Efficiently allocating resources to enable flights to land and take-off at an airport is a heavily constrained problem. Airlines request to use slots , where permission is granted to use airport infrastructure, which are allocated within the limits of the capacity of an airport. As demand for slots often significantly exceeds supply, this can lead to airlines being allocated undesirable slots that do not align with their intended operations. This issue is exacerbated when schedules are created independently at different airports across a network, as undesirable allocations may result in infeasible airline operations. This paper introduces a novel integer linear program (ILP) formulation for the network slot allocation problem, incorporating rejected requests, flight time flexibility and seasonality. We investigate solving the network-level slot allocation problem simultaneously across a network, compared to allocating slots at each airport independently. Our results show that scheduling over the network simultaneously ensures the feasibility of operational constraints that are not met when each airport is scheduled independently. Additionally, a matheuristic destroy-and-repair approach is developed to schedule flights over a network of ten of the largest airports across Europe. The flight request data used is derived from the real-world operations at each airport. The proposed matheuristic approach leads to comparable solutions to an exact solver within significantly shorter run times, contributing new tools that can be deployed by schedulers for real-world scenarios within a reasonable computational time.

Given a connected graph G , a set of vertices X ⊂ V ( G ) is a weak k -resolving set of G if for each two vertices y , z ∈ V ( G ) , the sum of the values | d G ( y , x ) − d G ( z , x ) | over all x ∈ X is at least k , where d G ( u , v ) stands for the length of a shortest path between u and v . The cardinality of a smallest weak k -resolving set of G is the weak k -metric dimension of G , and is denoted by wdim k ( G ) . In this paper, wdim k ( K n □ K n ) is determined for every n ≥ 3 and every 2 ≤ k ≤ 2 n . An improvement of a known integer linear programming formulation for this problem is developed and implemented for the graphs K n □ K m . Conjectures regarding these general situations are posed.

ABSTRACT This work presents an optimization approach for the stenter finishing process of knit fabrics in textile industries. An optimization model with Mixed Integer Linear Programming formulation was developed to minimize energy consumption and process costs with resizing and sequencing of batches in stenter‐type machines, the main energy bottleneck in the sector. The objective function to be minimized is the total operational cost, considering electricity and labor. A case study was conducted with real data from an industry located in the state of Paraná, Brazil, for four types of knit fabrics with a daily demand of 70 000 kg, distributed across six stenter units. Results demonstrated that the optimized solution prioritizes higher yield raw materials in higher capacity machines. A simulation was carried out replacing two machines with a more efficient unit, reducing total cost in 9.2%. It is concluded that the model is effective for strategic decision‐making and allows in the process.

Maximizing genetic response to selection while constraining inbreeding is a central challenge in breeding and conservation. Classic optimal contribution selection methods address this by managing average population coancestry. However, this often results in complex, non-linear optimization problems that cannot be guaranteed to reach a global optimum. Furthermore, many applications require a stricter pairwise constraint to avoid immediate inbreeding in offspring. Here, we present a binary integer linear programming formulation to select an optimal subset of individuals under a strict maximum tolerable pairwise genomic relationship threshold. We construct a binary matrix indicating whether each pair exceeds this threshold. This reformulation transforms the problem from a complex non-linear program into a binary integer linear program. While this formulation remains NP-hard, the linearity allows modern solvers to efficiently navigate the solution space and, when convergence is achieved within the imposed runtime and tolerance settings, certify global optimality, a key advantage over heuristic approaches. We demonstrate the method using two distinct datasets: a large Norway spruce breeding population and a conservation population of German Black Pied cattle. We explore the trade-offs between the selection response, the relationship threshold, and the maximum number of individuals that can be selected under the threshold. Although large, dense problem instances remain computationally demanding, our results show that typical applications can often be solved to proven global optimality in seconds, whereas denser instances may terminate with a remaining optimality gap. This method is a practical solution for breeders and conservation geneticists to select optimal subsets under a strict relationship threshold, enabling applications from maximizing gain in breeding populations to establishing genetic reserves for endangered species.

ABSTRACT Efficient neuron grouping is critical to minimize the communication cost between processing elements and ensure balanced computational workloads, especially in modern hardware accelerators. This paper presents a novel Integer Linear Programming (ILP)‐based method for communication‐aware and load‐balanced neuron grouping for neural network accelerators. The proposed ILP formulation supports fully connected and pruned neural networks, making it suitable for contemporary sparse architectures. To evaluate the effectiveness of the proposed method, we conducted extensive experiments on a diverse set of neural network benchmarks with varying sizes and connectivity patterns. Results demonstrate that our method significantly reduces execution time, achieving speedups of up to three orders of magnitude for fully connected networks, while maintaining optimality. Unlike prior ILP‐based approaches, which fail due to excessive memory consumption on large networks, our method successfully computes solutions for previously intractable benchmarks. However, ILP remains a computational bottleneck for large pruned networks, indicating the need for further scalability improvements. These findings establish our solver‐optimized ILP formulation as a practical tool for neuron grouping in high‐performance Network‐on‐Chip‐based manycore accelerators, bridging the gap between mathematical optimization and real‐world hardware constraints.

Abstract In the classical firefighter game, a fire breaks out on some vertices of an undirected connected graph at time zero. At each subsequent time step, a fixed number of firefighters can protect one vertex each from catching fire. Afterwards, the fire spreads from each burning vertex to every adjacent vertex that is neither burning nor defended. The game ends when the fire can no longer spread. The goal is to find a defense strategy that maximizes the number of non-burning (saved) vertices. In this work, we first revisit the classical integer linear programming formulation and then present several improvements for it, as well as two new formulations and tighter bounds on the maximum duration of the game. Moreover, we relax the classical assumptions that all vertices have uniform values and costs, i.e., we allow vertices to have different values and costs for being defended. Furthermore, instead of a fixed number of firefighters, we are given a defense budget that we can spend each time step to defend the vertices. We call this the cost-value firefighter game. We present three different integer linear programming formulations for the problem, along with a series of inequalities to strengthen the formulations and tight bounds on the maximum duration of the game.

This paper addresses the Distance-Constrained Inventory Routing Problem (DCIRP), a complex problem that combines inventory management and vehicle routing in a logistics context. The problem arises in the context of a specialty gas delivery company that maintains a specialty gas holding facility at each customer’s site and uses several trucks to deliver specialty gas, with the additional constraint that drivers are limited to the number of kilometers they can drive each day. A Mixed Integer Linear Programming (MILP) formulation is proposed to model the DCIRP. The DCIRP is a variant of the Inventory Routing Problem (IRP), and an NP-hard combinatorial optimization problem. The main objective of this research is to improve the efficiency and effectiveness of DCIRP resolution, while accounting for vehicle capacity constraints, customer inventory levels, and delivery route distance constraints. By optimizing routes and inventory management, the company’s operations become more sustainable. To solve the problem, three solution approaches are proposed. The first is an exact method based on the MILP formulation. The second is a matheuristic that uses an inventory-first, route-second (IFRS) approach, including a minimum route cost approximation and a local search procedure. The results show that the proposed matheuristic produces high-quality solutions with a reasonable computational effort.

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.

This work addresses the increasing complexity of urban mobility by proposing an intelligent optimization and resource-allocation framework for Vehicle-to-Infrastructure (V2I) communications. The model integrates a macroscopic mobility analysis, an Integer Linear Programming (ILP) formulation for optimal Road-Side Unit (RSU) placement, and a Smart Generic Network Controller (SGNC) based on Q-learning for dynamic radio-resource allocation. Simulation results in a realistic georeferenced urban scenario with 380 candidate sites show that the ILP model activates only 2.9% of RSUs while guaranteeing more than 90% vehicular coverage. The reinforcement-learning-based SGNC achieves stable allocation behavior, successfully managing 10 antennas and 120 total resources, and maintaining efficient operation when the system exceeds 70% capacity by reallocating resources dynamically through the -based alert mechanism. Compared with static allocation, the proposed method improves resource efficiency and coverage consistency under varying traffic demand, demonstrating its potential for scalable V2I deployment in next-generation intelligent transportation systems.

The main objective of this work is to estimate the carbon dioxide (CO₂) emissions from natural gas-fired combined cycle gas turbine (CCGT) units in Libya and to integrate these estimations within an environmental power dispatch model that considers several power plants. The study begins with a preliminary design aimed at calibrating the model using the limited data provided by manufacturers. Off-design operating points are also investigated in order to estimate emissions across the full operating range of the units. The results show good consistency with emission coefficients reported in the literature for this type of units. Subsequently, carbon costs are used as input parameters in a Unit Commitment (UC) problem, where a Mixed Integer Linear Programming (MILP) formulation is applied to minimize the total emissions of a set of units within the Libyan power grid. The emission factors obtained for the simulated network display values close to the recorded field data, validating the developed model. Finally, a tightened formulation of the dispatch problem is introduced, aiming to reduce computational time while ensuring high-quality performance of the returned solutions. and Results show that prioritizing newer and more efficient plants reduces national emissions by 10–15%. Keywords: Combined Cycle Gas Turbine, Design, CO₂ Emissions, Environmental Unit Commitment, Power Dispatch, Optimization.

Scheduling challenges in multi-line garment production: Application to an Algerian case study

Inland waterways can be an attractive under-utilized alternative to road transport. In the current situation, heavy trucks transport residual household waste from municipalities to incineration plants around the Netherlands. Logistics research groups have suggested using barge pushing ships for household waste transport to reduce emissions and costs. We analyze this suggestion for a case study involving the residual household waste of 55 municipalities across three provinces in the Netherlands. A Mixed Integer Linear Programming formulation is used to find the optimal combination of trucks and barge pushing ships in this waste network. The results demonstrate that adopting electric pusher ships can achieve significant reductions in costs (19%), emissions (41%), and waste carrying truck traffic (48%), compared to truck-only solutions. Diesel cargo ships are also shown to outperform truck-only approaches but are less effective than electric alternatives in most metrics. Sensitivity analysis shows that the solutions are fairly robust to parameter variations.

Industrial Policies for Multi-Stage Production: The Battle for Battery-Powered Vehicles

This study introduces a variant of the drone delivery problem called the heterogeneous fleet drone delivery problem with lateness considerations. The problem considers a fleet of drones that differ in speed, payload capacity, and battery endurance, with the objective of minimizing the total lateness, computed by considering each customer's scheduled delivery time for all customers. Two mixed integer linear programming formulations are proposed to find the optimal solution of the stated problem. The mathematical models vary in the number of variables and constraints, and their effectiveness is compared using test instances generated in this study. In addition to the mathematical models, a metaheuristic algorithm based on modifications to the farmland fertility algorithm (FFA) is developed. This metaheuristic incorporates two local search methods with different encoding schemes. Comparative experiments indicate that the proposed Modified-FFA outperforms both the Classical-FFA and simulated annealing in solution quality. The results also show that local search methods with different encoding schemes exhibit distinct performances, highlighting the impact of encoding choices on efficiency. Furthermore, a comprehensive sensitivity analysis is also conducted to explore the effects of drone-related parameters, such as payload and velocity, on the total weighted lateness.

Kidney exchange problems with immunosuppressants extend the classical kidney exchange problem by allowing a limited number of arcs that do not belong to the compatibility graph to be included in the solution. Among these, the kidney exchange problem with reserve arcs (KEP-RA) assumes that any arc can be made compatible, whereas the kidney exchange problem with half-compatible arcs (KEP-HCA) assumes that this is the case only for a subset of arcs. Starting with KEP-RA, we first show that existing integer linear programming formulations for the kidney exchange problem can easily be extended to include reserve arcs. We then demonstrate that there always exists an optimal KEP-RA solution in which every cyclic set of exchanges contains at most one reserve arc, and we use this property to develop effective variable reduction procedures and new ad hoc modeling structures. We also extend these findings to the case where nondirected donors are included. Experiments show that trivial model extensions are not able to cope with medium-sized instances, whereas our enhanced models can solve instances with up to a thousand recipient-donor pairs. We also evaluate the number of transplants enabled by each reserve arc in various settings, demonstrating that although reserve arcs tend to have a diminishing return, there are instances for which this is not the case. Finally, we demonstrate how our techniques can be integrated into a variable and constraint generation algorithm to solve KEP-HCA and show that its performance complements that of a trivial model extension. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: D. Manlove was supported by the Engineering and Physical Sciences Research Council [Grant EP/X013618/1]. This work used the Dutch national e-infrastructure with the support of the SURF Cooperative [Grants EINF-8220 and EINF-12272]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.1071 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.1071 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Threshold logic is an alternative representation of conventional Boolean logic and re-attracted researchers’ attention in recent years. Previous works have demonstrated that a 2 nd -order threshold logic gate (2-TLG) could have a lower area cost than a 1 st -order TLG (1-TLG) and proposed an integer linear programming (ILP)-based method for identifying 2-TLGs. However, the method could suffer from inefficiency for complex Boolean functions. In this article, we first enhance the ILP-based method for transforming a 1-TLG into a 2-TLG with a lower area cost. We observe that for a 2-TLG, most of the 2 nd -order weights (2-weights) are zero. That is, in the ILP formulation, most of the variables for the 2-weights can be set to zero without quality sacrifice. Thus, to identify the 2-weights that are more likely to be non-zero, we first propose sufficient conditions to derive a 2-TLG from a 1-TLG by extracting 2-weights. We then simplify the ILP formulation by eliminating the non-extracted 2-weights to facilitate the ILP-solving process. Furthermore, we propose a synthesis scheme for 2 nd -order threshold logic based on the enhanced ILP-based method. We leverage the state-of-the-art 1 st -order threshold logic synthesis technique to generate a 1 st -order threshold logic network (1-TLN) first and then transform it into a 2 nd -order TLN (2-TLN). The experimental results demonstrate that when transforming a set of 1-TLGs into 2-TLGs, the enhanced ILP-based method reduces the total CPU time by approximately 31% across all 1-TLGs, with only an average quality loss of 0.07% in terms of the area cost reduction rate. Additionally, when transforming two sets of 1-TLNs with different maximum fanin counts into 2-TLNs, the proposed method achieves average area cost reductions of 8.04% and 22.18%, respectively.

Effective scheduling and resource management remain an enduring challenge in large-scale cloud computing contexts. Intermittent workloads, coupled with workloads that have dependencies, can affect system performance. This paper proposes a novel hybrid model, VmSS–TGDA (Virtual Machine Speed Selection with Task Grouping and Dependency Analysis), to improve cloud resource utilization. The approach centers on simultaneous execution time optimization, energy efficiency, and resource fairness. The proposed workflow units are produced by using GScore-based grouping and probabilistic task dependency prediction to generate workflows with high levels of correlation. The workflow units are then executed according to an Integer Linear Programming (ILP) formulation that holds the virtual machine speed, or the selected speed of the virtual machine, as the guiding metric. The theoretical structure and framework of the presented model is based on a set of analytical equations that include all aspects of delay, utilization, energy, and reliability and establish the relationships between them. The experimental results confirm that we can achieve substantial improvements in both Task Throughput Efficiency (TTE) and Resource Allocation Fairness Index (RAFI) when compared with legacy scheduling models, achieving up to 22% reductions in execution times and up to 35% reductions in resource utilizations. This research also confirms the balance between cost-effectivity and efficiently processing all workloads using a correlation heatmap and 3D multi-objective performance surface. Ultimately, Ultimately, the VmSS–TGDA paradigm provides theory-informed empirical and experimental evidence of improved cloud resource utilization in large-scale cloud systems.

Conflict detection and resolution models typically consider train separation distances based on a number of blocks corresponding to conventional fixed-block signalling systems. However, modern distance-to-go railway signalling systems, such as the European Train Control System (ETCS), use braking curve supervision, resulting in train- and speed-dependent train separation distances. This paper proposes a modelling approach that incorporates train- and speed-dependent brake indication points and the resulting blocking times, enhancing conflict detection and resolution models for distance-to-go signalling. By integrating these enhancements into the state-of-the-art RECIFE-MILP model, a mixed integer linear programming formulation explicitly representing fixed-block distance-to-go signalling is obtained. The enhanced model is evaluated considering the state-of-practice fixed-block distance-to-go signalling system ETCS Level 2, and is compared with the original model for conventional fixed-block signalling in two real-world case studies. Results show that the shorter train separation under distance-to-go signalling leads to different rescheduling decisions, including a significant number of reroutings and some reorderings. With that, reductions in total train delay are achieved for 98% and 55% of the respective case study instances. While the mean reductions are below 1%, reductions of up to 7% are observed. These findings illustrate the operational relevance of incorporating distance-to-go principles into conflict detection and resolution modelling.

This paper investigates a load balancing problem within the context of postal sorting operations at La Poste, the French postal service. Faced with declining mail volumes, La Poste must reorganise its processes to maintain service quality and operational efficiency. Mail sorting is modelled as a Simple Assembly Line Balancing Problem (SALBP-2), where mail items (tasks) are assigned to containers (stations) in a way that minimises load imbalances while respecting precedence constraints. These constraints take the form of independent chains, as each mail route follows a fixed delivery sequence. We propose three resolution methods: an exact approach based on a Mixed Integer Linear Programming (MILP) formulation, a metaheuristic algorithm based on simulated annealing, and a fast heuristic designed for industrial deployment, which exploits the precedence constraints structure for faster convergence. The metaheuristic and the heuristic are tested on academic and real-world datasets much larger than those commonly used in the literature. In order to use them several times a day, the resolution method needs to be fast in terms of calculation time. Due to its strong performance and low computation time, the heuristic we propose has been implemented on industrial platforms at La Poste and is now used daily.

This study introduces two different Linear Programming (LP) formulations and a Mixed Integer Linear Programming (MILP) formulation to optimize Energy Storage System (ESS) sizing in different scenarios, aiming to identify the solution that maximizes the return on investment associated with ESS installation. The proposed models are suitable for both railway substations supporting train operations with integrated photovoltaic (PV) energy and on-board ESS. The models consider operational variables, energy tariffs, load demands, and economic implications, proposing adaptable solutions across a variety of scenarios. Two real-world case studies are used to validate the models, and extensive numerical tests are performed to assess the effectiveness of the proposed models and study the impact of different parameters on the installation choices and the profitability of the investment. In the first case study, financial benefits have been analyzed by examining the impact of varying installed capacity of PV plants and cost-to-price ratios. Results demonstrate that, under current cost parameters, installing an ESS is economically advantageous. Moreover, limiting the State of Charge (SoC) to an interval between 20% and 100% doubles the profitability index (PI) of the investment, compared to scenarios with no SoC restrictions. In the second case study, concerning the deployment of an on-board ESS for hybrid trains in non-electrified track scenarios within the European context, results show that optimizing battery capacity and power line allocation enables partial electrification, significantly reducing infrastructure costs while ensuring operational requirements.