A Branch-and-Price-and-Cut Algorithm for Resource-Constrained Pickup and Delivery Problems

Abstract

We study a multi-commodity multi-period resource constrained pickup-and-delivery problem inspired by the short-term planning of maintenance services at offshore wind farms. In order to begin a maintenance service, different types of relatively scarce servicemen need to be delivered (transported) to the service locations. We develop resource-exceeding route (RER) inequalities, which are inspired by knapsack cover inequalities, in order to model the scarcity of servicemen. In addition to a traditional separation approach, we present a column-dependent constraints approach so as to include the RER inequalities in the mathematical formulation. An alternative pricing strategy is developed to correctly include the column-dependent constraints. The resulting approach is broadly applicable to any routing problem that involves a set of scarce resources. We present a branch-and-price-and-cut algorithm to compare both approaches that include RER inequalities. The branch-and-price-and-cut algorithm relies on efficiently solving a new variant of the Elementary Resource Constrained Shortest Path Problem, using a tailored pulse algorithm developed specifically to solve it. Computational experiments show that the RER inequalities significantly tighten the root node relaxations. The column-dependent constraints approach searches then the branch and bound tree more effectively and appears to be competitive with the traditional separation procedure. Both approaches are able to solve instances of up to 92 nodes over 21 periods to optimality.

Stochastic inventory routing with time-based shipment consolidation

“…Finally, including these inequalities requires some standard adaptations of our labeling algorithm, because the subset-row inequalities considered in this paper are so-called "non-robust cuts." We have made similar changes to those outlined in, for instance, Costa et al (2019), Schrotenboer et al (2019), and thus introduce new label elements for each included subset-row cut to keep track on the number of visited retailers associated with the cut. This is needed because a variable only enters a subset-row inequality if at least two of the three associated retailers are visited.…”

A Review of Predictive and Prescriptive Offshore Wind Farm Operation and Maintenance

“…The most common areas of research have focused on scheduling of day-to-day maintenance tasks [143][144][145][146] and the routing of maintenance vehicles [138,147,148]. In particular, the uncertainty of weather forecasts make scheduling maintenance for more than a few days ahead difficult.…”

“…They compare this with common policies such as predictive and scheduled and find higher average profit using the reinforcement learning approach. Schrotenboer et al [146] solve a variant of the resource-constrained shortest-path problem to optimise maintenance task scheduling taking into account the relative scarcity of service personnel available.…”

Mixed Integer Programming models for planning maintenance at offshore wind farms under uncertainty

“…The short-term planning of maintenance tasks in offshore wind farms has become increasingly popular among researchers. A series of research articles (Dai et al 2015, Irawan et al 2017, Raknes et al 2017, Schrotenboer et al 2019, 2018 discuss this problem, leading to a branch-andprice-and-cut method for the single wind farm case (Schrotenboer et al 2019), and a metaheuristic approach for the multiple wind farm case (Schrotenboer et al 2018).…”