants of the periodic arc routing problems in order to integrate different modeling features, such as considering the irregularity of the arcs service (Monroy et al 2013), incorporating decisions related to inventory (Riquelme-Rodrı ´guez et al, 2014a and2014b), including the service facilities location along the arcs (Huang and Lin 2014;Riquelme-Rodrı ´guez et al, 2016), considering operational time restrictions (Tirkolaee et al 2018;Thomaz et al 2018) and more recently involving the multi-objective aspect into the optimization model (Tirkolaee et al 2019).…”