Efficient routing of vehicles and storage assignment of stock in automated warehouses reduce the operational costs and improve service levels. However, most approaches to the Vehicle Routing Problem (VRP) in warehouses treat routing and storage assignment separately, often overlooking the effects of three-dimensional layouts, item priorities, and real-time traffic congestion. This paper addresses the VRP in three-dimensional warehouse environments through a Deep Reinforcement Learning (DRL) framework based on the Gated Recurrent Unit (GRU)-Attention network. The GRU-Attention network effectively captures complex temporal dependencies and dynamically identifies critical storage and routing features, which enables more adaptive and coordinated decisions in warehouse settings. This method jointly optimizes Automated Guided Vehicle (AGV) routing paths and item storage assignment while considering storage priorities, item turnover rates, and physical weights. In this framework, DRL handles path planning and storage assignment decisions. The proposed model integrates a dynamic storage allocation with an DRL architecture to minimize operational costs. Computational experiments are conducted on real-world and synthetic datasets across various storage policies and warehouse layouts. The experimental results suggest that the GRU-Attention network achieves reductions of 12.65%–19.60% in warehouse scenarios with 50 items compared to traditional and existing algorithms. Additionally, the semi-circle storage policy proves superior to the random, within-aisle, and across-aisle approaches by minimizing AGV travel distances and alleviating congestion within the warehouse. A comparative analysis of warehouse layouts reveals that designs without a central main aisle improve efficiency by minimizing bottlenecks. These findings offer practical insights for optimizing real-time, multi-objective warehouse management automated warehouse systems.
Data envelopment analysis (DEA) methods for fixed-sum outputs have received increasing attention in recent years. Among them, the generalized equilibrium efficient frontier DEA method (GEEFDEA) has gained widespread application due to its computational convenience. However, its uniform weight assumption is inconsistent with the differentiated weighting principle of traditional DEA models, which simplifies the structure of the generated equilibrium efficient frontier (EEF), limiting its ability to accurately reflect real-world production processes. Although recent studies have addressed the uniform weighting issue in single-stage systems, their approaches are not readily applicable to more complex systems. To address this limitation, this study develops a novel evaluation approach for network decision-making units (DMUs) with shared undesirable fixed-sum outputs. The proposed approach extends the relaxation of the uniform weight assumption to the two-stage network setting, allowing DMUs to select their preference weights when constructing the EEF. Depending on the presence of a central authority, EEF construction models are developed under centralized and decentralized scenarios. After obtaining the adjusted DMUs, the adjusted extreme efficient DMUs are further identified to form the corresponding locally supported extreme efficient DMU set (LSEEDS) for evaluating the original DMUs. Notably, the model for constructing the EEF is nonlinear. We demonstrate that it can be linearized when there is a single fixed-sum output and propose a parametric iterative algorithm for the case of multiple fixed-sum outputs. Finally, we verify the proposed algorithm through a numerical example and apply the approach to evaluate energy production-utilization efficiency in 30 Chinese provincial administrative regions.
Motivated by recent applications in power and energy scheduling, this work investigates a class of nonlinear Knapsack problems, called the covering problem under a constant-rank quadratic constraint. In this problem, the constraint is represented as a sum of a constant number of squared linear functions. Since the problem is NP-hard, existing research has primarily focused on developing polynomial-time approximation algorithms with provable performance guarantees. In this work, we advance this line of research by presenting the first polynomial-time approximation scheme (PTAS) for the case where the constraint consists of the sum of two squares of nonnegative linear functions, thereby significantly improving upon the previously best-known quasi-polynomial-time approximation scheme (QPTAS) for this setting. For the more general case involving a constant number of linear functions, we present an n-approximation algorithm and establish the existence of a resource-augmentation algorithm. In addition, we conduct numerical experiments to demonstrate the practical relevance and effectiveness of the proposed approximation scheme.
Today’s supply chains are increasingly complex, creating challenges in achieving transparency and leading to issues such as recalls, reputational risks, susceptibility to disruptions, and compliance difficulties. Legislative measures like the California Transparency in Supply Chains Act and the U.S. Dodd-Frank Act require companies to disclose efforts addressing human trafficking, slavery, and the use of conflict minerals within their supply chains. Emerging technologies such as blockchain and artificial intelligence offer promising solutions for enhancing supply chain traceability and transparency. However, achieving comprehensive traceability requires participation from most, if not all, supply chain members to avoid undetected irregularities. While the benefits of traceability are clear, implementation entails costs. Some participants may find the benefits outweigh these costs, but to encourage broader adoption, downstream firms might consider subsidizing upstream partners. Supply chain leaders, such as Inditex, are often assumed to pursue traceability to enhance transparency and reduce risk, and may take on a leadership role in promoting and implementing such a subsidization model.This paper employs a cooperative game framework to explore scenarios within supply chain networks, aiming to distribute the benefits of technology implementation and foster widespread adoption. Starting with a basic supply chain modeled as a tree graph, we propose an algorithm to identify allocations that promote technology adoption. The analysis then extends to broader supply chain networks, introducing an algorithm that simplifies the problem and reduces dimensionality for efficient analysis. When the full network is not immediately solvable, we propose two complementary interventions: game reduction, for which the exact optimization problem is NP-hard and for which we provide both an exact algorithm and a polynomial-time min-cut heuristic, and benefit augmentation, which we formulate as a polynomial-time linear program that identifies the minimum additional benefit or cost reduction required for full adoption. We conclude with a simulation that applies the proposed framework to a larger, hypothetical apparel supply chain inspired by Inditex.
A substantial body of literature has examined the link between a firm’s sustainability and its operational and financial outcomes. However, limited attention has been given to how supplier sustainability is associated with the performance of buying firms. This study addresses that gap by empirically investigating the relationship between supplier sustainability and both airline efficiency and financial performance, using a unique panel dataset covering U.S. airlines and their suppliers. We also propose a novel framework that integrates the ESG pillars into a Network Data Envelopment Analysis model to assess airline efficiency. By embedding ESG pillars as model outputs, our approach enables a more comprehensive evaluation of both operational and sustainability efficiency, offering deeper insights into sustainability-driven performance. The results show that airlines benefit from more sustainable suppliers, improving both efficiency and financial outcomes. Among ESG dimensions, the Environmental pillar is most strongly associated with airline efficiency, whereas the Governance pillar shows the strongest relationship with financial performance. These findings offer key managerial insights, showing that partnering with ESG-conscious suppliers boosts both operational and financial performance. From a policy standpoint, the study highlights the need for greater ESG transparency and supportive regulations to integrate sustainability across aviation supply chains. The results provide managerial guidance for integrating supplier ESG performance into sourcing and evaluation decisions and offer policy insights for encouraging sustainability-driven partnerships in the aviation sector.By linking ESG and DEA methods, this research contributes theoretically and provides practical guidance for sustainable decision-making.
This study investigates the incentives of a competitive supplier (CS) and an original equipment manufacturer (OEM) to engage in a co-opetitive supply partnership. The CS is an internally decentralized firm comprising a component supply subsidiary and an end-product retail subsidiary. It chooses whether to supply a key component to the OEM, while the OEM chooses between the CS and a non-competitive supplier (NS). Both suppliers can invest in innovation to increase component quality. In setting wholesale prices, the CS may offer its retail subsidiary a discount, which is, however, restricted under the arm’s length regulation (ALR). By exploring the interaction between the ALR and innovation investment, we show that without the ALR, innovation investment can shift the equilibrium from competition to co-opetition, as the CS’s higher innovation level enhances its attractiveness to the OEM relative to the NS. In contrast, under the ALR, while co-opetition is the equilibrium without innovation investment, such investment can lead to a competition equilibrium. This shift occurs because supplying the OEM may reduce the CS’s profit, even though the OEM consistently prefers to source from the CS. Our analysis therefore reveals that the ALR fundamentally reshapes the co-opetition game by reallocating decision-making power from the OEM to the CS. Moevoer, we show that the ALR’s impact on the CS’s innovation level and firms’ profits varies with investment efficiency and market competition intensity, potentially leading to lose-lose or win-win outcomes for both the CS and the OEM.
E-commerce retailers are increasingly establishing forward distribution centers to preposition inventory for rapid delivery. Benefiting from economics of scale, prepacks that bundle stock keeping units with fixed batch sizes, have been widely used in retail supply chains. However, their inherent rigidity and discrete handling requirement introduce significant complexity for operating two-echelon distribution networks. Motivated by this practical challenge, this paper studies the joint optimization of inventory and fulfillment using retail prepacks over a multi-period horizon. In each period, multifaceted operations including prepack procurement, prepack unpacking, inventory allocation, and demand fulfillment must be seamlessly integrated to minimize the expected total cost. Given the distributional ambiguity, we formulate a distributionally robust optimization model based on partial demand information. To solve the model efficiently, we propose a two-phase decomposition framework. Phase 1 applies an optimal static rule for integer prepack decisions under a target-oriented reformulation. We also develop an exact binary search algorithm to enhance the computational efficiency for the deterministic counterpart. Fixing prepack decisions, Phase 2 utilizes a linear decision rule to approximate adaptive continuous decisions. We evaluate the performance, benefit, and practical applicability of implementing the proposed framework through extensive numerical experiments using both synthetic data and real-world demand data from JD.com. Some technical and managerial insights are derived from the numerical results.
We study robust chance-constrained problems with mixed-integer design variables and ambiguity sets consisting of discrete probability distributions. Allowing some classes of non-convex constraint functions, we develop a branch-and-cut framework using scenario-based cutting planes to generate lower bounds. The cutting planes are obtained by exploiting the classical big-M reformulation of the chance-constrained problem in the case of discrete distributions. Furthermore, we include the calculation of initial feasible solutions based on a bundle method applied to an approximation of the original problem into the branch-and-cut procedure. We conclude with a detailed discussion about the practical performance of the branch-and-cut framework with and without initial feasible solutions. In our experiments we focus on gas transport problems under uncertainty and provide a comparison of our method with solving the classical reformulation directly for various real-world sized instances.
The growing prevalence of direct-to-consumer channels has intensified supplier encroachment concerns for retailers. While retail service effort is commonly used to stimulate demand and deter supplier encroachment, its effects often persist across selling seasons through a carry-over effect. Despite its practical relevance, the role of the carry-over effect in shaping supplier encroachment decisions remains largely unexplored. In this paper, we examine how the carry-over effect of retail service effort influences supplier encroachment and the effectiveness of retailer deterrence strategies. We develop a two-period Stackelberg game-theoretic model between a supplier and a retailer, informed by consumer survey data and practitioner interviews with retailer and supplier firms. Our results show that retail service effort does not always deter supplier encroachment. When the carry-over effect is sufficiently strong, the supplier can partially free-ride on the retailer’s past service effort, making supplier encroachment attractive even at higher direct selling costs. We further find that strategic inventory complements service effort only when the retailer carries a limited amount of inventory across selling periods. Interestingly, moderate order quantity restrictions imposed by the supplier facilitate supplier encroachment, whereas excessive restrictions suppress demand and reduce the supplier’s incentive to encroach. Finally, under upstream supplier competition, supplier encroachment becomes more likely when competing products are highly substitutable, and the carry-over effect is strong. Overall, our findings demonstrate that the carry-over effect is a critical driver of supplier encroachment decisions and alters the effectiveness of traditional retailer deterrence mechanisms.
The vehicle routing problem with load-dependent cost is an extension of the classical capacitated vehicle routing problem in which the cost of traveling along an arc is dependent on the load carried by the vehicle. For the benefit of generalization, this work considers the vehicle routing problem with simultaneous delivery and pickup, time windows, and load-dependent cost (VRPSDPTW-LDC). We utilize both continuous and discontinuous monotonically non-decreasing load-dependent cost functions. These cost structures are justified by real-life applications: First and foremost, transportation cost rises in load due to increasing fuel cost. In addition, cost functions may also show discontinuities due to toll-by-weight schemes, weight restricted passage, and lift axles that may be raised when the vehicle is empty or lightly loaded, therefore decreasing tire wear. We employ a fully equipped branch-price-and-cut algorithm to solve the VRPSDPTW-LDC. A major complication in its development is the consistent handling of the load-dependent cost in the column-generation subproblem when solved by bidirectional labeling algorithms. Indeed, in the VRPSDPTW-LDC, the precise load on board is not known when a partial path is constructed. We provide a unifying description of the associated resource extension function for forward and backward labeling. In several computational experiments, we analyze algorithmic components of the branch-price-and-cut algorithm, and give managerial insights on the impact of the cost structure on key metrics such as total cost, the number of routes, and the average load carried in an optimal solution.
Online food-delivery platforms rely on delivery-time benchmarks to manage service quality and customer expectations. This paper studies how the design of these benchmarks affects operational decisions when delivery outcomes are uncertain and lateness is penalized more heavily than early delivery is rewarded. We model a platform that chooses dispatch intensity over time while performance is evaluated against a benchmark that may either remain fixed or updated based on recent deliveries. The analysis shows that benchmarks which adapt to recent performance can reduce dispatch effort: when a series of fast deliveries causes future service standards to become more demanding, a forward-looking food-delivery platform may restrain current dispatch intensity, such as courier prioritization or surge deployment, to limit exposure to higher penalties from subsequent late orders. In volatile environments where delivery times are heavily influenced by traffic, restaurant delays, or weather, fixed externally anchored benchmarks perform better by insulating service standards from noise. In more stable settings where performance is predictable and improvements persist, internally adaptive benchmarks perform better by allowing standards to reflect underlying capability. We provide sufficient conditions for preference of each regime and develop an asymptotic characterization showing why optimal benchmark design tends to select externally anchored or internally adaptive regimes, rather than intermediate hybrids, as the state space grows. We illustrate the theory using two stylized delivery environments that represent distinct operational regimes commonly faced by food-delivery platforms.
In this work, we extend the Multi-Depot Cumulative Capacitated Vehicle Routing Problem (MDCCVRP) to consider two objectives. Besides its cumulative aspect, i.e., minimizing the sum of customers’ waiting time, we also consider the travel cost minimization. To tackle this problem, we propose a novel matheuristic framework, called Math-AUGMECON-II, consisting of two stages. In the first stage, a multiobjective memetic algorithm based on the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to obtain an approximation to the Pareto front. This approximation of the Pareto front is then optimized in a second stage using the Augmented ɛ-Constraint II (AUGMECON-II) approach. The performance of NSGA-II, AUGMECON-II, and Math-AUGMECON-II is evaluated by their application to a set of well-known instances of the MDCCVRP with different sizes. The analyses based on different metrics, such as the number of solutions, hypervolume, and set coverage, reveal that AUGMECON-II is a suitable choice for small instances, while Math-AUGMECON-II is more appropriate to deal with medium and large instances, including instances with a reduced fleet size. Finally, a trade-off evaluation was carried out to examine the extent to which enhancing one objective impacts the other. It revealed that improving latency leads to an increase in travel cost, while improving travel cost results in a deterioration of latency. This highlights the asymmetric compromise between both objectives.
With Industry 4.0 advancements, production environments are becoming increasingly automated. However, integrating smart robots introduces new scheduling challenges for efficiently coordinating tasks such as manufacturing assembly, product transport, and material supply. Unlike previous studies that address these tasks separately or in pairs, we address their simultaneous scheduling in a pull-based production line, where assembly tasks depend on product delivery by automated guided vehicles (AGVs) and material supply by autonomous mobile robots (AMRs). The problem is to assign product transport tasks to AGVs and material supply tasks to AMRs, sequence these tasks on each robot, and schedule assembly tasks at workstations, with the objective of minimizing the makespan. We formulate a mixed-integer linear programming model, and develop a matheuristic based on iterated local search and linear programming to tackle computational complexity of larger instances. Using a real battery manufacturing case study, we evaluate the efficacy of our methods in varying fleet sizes, the number of jobs, and the number of assembly lines. Our computational results reveal that the proposed matheuristic significantly outperforms current practice, with makespan reductions of 22% on average.
