ABSTRACT Advancements in computer hardware and commercial software have enabled the use of branch‐and‐cut (BC) methodologies to address medium‐scale vehicle routing problems (VRPs). Despite the introduction of efficient heuristics in the literature, tailoring these approaches to suit various VRP variants, such as the electric vehicle routing problem with time windows (EVRPTW), remains a difficult task. EVRPTW is an extension of the classic VRP with time windows in which internal combustion engine vehicles are replaced by electric vehicles. In this study, we develop a POPMUSIC matheuristic to solve the EVRPTW that relies solely on BC (termed BC‐POPMUSIC), and can be implemented using commercial optimisation software such as Gurobi. We introduce new battery infeasibility inequalities, along with capacity cuts, reachability cuts, ‐path cuts and polar cuts, and incorporate them into Gurobi to tighten the linear programming (LP) relaxation of the mixed integer linear program (MILP) model. Through extensive experiments, we show that this tightening can improve the quality of solutions. Since the EVRPTW requires visits to recharging stations when the battery is depleted, we propose an improvement heuristic to efficiently manage these recharging stops. We demonstrate the effectiveness of BC‐POPMUSIC on known benchmark instances of EVRPTW and compare it with state‐of‐the‐art exact solutions. Our result shows that the approach achieves comparable or better performance, especially on larger problems. In addition, we present new best known solutions for several benchmark instances.
ABSTRACT This paper addresses a vehicle routing problem with synchronization constraints, in which pickup‐and‐delivery requests for single items are carried out using two types of vehicles: active and passive. The vehicles operate jointly, as passive vehicles, which are capacitated trailers, require active vehicles, which are autonomous trucks without stowing capacity, for repositioning. The problem features flexible transportation practices that allow active and passive vehicles to be coupled and decoupled at any pickup or delivery location, as well as the transshipment of items. This active‐passive vehicle routing problem with item transshipments (APVRPIT) involves interdependent precedence constraints: spatial dependencies between passive vehicles arising from item transshipments propagate to active vehicles, and exchanges of passive vehicles between active vehicles create further movement dependencies. This previously unexplored routing problem arises in steel plant logistics. We propose a metaheuristic algorithm based on a variant of the large neighborhood search (LNS), called nested‐LNS, and we evaluate its performance using test instances that replicate real‐world data. Since the APVRPIT generalizes the established active‐passive vehicle routing problem (APVRP), we demonstrate that the nested‐LNS algorithm attains new best results on several APVRP benchmark instances, outperforming state‐of‐the‐art APVRP methods.
ABSTRACT Rising food insecurity is a pressing global concern. Many developing countries rely on a combination of international trade and food aid to satisfy the nutritional and caloric demands of their populations. Trade openness has been shown to have positive long‐term effects on food security; however, it can cause short‐term crises in food availability and affordability. Strategic grain reserves are among the tools governments use to control food prices and ensure availability while maintaining trade openness. This paper constructs a multicommodity trade network equilibrium model with mixed demand to examine the implications of strategic grain reserves for food security. The model incorporates fixed and elastic demand components, representing commodities held in reserves and those entering markets through trade, respectively. The equilibrium conditions are stated, and alternative variational inequality formulations are presented. Several simple examples are solved analytically for illustration, and an algorithmic framework for computing equilibrium solutions to larger cases is provided. A set of numerical examples is presented, inspired by wheat exports from the Black Sea region to North and Sub‐Saharan Africa, as well as purchases by the World Food Program. The impacts of the Russo‐Ukrainian war on trade patterns and the effects of varying strategic reserve levels are assessed. We observe that each additional one million metric tons of fixed demand raises the corresponding market's equilibrium demand price by $0.830–$0.886 per metric ton, with the cumulative increase reaching approximately $11 per metric ton over the reserve levels considered and substantial cross‐market spillovers.
ABSTRACT We present two picker routing problems in a warehouse split into multiple disjoint zones with a picker assigned to each zone. Scattered storage is applied, meaning an article can be stored at several pick positions in one or more zones, and capacity restrictions limit the number of collected articles for each picker. Both problems seek picker tours that collect all requested articles, with each tour operating within one zone. While the multi‐zone picker routing problem (MZPRP) minimizes the total length of all picker tours, the balanced multi‐zone picker routing problem (BMZPRP) balances the tour lengths by minimizing the length of the longest picker tour. Both problems constitute a three‐level optimization problem. While on the higher levels, zone assignment decisions and the selection of pick positions must be made, on the lower level, picker tours for each zone are determined. To solve both problems, we use a network‐flow model with covering constraints and varying objectives. This type of model was recently presented for the single picker routing problem with scattered storage, building on an extended state space of the dynamic‐programming approach by Ratliff and Rosenthal. Our model contains a network for each zone, and demand‐covering constraints across all zones ensure that the requested articles are collected. Computational experiments, including large instances with up to 200 articles, show that our solution approach efficiently solves the two problems within (milli‐)seconds. An analysis of the number of zones demonstrates that in larger warehouse layouts, zoning reduces routing costs compared to single‐zone picker routing.
ABSTRACT In response to the rapidly increasing demand for higher bandwidth and the necessity for more flexible and efficient resource allocation, elastic optical networks have emerged as a promising solution for next‐generation high‐capacity optical communication systems. These networks leverage flexible spectrum management techniques, such as flexible grid and adaptive modulation formats, to enhance spectral utilization and support fluctuating traffic demands. However, the design and operation of these networks pose significant challenges, particularly in the context of the constrained routing and spectrum assignment (C‐RSA) problem, which involves determining optimal routing paths and spectrum allocations while satisfying various constraints such as spectrum contiguity, continuity, and nonoverlapping requirements. In this paper, we introduce an integer linear programming formulation for the C‐RSA problem and conduct a polyhedral investigation of the associated polytope. We describe several valid inequalities, present necessary and sufficient conditions under which these inequalities are facet‐defining, and then discuss the related separation problems. Based on these results, we develop a Branch‐and‐Cut algorithm to solve the problem. Additionally, we present computational results that demonstrate the effectiveness of our approach using various instances. Moreover, we compare our approach with existing methods from the literature as well as various state‐of‐the‐art MILP solvers.
