In logistics, customer clusters are often predefined based on geographic locations to optimize resource management and workload distribution. However, this approach frequently leads to significant cluster imbalance, particularly when not all customers require daily service or when operational constraints restrict the possibility of reallocating customers across clusters. These imbalances may affect workload equity, routing efficiency, and overall service performance. This paper addresses the problem of balancing customer clusters under relocation constraints by introducing two alternative criteria for measuring imbalance and enforcing them within a constrained reassignment framework. Our goal is to redistribute the set of customers so as to construct new clusters whose cardinalities are as balanced as possible while fully respecting the reassignment limitations. After formulating both nonlinear optimization models, we propose an exact algorithm that systematically reallocates customers through sequences of feasible moves, thereby ensuring progress toward a balanced configuration. We provide formal proofs showing that the algorithm always converges to an optimal solution for both imbalance criteria after a finite number of iterations. From these results, it follows that both models yield the same optimal solution. In addition, computational experiments demonstrate the efficiency of the method, showing that optimal solutions are obtained with very low running times for large-scale instances.
This paper presents the Hazardous Team Orienteering Problem (HTOP), an extension of the Hazardous Orienteering Problem designed for multiple vehicles. In HTOP, visiting certain customers exposes the vehicle to a time-dependent risk of catastrophic loss. Each hazardous customer has an associated exponential failure rate, meaning that if an explosion occurs, the entire profit earned from that route is lost. The goal is to maximize the total expected profit collected by a fleet of vehicles while adhering to time constraints and ensuring customer exclusivity. We introduce two solution approaches. First, we develop an exact Branch-and-Price algorithm based on a set-partitioning reformulation, where each column corresponds to a feasible hazardous route valued by its expected profit. Second, we create an Adaptive Large Neighborhood Search (ALNS) metaheuristic tailored to the nonlinear expected-profit structure of the problem. Computational experiments on benchmark instances derived from the existing literature on the Hazardous Orienteering Problem demonstrate that the pricing phase is the main computational bottleneck of the exact approach. Nevertheless, our method successfully solves small and medium-sized instances to optimality. The ALNS consistently generates high-quality solutions in a short amount of time and matches the optimal solutions for single-vehicle benchmarks while showing strong scalability in multi-vehicle scenarios.
Rolling stock units are critical resources because their schedule is constrained, and they are not available on demand. Given that all rolling stock units in the network share the same resources, such as tracks and infrastructure, the time and place to repair malfunctions while keeping the network in its optimal state are not easy to find. The goal of this research is to find an efficient solution to this scheduling problem. We define the problem as it occurs at the French national railway company and propose modeling it using a mixed-integer programming (MIP) model and a constraint programming (CP) model. We then solve the models using heuristic algorithms: a local branching heuristic for the MIP model and a variable partitioning local search heuristic for the CP model. We then evaluate these solutions on both generated and real data.
This paper presents a practical case study, conducted with Corporación Alimentaria Guissona S.A. (bonÀrea), on optimizing storage locations in a large-scale, automated warehouse for perishable foods. The objective is to minimize costly blockages on the facility’s conveyors, which disrupt throughput and risk the cold chain. We address this via item redistribution. This is a hard combinatorial optimization problem with a large search space. We model the problem using a derivative-free simulator and explore solutions using local search metaheuristic techniques. Unlike conventional optimization that seeks global optima in an unrestricted search space, our approach is limited by a defined local distance from the original solution. We show different approaches to tackle this set of problem constraints based around local search metaheuristics that ensure bounded exploration of the solution space. Our results demonstrate that a bounded exploration approach can reduce blockages by 45
Technological upgrading in the prepared dishes industry has become essential due to recurrent food safety issues. To better understand the dynamics of this process, the study employs evolutionary game theory to analyze the strategic interactions among the government, prepared dish producers, cold chain logistics service providers (LSPs), and consumers, with a particular focus on how media attention influences their decision-making. The main findings are as follows: first, government supervision, through regulatory measures and incentives, effectively drives technological upgrading. Second, media attention motivates participants, especially producers, to adopt proactive strategies, such as innovation in technology and enhanced cold chain control. Third, cold chain LSPs’ strategies are critical during the transition from government-led control to corporate self-regulation. Furthermore, cold chain efficiency improvement can further prompt innovation. Therefore, the government should combine policy tools and media guidance to foster coordination, drive technological advancement, and enhance food quality and industry competitiveness.
In this paper we introduce an approach to incorporate fairness constraints into LASSO regression. Assuming that a group of individuals need to be protected against discrimination, we address the problem of training the LASSO regression subject to a fairness constraint, enforcing that an equal proportion of individuals from the protected and non-protected groups have a predicted value above a given threshold. The LASSO model is then extended to account for this and is formulated as a Mixed-Integer Quadratic Program with linear constraints. We illustrate on real-world datasets that we are able to significantly improve fairness, in terms of our novel unfairness measure, without incurring a significant loss in prediction accuracy or sparsity.
The ℓ _1 -regularized optimization problem has been extensively studied, leading to the development of various numerical algorithms. The active-set proximal-Newton algorithm, introduced in [J. Sci. Comput., 85(3):57, 2020], effectively solves box-constrained ℓ _1 optimization problems by distinguishing between active and free variables and integrating the proximal gradient method with Newton’s method to ensure iterative convergence. In this paper, we prove the superlinear or quadratic local convergence of the active-set proximal-Newton algorithm under a specific strict complementarity-like condition. For problems that do not satisfy this condition, we propose a two-stage active-set proximal-Newton algorithm and establish its superlinear or quadratic local convergence without the need for the strict complementarity-like condition. Numerical results on a set of test problems illustrate that the two-stage algorithm outperforms the original active-set proximal-Newton algorithm.
We study a rich vehicle coordination problem met by Liège Airport, a major cargo airport in Europe. We focus on air cargo ground handling: a set of services should be provided by different vehicle types to different clients at different locations within defined time intervals, and various vehicle interdependencies exist. We first formalize the problem as a set of rich Vehicle Routing Problems that are bound together by multiple synchronization constraints. In particular, we consider compulsory vehicle pairings, precedence constraints between services, and goods transfers between vehicles of different types. The latter can involve more than two vehicles, implying cascading dependencies that greatly complicate the problem. We then develop a client-centered greedy heuristic using a recursive procedure that is able to solve the problem as a whole without having to handle constraints separately, as is often the case in vehicle routing problems with such complex structures. We seek to minimize total service time to produce safety time buffers that would help absorb the impact of disruptions and subsequently reduce the number and duration of aircraft delays. Tests on real instances show that the algorithm performs well.
This paper reviews the literature on trade-in programs, which have become increasingly common across various industries. A trade-in program offers consumers a rebate when they return used products and purchase new ones. These programs serve dual purposes: a marketing objective of promoting sales of new products, and an operational purpose of leveraging returned items for remanufacturing, refurbishing, or recycling, in order to generate additional revenue. Trade-in programs have been studied in the literature using models in monopoly and duopoly settings, as well as within supply chains. The review also covers contributions that explore the possibility of reselling purchased products in secondary markets, including peer-to-peer consumer transactions.
Uncertainty in demand and supply conditions poses critical challenges to effective inventory management, especially in collaborative environments. Traditional inventory models, such as those based on the Economic Order Quantity (EOQ), often rely on fixed parameters and deterministic assumptions, limiting their ability to capture the complexity of real-world scenarios. This paper focuses on interval inventory situations, an extension of classical models in which demand is represented as intervals to account for uncertainty. This framework allows for a more flexible and realistic analysis of inventory decisions and cost-sharing among cooperating agents. We examine two interval-based allocation rules, the interval SOC-rule and the interval Shapley rule, designed to distribute joint ordering costs fairly and efficiently under uncertain demand. Their theoretical properties are analyzed, and their practical applicability is demonstrated through a case study involving the coordination of perfume inventories across seven Spanish airports, based on 2023 passenger traffic data provided by AENA. The findings highlight the potential of interval-based models to enable a robust and equitable allocation of inventory costs in the face of operational uncertainty.
The Team Orienteering Problem with Service Times and Mandatory & Incompatible Nodes (TOP-ST-MIN) is a variant of the classic Team Orienteering Problem (TOP), which includes three features that stem from two real-world problems previously studied by the authors: service time at nodes, mandatory nodes and physical or logical incompatibilities between pairs of nodes. We gather all these ingredients for the first time in the same model and prove that even finding a feasible solution to this problem is NP-complete unlike the TOP where finding a feasible solution is straightforward. Two versions of this variant are considered in our study. For such versions, we proposed two alternative mathematical formulations, a route-based and a flow-based formulations. Based on the flow-based formulation, we developed a Cutting-Plane Algorithm (CPA) exploiting five families of valid inequalities, which are either new or have generally not been used as such in the TOP literature and separated by means of new algorithmic methods. Extensive computational experiments showed that the CPA outperforms CPLEX in solving the new benchmark instances, generated in such a way to evaluate the impact of the three novel features that characterise the problem. The CPA is also competitive for the TOP since it is able to solve almost the same number of instances as the state-of-art algorithms.
The Flow Refueling Location Problem (FRLP) is a stylized model for determining the optimal placement of refueling stations for vehicles with limited travel ranges, such as hydrogen fuel cell vehicles and electric vehicles. A notable extension, the deviation FRLP, accounts for the possibility that drivers may deviate from their preferred routes to refuel or recharge. While solution techniques based on various mathematical programming formulations have been thoroughly explored for this extension, there is a lack of theoretical insights into the relationships and strengths of these formulations. In this work, for the deviation extension, we study two prominent FRLP formulations from the literature and compare their strengths in terms of linear programming (LP) relaxations. We show that the LP relaxation of one formulation yields a bound that is at least as tight as that of the other, which may explain its observed superior performance. Building on these insights, we address a common modeling assumption in the FRLP that requires drivers to use the same paths for their outbound and inbound trips. Specifically, we relax this assumption and introduce the cyclic FRLP, where drivers may use different paths in each direction. We show how existing formulations can be naturally extended to accommodate this setting and describe a branch-and-cut algorithm to solve the problem. We provide numerical experiments highlighting the benefits of such asymmetric routing. For example, in an instance based on the Californian network, the original and cyclic FRLPs yield identical solutions when the deviation tolerance is small. However, differences emerge and become more pronounced as the deviation tolerance increases. When a 50
