Integer Linear Programming Model Research Articles

Locating Senior-Friendly Restaurants in a Community: A Bi-Objective Optimization Approach for Enhanced Equality and Convenience

Senior-friendly restaurants are dining establishments that cater specifically to the needs and preferences of older adults in a community. As the physical capabilities of seniors progressively decline and their activity spaces contract over time, determining optimal locations for such restaurants to ensure their accessibility becomes crucial. Nevertheless, the criteria for the location selection of senior-friendly restaurants are multifaceted, necessitating the consideration of both equality and convenience. First, these restaurants often receive government funding, which means that equitable access should be guaranteed for all community residents. Second, the daily activity patterns of seniors should be accounted for. Therefore, these restaurants should be situated in close proximity to other essential facilities utilized by seniors, such as recreational facilities that accommodate routine postmeal activities. Despite the long-standing application of spatial optimization approaches to facility location issues, no existing models directly address the location selection of senior-friendly restaurants. This study introduces a bi-objective optimization model, the Community Senior-Friendly Restaurants Location Problem (CSRLP), designed to determine optimal locations for senior-friendly restaurants, taking into consideration both service coverage and proximity to recreational facilities simultaneously. We formulated the CSRLP as an integer linear programming model. Simulation tests indicate that the CSRLP can be solved both effectively and efficiently. Applying the CSRLP model to two communities in Dongcheng District, Beijing, China, we explored Pareto optimal solutions, facilitating the selection of senior-friendly restaurant locations under diverse scenarios. The results highlight the significant value of spatial optimization in aiding senior-friendly restaurant location planning and underscore key policy implications.

Otimização do consumo energético em uma indústria gráfica

Abstract In this study, an integer linear programming model is proposed to support the Production Planning, Scheduling and Control sector of a printing company. The model considers two objective functions to deal with the problem, the first is to minimize the costs with electric energy consumption and the second is to minimize the machine operating time. Both objectives are related to the assignment to different sets of printing and finishing machines for the manufacture of the ordered items. Operating constraints at the factory are considered, such as the setup time limits, how the machine is operated, the types of printed item, the production capacity and the demand. In addition, a heuristic was developed to support the production schedule, allowing adjustments in the different production shifts but respecting the assignments obtained using the mathematical model. Computational tests were performed with a set of data provided by a printing company located in the state of São Paulo.

An integer linear programming approach for a location-allocation problem in online stores industry: A real world case study

As the population grows and demand increases, cities have seen a rise in the number of chain stores. To remain competitive, these companies must reduce costs and attract more customers. A key factor in achieving this is the strategic placement of store branches, which reduces the distance between stores and customers, instilling trust and increasing their appeal while also cutting costs by reducing the need for employees to navigate longer distances. In this study, an integer linear programming model is presented with the goal of dividing a zone in Ahvaz city into several scenarios to determine the optimal number of stores while maintaining control over the distance between active stores. This research is the first to include this specific limitation in the mathematical model of the problem. The results of the study demonstrate a significant reduction in the distance between customers and stores.

An optimisation-based system for the university course timetabling: a novel integer linear programming model

An optimisation-based system for the university course timetabling: a novel integer linear programming model

A flexible train composition strategy with extra-long trains for high-speed railway corridors with time-varying demand

To accommodate the uneven spatio-temporal distribution of passenger demand and improve the maximum transportation capacity for high-speed railway (HSR) corridors, this study proposes a demand-oriented flexible train composition strategy. The proposed strategy allows flexibility in selecting the number of train composition units (e.g., train carriages) for each train to accommodate the demand variations, where extra-long trains (longer than the length of the train station platform) might be utilized. Under such a strategy, a seat allocation method coupled with a train stopping position control strategy is proposed to avoid the need for cross-carriage walking during passenger boarding or alighting (for those extra-long trains). The train stopping position control strategy specifies the carriages that dock at or extend beyond the station platform, while the seat allocation method allocates seats within each carriage to specific origin-destination pairs. The studied problem can be formulated as an integer nonlinear programming model, where the weighted sum of the HSR operating cost and passenger travel time cost is minimized. The proposed model is then reformulated into an integer linear programming model via a series of linearization techniques. A tailored heuristic algorithm based on the variable neighborhood search (VNS) and GUROBI solver is designed to produce high-quality solutions for large-scale problems. Two numerical examples, i.e., a small example and a real-world Shanghai-Hangzhou HSR line example, are presented to illustrate the effectiveness of the proposed approach. The computation results show that, in comparison to traditional fixed and flexible train composition strategies without extra-long trains, the proposed strategy can significantly reduce the total operating cost and total travel time cost.

Integration of Google Maps API with mathematical modeling for solving the Real-Time VRP

Freight transportation is the backbone of urban economies and plays a critical role in the smooth functioning of cities. As such, devising efficient methods for freight transportation planning is of paramount importance. One of the most crucial aspects affecting the efficiency of freight transport is the variability in travel speeds, impacted by factors such as traffic congestion. While traditional approaches often rely on GPS technologies and associated routing services—which can be expensive—for planning, these methods also necessitate frequent re-optimization due to ever-changing traffic conditions. To address these challenges, we introduce a novel solution that integrates real-time traffic data into daily vehicle route planning. Specifically, our method incorporates Google Maps API for traffic congestion estimation and utilizes a Mixed Integer Linear Programming (MILP) model to determine optimal routes for an entire day. We tested our methodology in a major U.S. city and found that it outperforms conventional approaches by up to 18% in terms of routing time, underscoring its practical relevance and efficiency.

Optimal Operation of an Innovative Electric Vehicle Charging Hub directly fed by Renewables

The reduction of Green House Gases (GHGs) emissions has been the top priority of the European Union (EU) in recent times. The increase in use of Electric Vehicles (EVs) to combat climate change is viable only with the use of Renewable Energy Sources (RESs) to power them. Since the Paris Agreement in 2015, the integration of RESs into the charging infrastructure has increased in the EU. The increasing market share of EVs in various categories has called for immediate changes in the EV charging infrastructure and in the operation of charging hubs. This paper aims to present an Energy Management System (EMS) to efficiently manage an EV charging hub fed by RESs, reducing the daily costs of operation and GHG emissions. The mathematical model of the EMS is developed in Matlab as a Mixed Integer Linear Programming (MILP) model. The MILP-based EMS is applied to the real-world case of an innovative EV charging hub located in the Ligurian region of Italy and the results of the optimization are reported.

Heterogeneous multi-drone and helicopter routing problem for reconnaissance

Helicopters and drones are widely used in military and post-disaster reconnaissance. But less attention has been paid to collaborative reconnaissance between the two, especially when drones can be launched and retrieved multiple times. We propose a synchronous routing problem of helicopter and heterogeneous multi-drone for reconnaissance, which is a new variant of the orienteering problem (OP), where the drones can visit multiple mission nodes and can reconnoiter the retrieval nodes in a single trip, with the goal of maximizing the information collected. The problem is formulated as a mixed integer linear programming (MILP) model, and then an adaptive simulated annealing algorithm (A-SA) is designed to solve the problem. Specifically, a universal high-efficiency heuristics solution evaluation method based on segment sorting is proposed. The time complexity of this method is O(n). The numerical experiments illustrate the accuracy and efficiency of the algorithm. The results also show that allowing the drones to conduct reconnaissance on the retrieval nodes can positively impact the solution.

Solving blocking flowshop scheduling problem with makespan criterion using q-learning-based iterated greedy algorithms

This study proposes Q-learning-based iterated greedy (IGQ) algorithms to solve the blocking flowshop scheduling problem with the makespan criterion. Q learning is a model-free machine intelligence technique, which is adapted into the traditional iterated greedy (IG) algorithm to determine its parameters, mainly, the destruction size and temperature scale factor, adaptively during the search process. Besides IGQ algorithms, two different mathematical modeling techniques. One of these techniques is the constraint programming (CP) model, which is known to work well with scheduling problems. The other technique is the mixed integer linear programming (MILP) model, which provides the mathematical definition of the problem. The introduction of these mathematical models supports the validation of IGQ algorithms and provides a comparison between different exact solution methodologies. To measure and compare the performance of IGQ algorithms and mathematical models, extensive computational experiments have been performed on both small and large VRF benchmarks available in the literature. Computational results and statistical analyses indicate that IGQ algorithms generate substantially better results when compared to non-learning IG algorithms.

Integrated optimization of planning and operation of a shared automated electric vehicle system considering the trip selection and opportunity cost

<abstract> <p>Shared autonomous electric vehicle systems (SAEVS) combine autonomous driving technology with shared electric vehicle services to provide advantages over traditional shared vehicle systems, including autonomous vehicle relocation and rapid response to user needs. In this study, we seek to enhance the operational efficiency and profitability of SAEVS by considering trip selection and the potential opportunity cost associated with unmet user demands. An integer linear programming (ILP) model is developed using a spatio-temporal state network to optimize the system design planning (e.g., charging facility, vehicle fleet sizing and distribution) and operational decisions (e.g., vehicle operational relocation and trip selection strategy). To handle the computational complexities of this model, we propose a Lagrangian relaxation (LR) algorithm. The performance of the LR algorithm is evaluated through a case study. The results, along with a parameter sensitivity analysis, reveal several key findings: (ⅰ) Allocating vehicles to stations with concentrated early peak demand, distributing charging facilities to stations with high total demand throughout the day and implementing vehicle relocation after the early demand peak can mitigate uneven vehicle distribution; (ⅱ) Implementing trip selection enhances SAEVS profitability; (ⅲ) Increasing opportunity cost meets user demands but at the expense of reduced profit; (ⅳ) It is recommended that SAEVS be equipped with charging facilities of suitable charging power based on operational conditions.</p> </abstract>

A design and analysis of computer experiments based mixed integer linear programming approach for optimizing a system of electric vehicle charging stations

This paper formulates a mixed integer linear programming (MILP) model to optimize a system of electric vehicle (EV) charging stations. Our methodology introduces a two-stage framework that integrates the first-stage system design problem with a second-stage control problem of the EV charging stations and develops a design and analysis of computer experiments (DACE) based system design optimization solution method. Our DACE approach generates a metamodel to predict revenue from the control problem using multivariate adaptive regression splines (MARS), fit over a binned Latin hypercube (LH) experimental design. Comparing the DACE based approach to using a commercial solver on the MILP, it yields near optimal solutions, provides interpretable profit functions, and significantly reduces computational time for practical application.

Minimizing the maximum tardiness for a permutation flow shop problem under the constraint of sequence independent setup time

In this work, we will study a permutation flow shop scheduling problem under the constraint of sequence independent setup time. In our case, each machine requires a certain setup time to process all the different jobs assigned to it. Hence, this setup time will be independent of sequence of jobs, but will depend only on the nature of machine. The optimization objective is to minimize the maximum tardiness criterion. To solve this optimization problem, an exact method, heuristics and metaheuristics are the three main resolution methods that we have used. The exact method is represented by the mixed integer linear programming (MILP) model. In terms of the second category of resolution methods, we have been focused on two methods, the first is a modified heuristic based on Johnson rule (HBJR) while the second is based on the Nawaz–Enscore–Ham (NEH) algorithm. Finally, three metaheuristics have been used, namely the iterated local search (ILS) method, the iterated greedy (IG) algorithm and the genetic algorithm (GA). Our numerical results indicate that for the problems with small size instances, the NEH heuristic outperforms HBJR approach, while for relatively large size instances, the developed IG algorithm gives best results than both other metaheuristics ILS and GA.

An integrated bus transit service for demand-responsive urban public transport

Recent mobility reports have highlighted the need of integrating Information and Communication Technologies (ICT) as an essential element in the development of intermodal and on-demand services to enhance transport flexibility. In this context, this paper investigates the improvements that could be obtained by integrating Dial-a-Ride into a bus transit service. We model the problem as a dynamic Dial-a-Ride problem with both fixed and dynamic requests. We extend an integer linear programming (ILP) model for its application to the dynamic case. To reduce computational effort, the problem is decomposed at the single vehicle level, where each best route is computed using an exact solver and new dynamic requests are assigned using a greedy insertion heuristic. We have developed the optimization model as a GIS-based tool and applied it to a realistic case of a bus transit service in the city of Benevento (Italy). The results show the benefits that could be obtained with the proposed integrated service when also compared to fixed routes and micro-mobility.

Development of a Linear Integer Programming Model for Solving Cutting Stock Problem in the Manufacturing Industry

Cutting stock problem is a problem generally encountered in many manufacturing industries such as the furniture, clothing, glass production, leather, paper, textile, metals industries amongst others most especially during mass production. The problem usually arises during roll slitting whereby a large role is to be cut into smaller pieces. The challenge may be further compounded due to constraints and different variants that arises from product customization, process and machinery as well as customer requirements and quality issues. To address this problem, this study develops a linear integer programming technique and provides a practical guided approach. First mathematical formulation (having objective function and constraints) comprising of a list of q orders, that requires p j pieces was formulated and a list of all possible cuts combination of configuration and patterns were derived. The linear integer program was solved in the MATLAB 2022 environment. The results indicated that the large rolls can be cut into the desired length, number, patterns and configuration in a time effective manner using the developed linear integer programming technique. The results further show that for the total wastes generated was 24 for the optimal solutions. This number of wastes can be considered to be minimal considering the volume of demand and patterns generated from the stock material. Furthermore, 6 out of the 7 pattern optimal solutions generated zero waste. This study provides theoretical and empirical findings that can assist the manufacturing industries in minimizing time and cost variables while addressing stock cutting problems.

Integer Linear Programming Model for Profit Maximization using Branch and Bound Algorithm in Retail Companies: Case of a Peruvian Company

This article presents an inventory management model for profit maximization in a Peruvian retail company (FIDEL) using linear programming techniques and the Branch and Bound algorithm. To introduce this paper we refute, through a review of previous studies in the same field, the use of this approach for its effectiveness in business decision-making. Gathering data on costs, demand and the available capital for the company’s different product lines was done through the use of interviews. The proposed model aims to maximize revenue based on the quantities of goods purchased, while considering minimum demand and capital constraints. Validation was performed with Lingo software to confirm the consistency and feasibility of the model. The resulting values revealed a significant increase in projected profits compared to actual data.

Two hybrid flow shop scheduling lines with assembly stage and compatibility constraints.

Two hybrid flow shop scheduling lines must be coordinated to assemble batches of terminated products at their last stage. Each product is thus composed of two jobs, each produced in one of the lines. The set of jobs is to be processed in a series of stages to minimize the makespan of the scheduling, but jobs forming a product must arrive at the assembly line simultaneously. We propose a mixed integer linear programming model. Then, based on the model, we propose a pull-matheuristic algorithm. Finally, we present two metaheuristics, a greedy randomized adaptive search procedure and a biased random key genetic algorithm, and compare all the methodologies with real-based instances of a production scheduling problem in the automobile manufacturing industry. The greedy algorithm yields high-quality solutions, while the genetic one offers the best computational times.

Supply chain disruption recovery strategies for measuring profitability and resilience in supply and demand disruption scenarios

This paper examines the recovery of a three-level manufacturing supply chain under supply and demand disruptions. The paper proposes new combined recovery strategies, which aim to cope with interruption by adjusting the supply chain structure and material flows. This study integrates both supply chain performance and supply chain capability dimensions. We develop a bi-criteria mixed integer linear programming model with profit and resilience maximization as the objective. The model combines supply-side supply expansion, manufacturer capacity impairment, and demand regulation on the demand side. In a numerical example, we find that a “reciprocal disruption overlay” occurs when supply and demand disruptions, but the supply chain still loses some profit. The results suggest that the combined recovery strategies reduce profit loss and increase supply chain resilience. Furthermore, the strategies are also the optimal recovery strategies under unilateral disruptions. This model facilitates the coordination of a disrupted supply chain and can help managers decide on the best recovery plan.

An Energy-efficient Multi Objectives MILP Model for Integrated Process Planing and Scheduling in RMS

The integration of process planning and scheduling(IPPS) is a crucial manufacturing strategy to optimize manufacturing resources utilization, which combines process planning and scheduling as an integrated function instead of two separated functions performing sequentially. Reconfigurable manufacturing system(RMS) is one of the latest manufacturing paradigms to meet unstable periodic market changes and environmental challenges. However, IPPS was seldom studied in context of RMS before. This paper proposed a multi objectives mixed integer linear programming model to solve IPPS problem in context of RMS, to optimize the makespan and total energy consumption in manufacturing. To be more realistic, the model considers transportation and reconfiguration factors, simultaneously meeting process planning flexibility.

Drone‐Assisted Long‐Distance Delivery of Medical Supplies with Recharging Stations in Rural Communities

In the past few years, drones have been adopted as a novel delivery tool towards medical supplies, improving delivery service efficiency due to fast speed and neglection of geographical limitations. However, the flight endurance of a battery‐operated drone is limited for long‐distance medical supplies delivery operations. Recharging stations, as a kind of drone facility, allow multiple stops for drones to supplement the power to overcome the flight‐range limitations. This paper studies drone‐assisted long‐distance medical supplies delivery with recharging stations in rural communities by a mixed integer linear programming model. To illustrate the applicability of this model and explore the key factors influencing delivery efficiency of medical supplies, a case study from China is conducted. The results indicate that enhancements on the speed of a truck or a drone can yield considerable delivery cost reduction. In addition, drone‐recharging technology advances can improve delivery efficiency of medical supplies in rural communities.

Модели и алгоритмы локального поиска для маршрутизации транспортных средств с возвратами и временными окнами

A vehicle routing problem for servicing objects with the possibility of distributing work between vehicle taking into account time windows is considered. We discuss approaches to constructing integer linear programming models and their modifications. A large neighborhood search algorithm is proposed to find approximate solutions. Here an improving solution is constructed using the “destroy” and “repair” methods at each step. A series of instances with various structures are proposed, in particular demonstrating the reason of returns to objects for vehicles. The results of an experimental evaluation of models and algorithms are presented.