One of the pivotal strategies for achieving net-zero aviation emissions is the replacement of conventional jet fuel with Sustainable Aviation Fuels (SAF). The very limited availability of SAF necessitates strategic allocation to flight routes to optimize costs and emission reduction. Addressing this challenge, this paper introduces an innovative adaptive robust optimization framework for the distribution of SAF to flight routes in Canada based on a range of domestic production scenarios, fuel transportation costs, and jurisdictional carbon prices. The objective is to identify the optimal location of potential SAF distribution centers and allocate SAF to flight routes over a 25-year period. This complex problem incorporates flight data from the International Civil Aviation Organization (ICAO) and uncertain projections for SAF production. Leveraging a column and constraint generation algorithm, the paper achieves global optimality in solving the problem. The findings reveal that the proposed robust model results in emission cost savings ranging from 7.13% to 18.19% across various distribution center capacities, consistently outperforming the deterministic model. This underscores the effectiveness of the proposed approach in efficiently distributing available SAF under production uncertainties. • Developed a Robust model for SAF distribution to Canadian flight routes over 25 years. • Accounted for uncertainty in SAF production, transport costs, and carbon prices. • Identified ideal SAF distribution centers and allocation strategies using real flight data. • Achieved an 8.06% reduction in emission costs compared to traditional models. • Supports aviation’s transition to net-zero emissions with efficient SAF deployment strategies.

The restoration efficiency can be significantly improved through the coordination of transmission and distribution systems. However, this process is hindered by challenges related to information aggregation, model complexity, and the uncertainty introduced by the penetration of renewable generation (RG). For this purpose, this paper proposes a novel distributed load restoration model for integrated transmission and distribution systems (ITDS) using the robust model projection method (RMPM). To achieve the distributed approach, the non convex restoration model for active distribution systems (ADSs) is first reformulated as a second-order cone programming (SOCP) problem using a sequential SOCP algorithm (SSA). The resulting high-dimensional SOCP model for ADSs is then projected into a low-dimensional space via a vertex-searching method (VSM). Next, the uncertainty of distributed RG in ADSs is considered, and the robust feasible region for the ADS restoration model is determined using the column and constraint generation (CCG) algorithm. This robust, convex feasible region is then integrated into the transmission system (TS) restoration model, which is formulated as a two-stage, three-level robust model considering the RG uncertainty. By adopting this restoration scheme, optimal coordination between ADSs and TSs is achieved with limited information exchange, thereby alleviating the communication burden. Moreover, the model's solvability can be ensured due to its low-dimensional, convex structure. Finally, the effectiveness of the proposed method, as well as its superiority over existing approaches, is validated through numerical experiments.

Multi-source network-level pavement friction measurements via instrumented and dynamically routed autonomous vehicles

Surgical trays are assembled with surgeons’ preference cards to satisfy the demand of multiple surgery types, leading to reprocessing waste when unused instruments are exposed in an open container. We explore a novel probabilistic tray optimisation problem on reducing surgical instrument waste by strategically incorporating peel packs (PPs). The problem involves multiple surgery types, instruments, and expected PP configuration design under expert guidance. Our primary goal is to minimise total tray processing costs via the probability of instrument usage while ensuring all required sterile instruments are available during procedures. The decision to open a custom PP hinges on the availability of its assigned instrument. Failure to immediately access the required instrument necessitates retrieving an entirely new surgical tray from the Sterile Processing Department, which is a costly scenario we aim to prevent. We formulate the tray optimisation problem (TOP) as a mixed-integer program (MIP) and propose two distinct solution approaches to tackle its computational complexity: (1) a Clustering-Based Decomposition Approach (CBDA) designed for computational efficiency, and (2) a Column Generation Decomposition Approach (CGDA) providing near-exact solutions. Through numerical experiments using simulated data, we analyse the scalability of the proposed methods. Our results indicate that an increase in the number of instrument types has a significantly impressive impact on the computational time of the CBDA compared to the CGDA. We demonstrate that the CBDA exhibits robust performance, effectively providing high-quality solutions, making it a practical method for implementation in hospital settings to achieve substantial reductions in instrument tray waste.

ABSTRACT This paper addresses peak-hour over-saturation in urban metro systems by collaboratively optimizing train scheduling and passenger flow control. The objective is to minimize total passenger waiting time while ensuring the waiting time for each origin-destination (OD) pair remains within a pre-determined threshold. A space-time network is constructed to represent train trajectories and passenger assignments, tightly integrating scheduling and flow control decisions. An integer programming model is formulated and reformulated into a path-based structure, solved using a Column Generation Fairness Priority (CG-FP) algorithm to handle large-scale computational complexity. Numerical experiments on simulated datasets and real-world Beijing Metro Line 5 data demonstrate that CG-FP achieves near-optimal solutions with significantly reduced computation time compared to the direct Gurobi solver. The proposed policy outperforms the conventional First-Come-First-Served (FCFS) policy in both efficiency and fairness, with advantages especially pronounced under limited train availability, where prioritizing short-distance passengers enables faster capacity turnover.

Background: The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimization problem with the goal to design shifts to cover prearranged bus tours. The objective takes into account the operational cost as well as the satisfaction of drivers. This problem is heavily constrained due to strict legal rules and collective agreements. Objectives: The objective of this article is to provide state-of-the-art exact and hybrid solution methods that can provide high-quality solutions for instances of different sizes. Methods: This work presents a comprehensive study of both an exact method, Branch and Price (B&P), as well as a Large Neighborhood Search (LNS) framework which uses B&P or Column Generation (CG) for the repair phase to solve the BDSP. It further proposes and evaluates a novel deeper integration of B&P and LNS, storing the generated columns from the LNS subproblems and reusing them for other subproblems, or to find better global solutions. Results: The article presents a detailed analysis of several components of the solution methods and their impact, including general improvements for the B&P subproblem, which is a high-dimensional Resource Constrained Shortest Path Problem (RCSPP), and the components of the LNS. The evaluation shows that our approach provides new state-of-the-art results for instances of all sizes, including exact solutions for small instances, and low gaps to a known lower bound for mid-sized instances. Conclusions: We observe that B&P provides the best results for small instances, while the tight integration of LNS and CG can provide high-quality solutions for larger instances, further improving over LNS which just uses CG as a black box. The proposed methods are general and can also be applied to other rule sets and related optimization problems.

ABSTRACT Carriers are often reluctant to collaborate with other carriers in delivering goods to customers despite potential cost reductions. A durable collaboration requires attention to more aspects. Carriers typically wish to remain competitive, unconstrained by the collaboration, increasing profits by attracting new customers and withholding information about their customers from the other carriers. They may also wish to provide good services, such as making all deliveries consistently at approximately the same time of the day. To facilitate this setting, we introduce a multi‐period collaborative model, the “consistent collaborative vehicle utilization” framework. Carriers engage in collaboration by borrowing trucks from each other. A borrowed truck first departs from the lender's depot to the borrowing carrier's depot and then visits delivery locations based on optimal routing decisions. Customers are served exclusively by their designated carrier and in an assigned time window, selected from a set of options specified by the customers. We formulate an integer programming problem and develop a branch‐and‐price algorithm to solve it. Additionally, to address larger instances, we propose two heuristics employing column generation techniques. Our experiments demonstrate reductions of up to 43% in the number of utilized vehicles, accompanied by a profit increase of up to 15.2%.

In Wireless Sensor Networks (WSNs), sensors transmit collected data to a sink using limited battery power. Deployment in remote or inaccessible areas often necessitates networks that remain operational for long periods. Since replacing batteries in numerous sensors is often unfeasible, extending network lifetime is a primary design goal. This is typically addressed by solving four key design problems: coverage, sink placement/routing, sensor activity scheduling, and data routing. These are usually studied individually, or rarely in combination. Network reliability is also crucial for protecting against attacks or failures, preventing coverage holes and data loss. Unlike most studies, this work addresses all four design problems and network reliability in an integrated manner. We propose strategies such as Single Copy (SC) for single-path data transmission, Double Copy (DC) for multi-copy transmission, and a Hybrid (H) strategy where copying occurs in sensors transmitting to central nodes. Tests under various scenarios reveal that the SC strategy is superior for network lifetime, while the DC strategy excels in reliability. The H strategy provides a balanced performance in both lifetime and reliability. Furthermore, to enable the H strategy to find solutions efficiently in large-scale scenarios, we apply a Lagrangian Heuristic (LH) approach. The Lagrangian subproblem is solved using a Dantzig-Wolfe column generation algorithm and a feasible solution is constructed from the Lagrangian subproblem solution at each step. The performance of this heuristic is demonstrated by comparing its results to those obtained with the Gurobi solver. The results show that the LH method provides higher network lifetime compared to Gurobi, especially for medium and large-scale networks.

This paper is motivated by a real-world challenge faced by Amazon in managing spare parts inventory across its extensive logistics network. Traditional single-echelon inventory systems often lead to high capital immobilisation and inconsistent service levels, creating inefficiencies in large-scale operations. To address this, we develop and implement a two-echelon inventory optimisation approach, structuring clusters of sites around central hubs to pool demand risk, reduce lead times, and enhance service reliability. The resulting mixed integer formulation is solved using a column generation algorithm that overcomes the computational limitations of standard MILP solvers. Through an extensive case study involving 24 Amazon sites across five clusters, we demonstrate significant operational and financial benefits, including a 14–27% reduction in immobilised working capital and a 0.4–3.2% improvement in service levels. These improvements correspond to projected capital savings on the order of tens of millions of dollars when extrapolated to Amazon's global network, along with reduced downtime costs. Beyond its methodological contributions, this study delivers actionable managerial insights by providing a scalable decision-support tool for firms seeking to optimise distributed inventory systems. The column generation algorithm enables real-world implementation for large-scale high-volume supply chains. By bridging optimisation theory with industry implementation, this research offers a concrete roadmap for improving supply chain resilience and cost efficiency in multi-echelon inventory management.

This study proposes an intelligent decision-making framework integrating blockchain technology, the Internet of Things (IoT), and a mixed-integer linear programming (MILP) model to optimize food distribution networks, targeting profit maximization. The framework leverages blockchain’s core capabilities—decentralization, immutability, and cryptographic security—to establish a trusted foundation for real-time, verifiable data sharing across the supply chain. IoT sensors continuously monitor critical parameters (i.e., temperature, humidity, location), with the blockchain platform (Hyperledger Fabric-based) ensuring the authenticity and tamper-proof storage of this data, enabling reliable cross-node interaction. This integration facilitates the dynamic coordination of temperature-controlled warehousing, transportation allocation, demand fulfillment, and quality-differentiated dynamic pricing strategies that account for market competition. Moreover, a column generation algorithm is proposed to solve the MILP model efficiently. Numerical experiments based on Walmart operational data validate the effectiveness of the proposed framework and derive management insights. The results suggest that retailers should prioritize optimizing internal pricing over reacting to competitors, especially for essential goods; warehouse deployment must balance scale and resource efficiency; and temperature zone settings should align with operational scale to minimize costs while preserving quality. By positioning blockchain as the reliable mechanism for enforcing quality requirements and supporting real-time decision-making in the MILP model, this study provides a practical tool for decision-makers to enhance profitability and ensure stringent quality compliance in food distribution networks.

Earthquake disasters often cause communication base stations to fail, severely hindering rescue operations and information transmission. While traditional air-ground collaborative emergency communication systems can rapidly restore communications, they still face challenges such as the “time gap” caused by the endurance limitations of unmanned aerial vehicle (UAV) and the “spatial blind spots” resulting from the uncertainty of road disruptions. These issues reduce the continuity and reliability of system services. To address the robustness of air-ground platform coordinated deployment and path planning under uncertain road disruptions, this paper proposes a two-stage distributionally robust deployment and path planning (DRDPRP) method for fixed-wing UAV and ground unmanned vehicles (UGVs) in post-disaster emergency communications. This method constructs a distributionally robust uncertainty set based on a probabilistic distance metric to characterize road disruption risks. It establishes a two-stage distributionally robust optimization model to jointly optimize the deployment and paths of fixed-wing UAV and UGVs. Concurrently, it employs the Column and Constraint Generation (C&CG) algorithm as the solution framework, combined with branch-and-bound and local optimization strategies to enhance computational efficiency. Simulation results demonstrate that this method generates more robust collaborative deployment plans under road disruption uncertainties, thereby enhancing the continuity and reliability of post-disaster emergency communication systems.

Effective monitoring is vital for maintaining interconnected infrastructure systems, where components are prone to failure without proper servicing. However, designing inspection routes remains computationally difficult due to high complexity and inherent uncertainties of large-scale infrastructure systems. This paper investigates the deployment of multi-vehicle fleets, such as unmanned aerial vehicles (UAVs), to inspect spatially distributed components subject to uncertain travel times, inspection durations, and failure risks. Notably, the probability of component failure depends on inspection timing, creating decision-dependent (endogenous) uncertainty. We model this as a variant of a stochastic multi-vehicle routing problem and formulate a two-stage stochastic mixed-integer program based on finite samples. We propose a scenario decomposition framework that integrates column generation and random coloring techniques to accelerate subproblem resolution. We further provide theoretical analyses of the algorithm’s finite convergence and optimality guarantees under a user-specified probabilistic error tolerance. Numerical experiments on networks of varying topologies, including IEEE and EPANET systems, demonstrate the computational efficiency and effectiveness of our approaches. Across all large instances, our algorithm achieves an optimality gap below 4% and consistently outperforms state-of-the-art optimization solvers and the adaptive large neighborhood search as a heuristic benchmark.

Abstract This article probes the origins of the Column Generation technique. It begins with Kantorovich’s classic 1939 work, correcting widespread misconceptions about his contributions to the Cutting Stock Problem. It then brings to light Kantorovich and Zalgaller’s lesser-known 1951 book, which is revealed to contain a complete Column Generation algorithm. The article also places these contributions in the context of the turbulent USSR’s political and ideological environment, essential for a deeper understanding of their significance.

Material waste from suboptimal cutting practices in Mechanical, Electrical, and Plumbing (MEP) systems presents challenges in building engineering projects. While Building Information Modeling (BIM) provides data foundations, effective utilization for cutting optimization remains unresolved. This study proposed an optimization methodology for large-scale one-dimensional cutting stock problems derived from BIM data. A method for MEP piping data collection and statistical analysis was established using Revit API. A mathematical model minimizing raw material consumption costs was constructed, considering pipe requirements and material supply constraints. A column generation algorithm applicable to single and multi-specification stock pipe cutting was developed to obtain optimal cutting schemes through iterative processes. Compared with Genetic Algorithms (GA) and Greedy Algorithms (GRA), the proposed method demonstrated superior performance. Under single-specification conditions, material waste rate reached 0.54% with 1040 m consumption. Multi-specification optimization maintained waste rates below 1% with 1025 m consumption, confirming the approach’s feasibility and providing theoretical foundations for complex resource optimization problems.

Operating room planning and scheduling are vital components of hospital management, contributing to improved efficiency, patient satisfaction, staff well-being, and overall quality of care delivery. In this paper, we propose a novel mixed integer programming model to formulate integrated operating room planning and scheduling problems, where several mandatory and elective surgeries are to be assigned and scheduled in operating rooms on different days. Aside from the standard working hours in each operating room, we also take into account the potential for performing surgeries in overtime periods. In addition, our approach also takes into account the availability of surgeons by considering their allowed surgical time on each day. We propose a column generation (CG) algorithm to solve large-scale instances. In order to enhance the CG, we integrate the Reinforcement Learning Algorithm and the Genetic Algorithm and develop a hybrid algorithm to generate initial columns for the CG algorithm. For our analysis, we employed two sets of test instances: one consisting of synthetic data and the other based on real-world cases from a local hospital in Naples, Italy. Computational experiments demonstrate that our proposed model and methodology yields an average optimality gap of 1.23% for synthetic instances and 1.49% on real-world scenarios, significantly outperforming previous solution methodologies in the literature. Additionally, we demonstrate that the developed CG algorithm provides a high-quality solution for large-scale instances where other models and methods fail to obtain even a feasible solution. To further evaluate robustness under uncertainty, we examined scenarios with ± 20 % variability in surgery durations. The results indicate that incorporating a 120-minute buffer time minimises the overall cost. Moreover, we investigated the impact of emergency surgeries by either introducing additional cases or escalating surgical priorities. For synthetic instances, the inclusion of emergency surgeries increased the total rescheduling cost by 4.13%, whereas in the real-world Naples cases, priority escalation led to only a 0.11% increase, highlighting the resilience of our proposed model in practical hospital settings.

Under the “dual carbon” goals, this study focuses on realizing energy exchange among multiple microgrids via shared energy storage to promote sustainable energy transition. Accordingly, a distributed robust optimwhichization strategy is proposed in this paper. Addressing the uncertainty of distributed renewable energy sources within microgrids, the scenario set generated by the Wasserstein generative adversarial network with gradient penalty and pruned by the K-means++ clustering algorithm serves as the initial renewable energy scenario for the distributed robust optimization set. Combining Nash theory, a cooperative game operation model is constructed. The benefit distribution model based on contribution factors ensures a fair benefit allocation scheme. The parallelizable column and constraint generation algorithm is employed to enhance computational efficiency. Case studies demonstrate that compared to scenes produced by other methods, the proposed model has the lowest alliance operating cost. It more effectively captures renewable energy uncertainty and lowers system operational costs. The respective efficiency improvement rates for each microgrid are as follows: 4.6%, 5.0%, and 4.1%, ensuring a fair profit distribution scheme. This study provides a technical reference for realizing the sustainable development of a multiple microgrid system, contributing to the global goal of low-carbon energy transition and sustainable development.

An efficient column generation approach for crew re-scheduling and recovery in urban rail transit systems under emergency conditions

Optimizing urban transport for disabled individuals with shared wheelchair and attendant services: A column generation heuristic

Model and algorithm for the quantity adjustment user equilibrium traffic assignment problem with link capacity constraints

Abstract In radiation therapy (RT), radiation from linear accelerators is used to kill malignant tumor cells. Scheduling patients for RT is difficult both due to the numerous medical and technical constraints, and because of the stochastic inflow of patients with different urgency levels. In this paper, we present a Column Generation (CG) approach for the RT scheduling problem. The model includes constraints such as different machine compatibilities and individualized patient protocols, as well as planned interruptions in treatments due to maintenance on machines. Data from Iridium Netwerk, the largest cancer center in Belgium, is used to evaluate the CG approach. The results show that using a dynamic time reservation method to handle uncertainty in future urgent patients works very well. Furthermore, the schedules generated by the CG algorithm are clinically validated and compared to historical clinical schedules for a time period of one year. The CG generated schedules are shown to decrease the average patient waiting time by 80%, improve the average consistency in appointment times by 80%, and increase the number of treatments scheduled on the best suited machine by more than 90% compared to the manually constructed clinical schedules. Thus, the CG approach to automatically generate schedules for RT can improve the quality of the schedules significantly while saving the clinic many hours of administrative work every week.