ABSTRACT A truck platoon is a set of trucks that drive behind one another at short headways to save fuel, reduce emissions, and improve traffic throughput. Despite the potential benefits of platooning, road operators have raised concerns about the impact of platoons on surrounding traffic. The use of dedicated platoon lanes helps prevent potentially dangerous situations when interacting with regular traffic. Furthermore, dedicated platooning lanes can help increase platooning benefits and prolong the life of infrastructure. Such types of infrastructure design decisions typically have to be made when the demand that the infrastructure needs to support is uncertain. One way to represent uncertain demand in optimization models is by means of possible realizations or scenarios. Using many scenarios is likely to produce better solutions, but it also creates computational challenges. We propose an approach that blends solutions, each obtained using an optimization model with relatively few scenarios. We use this approach in the context of locating dedicated truck platoon lanes. Computational experiments show that blending designs obtained with a few scenarios is as effective, but much more efficient, as creating a design using many scenarios.

ABSTRACT This paper introduces a variant of the dynamic Facility Location Problem with modular capacities. Inspired by the challenges faced by cellular telecommunication networks, the problem seeks to optimize the placement and equipment of facilities to meet the fluctuating demand of clients while minimizing installation and operational costs. Selected facilities must provide coverage to the whole considered area. In addition, clients must be served by the active facility that provides the best quality of service. We propose two integer linear programming formulations and analyze their theoretical properties in terms of lower bound. Furthermore, we propose a reinforcement for one formulation and valid inequalities. To evaluate the performance of the proposed formulations, we performed computational experiments with a commercial solver on instances with up to 20 candidate sites and 60 clients. The formulations proved to be very sensitive to the size of the instances. The analysis, both theoretical and numerical, provides meaningful insights on the formulations performance, and it constitutes a key starting point for developing further approaches, either exact methods or heuristics.

ABSTRACT A 2‐packing set for an undirected, weighted graph is a subset such that any two vertices are not adjacent and have no common neighbors. The Maximum Weight 2‐Packing Set problem that asks for a 2‐packing set of maximum weight is ‐hard. Next to 13 novel data reduction rules for this problem, we develop two new approaches to solve this problem on arbitrary graphs. First, we introduce a preprocessing routine that exploits the close relation of 2‐packing sets to independent sets. This makes well‐studied independent set solvers usable for the Maximum Weight 2‐Packing Set problem. Second, we propose an iterative reduce‐and‐peel approach that utilizes the new data reductions. Our experiments show that our preprocessing routine gives speedups of multiple orders of magnitude, while also improving solution quality and memory consumption compared to a naive transformation to independent set instances. Furthermore, it solves 44% of the instances tested to optimality. Our heuristic can keep up with the best‐performing maximum weight independent set solvers combined with our preprocessing routine. Additionally, our heuristic can find the best solution quality on the biggest instances in our data set, outperforming all other approaches. When using our data reduction rules for exact solvers, we can solve more instances to optimality and are overall multiple orders of magnitude faster.

ABSTRACT This article studies the impact of social constraints on the vehicle routing problem, with a particular focus on allowing overtimes for the drivers. Working overtime is common in practice, as it may improve driver utilization, but it also requires a more detailed cost structure in the routing problem. Motivated by an application at a florist company performing daily routes in a network of stores in Norway, we address a problem characterized by deliveries and split pickups, a heterogeneous fleet of capacitated trucks and a heterogeneous workforce of drivers. We tackle the problem by a route‐based mixed integer linear programming model. The objective of the model is to minimize a cost function, which includes route‐driving costs for ordinary working hours, overtime costs, plus the additional time picking up carts at pickup locations. The time workload of the drivers is also captured in several social constraints. The results outperform manually produced solutions and a commercial software, with cost reductions totaling 17.4%–36.4% and 9.7%–25.5%, respectively. The results also show how the routes and costs differ when different allowances of overtime are used in the model. Notably, the results illustrate that overtimes are beneficial for cost savings and they are most valuable to serve locations far away from the headquarters. We also compute results for when the cost minimization objective function is replaced by a distance minimization function. A comparison reveals that the distance minimization results may deviate significantly from the cost minimization results.

ABSTRACT Shortest path problems often arise in contexts where travel times are uncertain. In these settings, reliable paths are often valued more than paths with lower expected travel times. This has led to several variants of reliable shortest path problems (RSPP) that handle travel time reliability differently. We propose an algorithmic framework for solving RSPPs with non‐negatively correlated travel times and resource constraints. By building upon the flexibility of the pulse algorithm, our unified and exact algorithmic framework solves multiple variants of the RSPP: the ‐reliable shortest path (‐RSP), the maximum probability of on‐time arrival (MPOAP) problem, and the shortest ‐reliable path (S‐). We derive a bound on the reliability of path travel times and incorporate three pruning strategies: bounds, infeasibility, and dominance, leveraging properties of the normal distribution and non‐negative correlation structures. Computational experiments on large‐scale transportation networks (with up to 33 113 nodes and 75 379 arcs) demonstrate that the framework achieves a ten‐fold speed improvement over state‐of‐the‐art methods, highlighting its potential real‐world applications and extensions to related problems.

ABSTRACT Two‐echelon distribution systems with an intermediate urban consolidation centre are one of the key innovations proposed in city logistics. We focus on a business‐to‐business context in which urban retailers are delivered by suppliers via such a city hub. Specifically, we investigate the benefits of simultaneously optimising routing decisions from the Urban Consolidation Center and inventory decisions at the retailers. For this, we extend the classical Inventory Routing Problem (IRP) to an urban setting, considering complexities like time windows, heterogeneous vehicles, and multiple trips per vehicle per day. We propose a two‐phase matheuristic solution algorithm, and compare its results to a baseline approach in which inventory and routing decisions are made sequentially. Computational results demonstrate that the integrated approach consistently outperforms the traditional sequential approach. A detailed analysis of instance characteristics influencing the outcome of these scenarios highlights the impact of variables such as the number of retailers and suppliers, and holding costs. A sensitivity analysis identifies critical factors affecting the implementation of the integrated scenario, emphasising the importance of retailer storage capacity, order costs, and retailer participation. The findings highlight the overall potential benefits of integration, including cost savings, improved resource utilisation, and positive impacts on all stakeholders involved.

ABSTRACT This paper studies a combined delivery strategy involving a private vehicle and external carriers under stochastic customer demands. The routing problem focuses on a single private vehicle, while external carriers are allowed to determine their own routes independently and are compensated with a fixed price per unit demand served. A strategy incorporating routing re‐optimization is proposed, along with a new recourse mechanism that leverages outsourcing through external carriers. To enable routing re‐optimization, a novel approximate linear programming (ALP) approach is introduced. This offers a new pathway for addressing vehicle routing problems (VRPs) under stochastic demand considerations. The ALP approach is adapted to the specific structure of routing under stochastic demands, leading to the development of a decomposition‐based ALP solution framework. This adaptation arises from changes in the decision sequence of routing and restocking at each step of the Markov decision process (MDP), which differs from previous formulations of vehicle routing under stochastic demands. Additionally, further adaptations are made to facilitate the computation of the proposed strategy by exploring the relationships among variables and constraints specific to the problem context, as well as by developing a constraint sampling procedure designed to mimic the near‐optimal heuristic policy. Our numerical results show that the proposed outsourcing‐based policy yields notable operating‐cost savings, with an average improvement of 4.06% over the traditional recourse strategy in midpoint‐depot instances. Moreover, in small instances where the optimal policy within the traditional partial re‐optimization framework can be computed, the proposed price‐directed (PD) policy still provides cost advantages over this re‐optimization scheme, demonstrating the value of our ALP‐based framework.