Abstract Parallel structures are commonly used to describe production processes with multiple subsystems operating simultaneously and independently. These subsystems can either function similarly or complementarily, and proportional relationships exist between subsystem outputs. These relationships constitute a potential source of inefficiency, which has been largely overlooked in the existing literature. This study addresses this gap by investigating two‐function systems within parallel structures while incorporating these proportional relationships. We extend parallel network data envelopment analysis by introducing substitution and target proportional relationships and propose proportional efficiency measures for each. Overall efficiency is then measured based on the technical efficiencies of the subsystems and the proportional efficiency. In addition, we explore the process of target setting, prioritizing technical efficiency, followed by proportional relationship optimization. We illustrate our methodology with a numerical example and an empirical study of 30 Chinese provincial power generation systems, underscoring its practical relevance for decision‐making.
Abstract Within the current interconnected and volatile global economy, supply chain network design has become a strategic priority for organizations aiming to enhance resilience, efficiency, and sustainability. The physical internet (PI) paradigm offers a transformative approach to logistics by promoting hyperconnectivity, interoperability, and dynamic reconfiguration. However, designing PI‐based supply chain networks, especially those involving multipath routing and decentralized decision‐making, poses significant computational challenges that traditional optimization methods have not yet addressed. This paper introduces a series of biased‐randomized matheuristic algorithms tailored to the design of PI supply chain networks. Two problem variants are considered: a basic model and a multipath model incorporating network connectivity constraints. Both are formulated as mixed‐integer programming models, which become computationally inefficient for large‐scale instances. Hence, scalable matheuristics are also proposed, based on greedy and biased‐randomized strategies, and on an extended Dijkstra's algorithm in the case of the multipath version. Computational experiments show that these methods have strong potential for real‐world logistics applications, offering robust and time‐efficient tools for complex supply chain network design.
Abstract The traveling salesman problem (TSP) is a well‐known NP‐hard problem in combinatorial optimization, with numerous applications in logistics and elsewhere. This paper introduces a machine learning‐based approach to estimate the optimal tour length of the TSP, using linear regression, random forests (RF), and neural networks, including Kolmogorov–Arnold networks (KANs). A key limitation of one of the most accurate published neural‐network estimators for the TSP is that it relies on size‐specific architectures: Each model is bound to a fixed instance size and cannot be applied to larger instances without retraining. We address this through size‐independent features enabling bidirectional scalability: a single model applicable to instances of any size without retraining. Under equivalent conditions, our best model achieves 1.51% mean absolute percentage error, outperforming the state‐of‐the‐art approach (2.02%). We conduct systematic generalizability analysis on challenging out‐of‐distribution instances, such as instances (a family of instances whose two‐dimensional projections form the edges of a tetrahedron) and on triangular distributed instances, revealing that KAN models generalize remarkably well, while RF requires representative training examples from each distribution. Through KAN's interpretability framework, we extract analytical formulas that recover classical relationships from early theoretical work, bridging machine learning and traditional analytical methods. Our findings provide practical guidance for model selection and demonstrate that machine learning techniques can achieve high accuracy, robust generalization, and interpretability for TSP tour length estimation.
Abstract Manufacturers’ product advantage and platforms’ information advantage have been reshaping operational modes of multi‐channel platform supply chains. To investigate this reshaping mechanism, this study builds Stackelberg game models composed of a manufacturer and a platform under reselling‐direct and agency‐direct selling scenarios. Four types of order quantity and pricing games involving product collaboration and information sharing are developed to support channel selection and strategy optimization. The study finds that in the agency selling channel, information sharing can achieve a Pareto improvement in profits for both parties only when the substitution rate is low after product collaboration. In this scenario, social welfare is maximized. If the platform sets a higher commission rate, both parties tend to maintain the agency selling channel; otherwise, the platform always prefers the reselling channel. Moreover, information sharing expands the selection space for both parties to retain the agency selling channel. In the reselling channel, a Pareto improvement in profits for both parties requires product collaboration as a prerequisite, and product collaboration can weaken the competitive effect from information sharing. Extending the models to three‐channel scenarios, this study reveals: given the coexistence of the manufacturer's agency channel and the platform's private brand direct channel, the platform will refuse to facilitate the manufacturer's entry into the reselling channel. Furthermore, product collaboration serves as a necessary prerequisite for the manufacturer to achieve profit increases when hybrid channels are unavailable. This study uncovers the interplay mechanism of information sharing strategies considering product collaboration on firms’ operational decisions and sales channel selection.
Hospital at home (HaH) is a hospital service where acute hospitalized patients are treated at their homes. These services reduce hospital length-of-stay, improve patient safety, and accelerate the recovery process, while reducing hospital costs and increasing the availability of beds. In this article, we introduce the HaH concept in the operations research & management science literature by addressing a hospital at home routing and scheduling problem of a Portuguese public hospital, where teams of physicians and nurses must visit different sets of patients on a daily basis. We propose a bi-objective mixed integer linear programming model to minimize travel time and maximize a continuity of care score. To find the Pareto front, we use an exact -constraint method. Computational experiments are performed in real instances from hospital records and in instances adapted from benchmark instances for home health care problems. Results show the suitability of the proposed method for planning the case study HaH unit, and solutions are consistently better than the ones adopted by the hospital, considering both objectives.
The rapid growth of e-commerce has led to multiple carriers operating in the same regions, creating opportunities for collaboration. However, logistics companies typically operate independently, leading to inefficiencies. Horizontal cooperation, where carriers share resources and infrastructure, can improve efficiency and reduce costs. This study explores the requirements for a parcel exchange framework through a game-theoretic lens. We focus on auction-based mechanisms to facilitate horizontal cooperation, optimize exchanges, and minimize delivery costs and emissions. Our approach prioritizes ensuring that carriers report accurate marginal delivery costs while maintaining business privacy. First, we define the key properties of an exchange mechanism for redistributing parcels among carriers. Our analysis reveals a conflict between incentive compatibility and budget balance when non-free disposal is enforced. Among the mechanisms considered, the Vickrey-Clarke-Groves (VCG) mechanism is the most suitable, though it tends to overpay carriers. The rationale for using VCG is that we consider incentive compatibility and allocation of all parcels more important than budget balance to ensure long-term participation of carriers and delivery fulfillment. In a computational study, we analyze a VCG-based parcel exchange under realistic settings. The experiment considers several parcel carriers within a region with heterogeneous market shares. In the simulated auctions, carriers compute marginal costs for the parcels, and the winner determination problem is solved via a linear program. A random parcel assignment serves as proxy for noncooperative behavior. The results demonstrate that second-price premium reward payments are typically moderate and that second-price compensation for allocated parcels remains superior to noncooperative last-mile parcel logistics.
As environmental awareness grows, companies are rolling out emission-reduction initiatives to offer more low-carbon products. The two commonly adopted strategies for companies are direct carbon reduction investment (R strategy) and carbon offset (O strategy), and they differ in costs and consumer perception of their effects: the former requires substantial upfront technological investment and is therefore highly sensitive to demand fluctuations, whereas the latter involves demand-dependent costs but may suffer from credibility concerns. The choice between them is further complicated by demand uncertainty, which is often amplified by information asymmetry, as retailers typically possess more accurate demand information. We develop a game-theoretic model in which a manufacturer chooses a low-carbon strategy, while a retailer decides whether to share demand information. Our results show that the optimal strategy depends jointly on market potential demand, consumer acceptance of carbon offsets, and information availability. Carbon reduction is preferred when demand is sufficiently high or consumer acceptance of offsets is low, whereas carbon offset becomes more attractive under weak demand due to lower downside risk. Information sharing reduces demand uncertainty and lowers the threshold for manufacturers to adopt carbon reduction, thereby promoting genuine emission abatement. Moreover, under a hybrid strategy, the presence of an offset mechanism encourages deeper carbon-reduction efforts by mitigating investment risk and strengthening incentives for technological abatement.
Scheduling connected and automated vehicles (CAVs) at reservation-based intersections faces a fundamental trade-off: existing methods sacrifice either optimality for computational efficiency or real-time applicability for optimal solutions. We bridge this gap by proposing a dynamic programming (DP) algorithm with dominance pruning () that simultaneously achieves optimal batch formation, polynomial-time complexity, and superior solution quality. introduces a novel dominance rule that eliminates suboptimal child nodes by comparing analytically derived lower bounds, enabling batch-based processing of CAVs while guaranteeing optimality. Unlike existing approaches that assume predetermined batches or sacrifice optimality, integrates optimal batching decisions directly into the scheduling algorithm. The proposed method achieves a substantial improvement over existing exact algorithms with worst-case and best-case time complexity. Extensive experiments demonstrate that reduces computation time by 91% and 99% compared to a state-of-the-art DP algorithm and Gurobi solver, respectively, while consistently delivering superior performance in makespan, average delay, and maximum delay metrics across diverse traffic scenarios. Furthermore, outperforms heuristic algorithms in achieving better solution quality and comparative computational efficiency. Sensitivity analysis reveals that 's dominance rule remains effective across varying mean headways, CAV counts, and batch proportions, with performance benefits extending beyond simple batch processing to complex traffic patterns.
Abstract This study addresses the aerial firefighting resource allocation problem, formulated as the strategic prepositioning of a heterogeneous aerial firefighting fleet across capacity‐constrained airbases. A novel bi‐objective model is proposed that simultaneously optimizes efficiency (aggregate risk‐weighted accessibility) and equity (minimized regional service disparities). The model employs an enhanced spatial accessibility method with a distance‐decay function to evaluate coverage effectiveness and distribution fairness. A multi‐objective genetic algorithm is implemented to generate Pareto‐approximate solutions, revealing quantifiable trade‐offs. Applied to a national‐scale case study in Greece using 25 years of wildfire data, results demonstrate that the proposed framework provides significantly wider coverage than current practices, thereby extending protection to underserved regions while reducing redundant overlap. Sensitivity analyses confirm robustness across various real‐world conditions, such as different budget levels and aircraft availability. This transferable tool enables policymakers to make data‐driven decisions by quantifying the balance between response effectiveness and social fairness in wildfire‐prone regions.
Branch-and-price is one of the most commonly used methodologies for solving routing problems. In recent years, several studies have investigated advanced labeling algorithms to solve the related pricing problem, which is usually a variant of the elementary shortest path problem with resource constraints. Such algorithms include efficient techniques such as decremental state space relaxation, ng-route relaxation, and several hybridizations of these two relaxation methods. In this study, we compare the performance of these labeling algorithms in a branch-and-price framework when applied to the vehicle routing problem with time windows and a variant of this problem in which waiting times have a linear cost. For the latter problem, we also propose an appropriate label structure with associated resource extension functions and dominance rules. We perform these comparisons by using a rigorous methodology, which consists of parameterizing several features of these algorithms, obtaining a good parameter configuration for each algorithm, and analyzing the performance of these configurations on benchmark instances. In order to obtain good configurations, we make use of irace, which is a tool for automated parameter tuning, while statistical tests are used for performance comparisons. Our results show that a class of hybrid algorithms with certain features based on ng-route relaxation outperforms all the others.
Understanding how citizen satisfaction varies within a fragmented metropolis requires more than a single pooled index. This paper develops a transferable cross-group MUlticriteria Satisfaction Analysis (MUSA) framework that fits comparable preference-disaggregation models for municipalities and socio-geographically grouped municipalities, enabling like-for-like comparison of importance and satisfaction on common scales. Its novelty lies in making such comparisons methodologically consistent and substantively interpretable across territorial units, with a policy contribution that is primarily diagnostic and comparative rather than prescriptive. Using an original trilingual survey in the Brussels-Capital Region, we fit pooled, municipality-level, and municipality-group models across four dimensions: mobility and infrastructure, health and education, culture and community, and public safety and order. The pooled model indicates moderate overall satisfaction. Health and education emerges as the most influential and best-performing dimension, whereas public safety and order combines high importance with the weakest satisfaction. Municipality-level models reveal substantial spatial dispersion, but because single-municipality samples are uneven, municipality-group models provide the main comparative lens. At that level, the results show distinct priority structures: some groups exhibit one dominant high-importance, low-performance lever, whereas others require broader multi-criteria improvement. The framework, therefore, helps identify priority domains within territorial units and benchmark municipalities and municipality groups on a common analytical basis, while making sample imbalance and model uncertainty explicit.
This paper introduces the bilevel tree-of-hubs location and pricing problem, a multiple-allocation hub location problem in which both the design and pricing of a tree-shaped hub backbone network are determined. Two types of decision-makers are considered: a leader, who defines the network structure and sets usage prices, and a follower, who selects the optimal way to use the network for shipping commodities. The leader aims to maximize profit, while the follower seeks to minimize transportation costs. A bilevel optimization formulation is proposed and reformulated into a single-level equivalent model. To solve it efficiently, we develop a Co-Evolutionary Algorithm (Co-EA) and test it on three well-known datasets adapted to our problem. The novelty of the proposed Co-EA lies in the interaction between its co-evolving populations: rather than representing leader and follower solutions separately, each population is associated with a subset of the leader's decision variables. For each leader decision, the follower's optimal response is computed, ensuring bilevel feasibility. Extensive computational experiments demonstrate the effectiveness of the proposed Co-EA compared with general-purpose solvers applied to the reformulated model. The best Co-EA solutions are also used as warm-starts for the exact solver, confirming the quality of the heuristic results. Finally, managerial insights are derived regarding how the number of hubs affects the backbone network configuration. The paper concludes with directions for future research on bilevel hub location and pricing models.
Media platforms' business model choices and pricing affect user engagement under competition. In practice, information asymmetry exists between users: advertisers are aware of subscription prices, while consumers remain unaware of advertising charges, creating strategic opportunities for price disclosure by platforms. This study therefore investigates competing media platforms' optimal business-model choices with price information disclosure strategies. We develop a Hotelling model in which platforms adopt one of three business models: ad-sponsored (charging only advertisers), subscription-based (charging only consumers), and hybrid (charging both), while accounting for content production. The results reveal that, contrary to intuition, information asymmetry between users negatively impacts platform profits. The price information disclosure strategy always dominates the nondisclosure strategy. Second, although the hybrid model may not be optimal under some conditions, it always helps platforms attain the largest consumer base by either subsidizing consumers or increasing content production. Third, the optimal choice of business model depends on the interplay among advertiser competition, content costs, attention valuation, and ad aversion. Surprisingly, platforms adopt a subscription-based model primarily due to intense advertising market competition, not higher ad aversion as commonly expected.
Multi-restart metaheuristics can be highly effective for complex optimization problems, yet their performance depends critically on how restarts and algorithmic parameters are selected. This paper introduces a reinforcement learning approach for managing restart-level decisions and parameter configurations in the UES-CMA-ES hybrid metaheuristic. Rather than modifying the underlying optimizer, we focus on the design of the reinforcement learning environment, formulating restarts as high-level decision points governed by a learned policy. We propose an environment that anchors restarts at the final solution of each execution and jointly controls key metaheuristic parameters, guided by a stagnation-aware reward function. Experiments on the IEEE CEC'13 benchmark suite show that the proposed approach achieves consistent performance improvements over static multi-restart strategies and simpler environment formulations, with average gains of up to 15-30% on multimodal and composition functions. A single agent trained on 30-dimensional problems generalizes effectively to 100-dimensional benchmarks without retraining. These results highlight the central role of environment design and reward shaping in reinforcement learning-enhanced optimization and suggest a principled pathway toward data-driven metaheuristics that adaptively refine multi-restart strategies.
This study tackles the multiple allocation -hub location problem (MApHLP) in the context of video-on-demand services, where digital content is partitioned into segments and stored exclusively at selected hub locations. Users, distributed across a wide geographical area, can connect to multiple hubs based on demand patterns, with all hubs assumed to be fully interconnected. The goal is to jointly determine hub locations, segment placement, user-to-hub assignments, and optimal routing paths to minimize total routing costs. To solve this complex problem, an enhanced adaptive large neighborhood search (EALNS) algorithm is proposed. The algorithm features an efficient objective evaluation strategy for rapid assessment of candidate solutions and employs adaptive operator selection that dynamically updates neighborhood strategies based on their past performance. The proposed EALNS algorithm is benchmarked against solutions obtained from CPLEX and a differential evolution-based metaheuristic. The reported results confirm its efficiency and competitiveness in addressing large-scale MApHLP instances.
We simulate impacts of a global energy crisis on supply chains (SCs). First, we articulate the specific features that frame a global energy crisis as a unique type of SC large-scale systemic shocks characterized by a long-term disruption existence, disruption propagations (i.e., the ripple effect), a combination of immediate and delayed effects, cross-industry ripple effects, and mutual interrelations of SC and economic impacts. Second, we demonstrate how simulation-based methodology can be used to examine and predict the impacts of global energy crises on SC performance using the example of the Strait of Hormuz blockage and anyLogistix software. The major observation from the simulation experiments is that global energy crisis impacts resemble the COVID-19 pandemic patterns and ripple effects in 2020-2022 with reduced logistics capacities, delivery delays, and production shutdowns, supplemented by inflation effects observed in tariff turbulences in 2025. Other important factors influencing the shock impacts and propagation mechanisms are the duration of the energy crisis and SC viability. We observe that viable SCs with greater variety in production, supply, logistics, and energy structures are better able to absorb shocks. The outcomes of this research can be used by decision-makers to predict the operational and long-term impacts of global energy crises on SCs and to develop viability strategies. Our models are readily available to be used in practice for SC stress testing. They offer recommendations on proactively building adaptability and reconfiguring in response to disruptions to survive in a world without a reliable energy supply, incorporating large-scale systemic shocks into operational models.
High sales costs and limited procurement capital faced by small- and medium-sized resellers (SMRs) constitute significant barriers that erode manufacturers' profitability and impede improvements in overall supply chain performance. To address these challenges, manufacturers commonly adopt cost-sharing contracts to partially subsidize SMRs' sales expenditures and support them in obtaining bank financing for procurement. To investigate the interplay among cost-sharing mechanisms, financing decisions, and operational dynamics, this study develops a wholesale price signaling game model and derives several key insights. First, irrespective of the retail price level, when the manufacturer's cost-sharing ratio is low, the cost-sharing contract incentivizes the manufacturer to offer differentiated wholesale prices to SMRs with higher initial capital. Conversely, when the retail price is low and the manufacturer's cost-sharing ratio is elevated, the manufacturer is incentivized to offer a pooling wholesale price to SMRs with higher initial capital. Moreover, under the cost-sharing contract, even when SMRs have lower initial capital, the manufacturer would offer differentiated wholesale prices to help banks distinguish between SMR types, thereby offering tailored financing rates. Lastly, cost-sharing contracts are found to increase the motivation of manufacturers with low production costs to differentiate between SMR types while diminishing the same motivation for manufacturers with higher production costs.
With the rapid growth of the electric vehicle (EV) industry, efficient recycling of retired power batteries is essential for achieving circular economy objectives and environmental sustainability. This study examines the integration of a deposit-refund system (DRS) and blockchain technology within the power battery closed-loop supply chain. Three operational models are developed: a baseline model without a DRS, a manufacturer-implemented DRS model, and a blockchain-enhanced DRS model. Based on Stackelberg game formulations, equilibrium decisions on pricing, recycling, and traceability investment are analytically derived. Comparative analyses show that although blockchain adoption increases initial costs and product prices, it substantially improves traceability, consumer confidence, and overall supply chain profitability. Sensitivity analyses identify threshold effects of deposit levels, government subsidies, and the proportion of batteries suitable for comprehensive utilization. Life-cycle assessment further demonstrates that the DRS, particularly when combined with blockchain, significantly reduces environmental impacts per unit product. This study provides theoretical insights into the interaction between digital technologies and circular economy mechanisms, and offers actionable implications for policymakers and industry practitioners seeking to enhance sustainability and efficiency in the EV battery supply chain.
