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mixed-integer linear programming for project scheduling under various resource constraints

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期319卷 79-88页

作者： Klein, Nicklas Gnagi, Mario Trautmann, Norbert Univ Bern Dept Business Adm Engehaldenstr 4 CH-3012 Bern Switzerland

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget;and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

关键词： Project scheduling mixed-integer linear programming Resource-constrained project scheduling Consumption and production of resources

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mixed-integer linear programming Approaches for Tree Partitioning of Power Networks

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IEEE Transactions on Control of Network Systems 2025年第2期12卷 1805-1814页

作者： Lan, Leon Zocca, Alessandro Amsterdam University College Amsterdam Netherlands California Institute of Technology California United States

In transmission networks, power flows and network topology are deeply intertwined due to power flow physics. Recent literature shows that a specific more hierarchical network structure can effectively inhibit the propagation of line failures across the entire system. In particular, a novel approach named tree partitioning has been proposed, which seeks to bolster the robustness of power networks through strategic alterations in network topology, accomplished via targeted line switching actions. Several tree partitioning problem formulations have been proposed by considering different objectives, among which power flow disruption and network congestion. Furthermore, various heuristic methods based on a two-stage and recursive approach have been proposed. The present work provides a general framework for tree partitioning problems based on mixed-integer linear programming (MILP). In particular, we present a novel MILP formulation to optimally solve tree partitioning problems and also propose a two-stage heuristic based on MILP. We perform extensive numerical experiments to solve two tree partitioning problem variants, demonstrating the excellent performance of our solution methods. Lastly, through exhaustive cascading failure simulations, we compare the effectiveness of various tree partitioning strategies and show that, on average, they can achieve a substantial reduction in lost load compared to the original topologies. © 2014 IEEE.

关键词： mixed-integer linear programming

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mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy

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APPLIED MATHEMATICAL MODELLING 2022年 105卷 438-453页

作者： Ghandehari, Najmeh Kianfar, Kamran Univ Isfahan Fac Adm Sci & Econ Dept Management Esfahan *** Iran Univ Isfahan Fac Engn Esfahan *** Iran

The planning of operating rooms under block strategy is addressed in this study. The decisions are about opening the operating rooms and assigning specialties and surgeons to blocks at the tactical level, and sequencing the surgeries at the operational level. This problem aims to minimize the costs of opening the operating rooms and their overtime, the waiting costs of patients, and the surgeons' idle costs. We propose two mixed integer linear programming models, a constraint programming (CP) model and a constraint programming-based column generation (CPCG) method for handling the problem. The performance of the models is evaluated by random test instances. The results indicate that CP and CPCG models are more efficient than the linear programming models in terms of computational time, and the number of variables and constraints. The proposed method CPCG generates optimal solutions for problem instances of up to 30 surgeries in less than 4 min. The CP model finds the optimal solutions in about one minute but proving the optimality of the found solutions is time-consuming in some instances. The maximum optimality gap for the proposed two-step linear programming model is 2%, while its run time is less than 20 s. A sensitivity analysis is done on the main parameters of the problem like objectives' weights, opening cost of ORs, unit waiting cost of patients, and the maximum available time in surgery blocks. Among the three objectives, the unit waiting cost of patients has the most sensitivity to variations of the objective function weights.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Operating room planning Block strategy Master surgery schedule mixed-integer linear programming Constraint programming Column generation

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mixed-integer linear programming models for the type-II resource-constrained assembly line balancing problem

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ASSEMBLY AUTOMATION 2022年第5期42卷 585-594页

作者： Michels, Adalberto Sato Costa, Alysson M. Univ Melbourne Sch Math & Stat Melbourne Vic Australia

Purpose Resource-constrained assembly lines are widely found in industries that manufacture complex products. In such lines, tasks may require specific resources to be processed. Therefore, decisions on which tasks and resources will be assigned to each station must be made. When the number of available stations is fixed, the problem's main goal becomes the minimisation of cycle time (type-II version). This paper aims to explore this variant of the problem that lacks investigation in the literature. Design/methodology/approach In this paper, the authors propose mixed-integer linear programming (MILP) models to minimise cycle time in resource-constrained assembly lines, given a limited number of stations and resources. Dedicated and alternative resource types for tasks are considered in different scenarios. Findings Besides, past modelling decisions and assumptions are questioned. The authors discuss how they were leading to suboptimal solutions and offer a rectification. Practical implications The proposed models and data set fulfil more practical concerns by taking into account characteristics found in real-world assembly lines. Originality/value The proposed MILP models are applied to an existing data set, results are compared against a constraint programming model, and new optimal solutions are obtained. Moreover, a data set extension is proposed due to the simplicity of the current one and instances up to 70 tasks are optimally solved.

关键词： Assembly line balancing Resource constraints Type-II problem mixed-integer linear programming

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mixed-integer linear programming Model to Assess Lithium-Ion Battery Degradation Cost

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ENERGIES 2022年第9期15卷 3060-3060页

作者： Oliveira, Debora B. S. Gloria, Luna L. Kraemer, Rodrigo A. S. Silva, Alisson C. Dias, Douglas P. Oliveira, Alice C. Martins, Marcos A. I. Ludwig, Mathias A. Gruner, Victor F. Schmitz, Lenon Coelho, Roberto F. CERTI Fdn Ctr Sustainable Energy BR-88040900 Florianopolis SC Brazil AES Brazil R&D & Innovat BR-04578000 Sao Paulo Brazil Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil

This work proposes a mixed-integer linear programming model for the operational cost function of lithium-ion batteries that should be applied in a microgrid centralized controller. Such a controller aims to supply loads while optimizing the leveled cost of energy, and for that, the cost function of the battery must compete with the cost functions of other energy resources, such as distribution network, dispatchable generators, and renewable sources. In this paper, in order to consider the battery lifetime degradation, the proposed operational cost model is based on the variation in its state of health (SOH). This variation is determined by experimental data that relate the number of charge and discharge cycles to some of the most important factors that degrade the lifespan of lithium-ion batteries, resulting in a simple empirical model that depends on the battery dispatch power and the current state of charge (SOC). As proof-of-concept, hardware-in-the-loop (HIL) simulations of a real microgrid are performed considering a centralized controller with the proposed battery degradation cost function model. The obtained results demonstrate that the proposed cost model properly maintains the charging/discharging rates and the SOC at adequate levels, avoiding accelerating the battery degradation with use. For the different scenarios analyzed, the battery is only dispatched to avoid excess demand charges and to absorb extra power produced by the non-dispatchable resources, while the daily average SOC ranges from 48.86% to 65.87% and the final SOC converges to a value close to 50%, regardless of the initial SOC considered.

关键词： battery energy storage system degradation cost model lithium-ion battery microgrid power dispatch mixed-integer linear programming

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Reactive tabu search and mixed-integer linear programming for multi-day assignment, scheduling, and routing problems of specialised education and home-care services

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年第5期63卷 1779-1802页

作者： Saleh, Mira Bou Chariete, Abderrahim Schwartz, Leo Grunder, Olivier El Hassani, Amir Hajjam Univ Lorraine LORIA F-54000 Nancy France Univ Technol Belfort Montbeliard SINERGIES F-90000 Belfort France

In this paper, we address the Multi-Day Assignment, Scheduling, and Routing Problem for Specialized Education and Home Care Services (SEHCS-MASRP), which involves heterogeneous employees and missions, posing a complex optimisation challenge. To tackle this, we propose a novel mixed-integer linear programming (MILP) model that considers employee qualifications, service requirements, scheduling constraints, routing decisions, and multiple objectives across the planning horizon. Additionally, we develop two metaheuristic approaches: a Reactive Tabu Search (RTS) algorithm incorporating either a Probabilistic Greedy Heuristic (PGH) or a Greedy Randomized Adaptive Search Procedure (GRASP) for initial solutions and a tailored genetic algorithm (GA). The three approaches aim to minimise wasted and overtime hours, total travel distances, and the number of assignments with an unsatisfied specialty while balancing wasted hours, overtime hours, and travel distances among the employees. Gurobi uses the proposed MILP model to find the optimal solutions, which are then compared with RTS and GA results across various instance sizes based on real-life SEHCS scenarios. Experimental results demonstrate the efficiency of MILP, RTS, and GA. MILP achieves proven optimal solutions for smaller to large instances. For huge instances, RTS generates high-quality solutions within reasonable computing times, outperforming GA performance. Notably, RTS consistently finds solutions within 5% of optimality for most instances.

关键词： mixed-integer linear programming reactive tabu search genetic algorithm assignment problems specialised education and home care services multi-day planning horizon

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A mixed-integer linear programming Model for Addressing Efficient Flexible Flow Shop Scheduling Problem with Automatic Guided Vehicles Consideration

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APPLIED SCIENCES-BASEL 2025年第6期15卷 3133-3133页

作者： Wang, Dekun Wu, Hongxu Zheng, Wengang Zhao, Yuhao Tian, Guangdong Wang, Wenjie Chen, Dong Zhengzhou Univ Sch Mech & Power Engn Zhengzhou 450001 Peoples R China Beijing Univ Civil Engn & Architecture Sch Machinery & Vehicles Beijing 100044 Peoples R China

With the development of Industry 4.0, discrete manufacturing systems are accelerating their transformation toward flexibility and intelligence to meet the market demand for various products and small-batch production. The flexible flow shop (FFS) paradigm enhances production flexibility, but existing studies often address FFS scheduling and automated guided vehicle (AGV) path planning separately, resulting in resource competition conflicts, such as equipment idle time and AGV congestion, which prolong the manufacturing cycle time and reduce system energy efficiency. To solve this problem, this study proposes an integrated production-transportation scheduling framework (FFSP-AGV). By using the adjacent sequence modeling idea, a mixed-integer linear programming (MILP) model is established, which takes into account the constraints of the production process and AGV transportation task conflicts with the aim of minimizing the makespan and improving overall operational efficiency. Systematic evaluations are carried out on multiple test instances of different scales using the CPLEX solver. The results show that, for small-scale instances (job count <= 10), the MILP model can generate optimal scheduling solutions within a practical computation time (several minutes). Moreover, it is found that there is a significant marginal diminishing effect between AGV quantity and makespan reduction. Once the number of AGVs exceeds 60% of the parallel equipment capacity, their incremental contribution to cycle time reduction becomes much smaller. However, the computational complexity of the model increases exponentially with the number of jobs, making it slightly impractical for large-scale problems (job count > 20). This research highlights the importance of integrated production-transportation scheduling for reducing manufacturing cycle time and reveals a threshold effect in AGV resource allocation, providing a theoretical basis for collaborative optimization in smart factories.

关键词： integrated scheduling flexible flow shop scheduling makespan AGV scheduling mixed-integer linear programming exact algorithm

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Optimal Operation of a Tablet Pressing Machine Using Deep-Neural-Network-Embedded mixed-integer linear programming

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INVENTIONS 2025年第2期10卷 29-29页

作者： Li, Jialong Wu, Lan Qin, Yuang Zhi, Haojun Univ Technol Sch Elect Engn Henan Zhengzhou 450007 Peoples R China Univ Liverpool Sch Elect Engn Elect & Comp Sci Liverpool L69 3GJ England

This paper presents a deep neural network (DNN)-embedded mixed-integer linear programming (MILP) model for fault prediction and production optimization in tablet pressing machines. The DNN predicts the probability of failures during the tablet pressing process by analyzing key operational parameters such as pressure, temperature, humidity, speed, vibration, and number of maintenance cycles. The MILP model optimizes the temperature and humidity settings, production schedules, and maintenance planning to maximize total profit while minimizing penalties for fault pressing, energy consumption, and maintenance costs. To integrate DNN into the MILP framework, Big-M constraints are applied to linearize the Rectified linear Unit (ReLU) activation functions, ensuring solvability and global optimality of the optimization problem. A case study using the Kaggle dataset demonstrates the model's ability to dynamically adjust production and maintenance schedules, enhancing profitability and resource utilization under fluctuating electricity prices. Sensitivity analyses further highlight the model's robustness to variations in maintenance and energy costs, striking an effective balance between cost efficiency and production quality, which makes it a promising solution for intelligent scheduling and optimization in complex manufacturing environments.

关键词： deep neural network mixed-integer linear programming fault prediction tablet pressing machines maintenance scheduling manufacturing systems

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mixed-integer linear programming based Maintenance Scheduling of Generating Units

Mixed-Integer Linear Programming based Maintenance Schedulin...

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IEEE International Conference on Environment and Electrical Engineering (EEEIC) / IEEE Industrial and Commercial Power Systems Europe (I and CPS Europe) Conference

作者： Nezhad, Ali Esmaeel Nardelli, Pedro H. J. Ghanavati, Farideh Sahoo, Subham Osorio, Gerardo J. LUT Univ Dept Elect Engn Sch Energy Syst Lappeenranta 53850 Finland Univ Aveiro Dept Ind Engn & Management Aveiro Portugal Aalborg Univ Dept Energy Technol DK-9220 Aalborg Denmark Univ Portucalense Infante D Henrique UPT R Dr Antonio Bernardino de Almeida P-4200072 Porto Portugal

ISBN: (纸本)9781665485371

This paper presents a mixed-integer linear programming model for the maintenance scheduling of generating units in the power system. The proposed model is investigated for weekly scheduling for one year addressing the crew availability constraint. The maintenance scheduling problem is modeled as an optimization problem to determine the optimal timing for handling the technical constraints of the power generation sector. In addition, the technical constraints for optimal scheduling of the tasks, like sequential tasks and rest time of the crews have been addressed in the scheduling management framework. The weekly peak power and spinning reserve have been considered in line with the economic issues for power generation in the whole system. The historical market clearing price (MCP) and mid-term load forecasting have been considered in the developed model.

关键词： Maintenance Scheduling mixed-integer linear programming Market Clearing Price Historical Data Power Generating Units.

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Stochastic transitions of a mixed-integer linear programming model for the construction supply chain: chance-constrained programming and two-stage programming

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OPERATIONAL RESEARCH 2024年第3期24卷 46页

作者： Koutsokosta, Aspasia Katsavounis, Stefanos Democritus Univ Thrace Dept Prod & Management Engn Xanthi Greece

This paper addresses the problem of optimal Construction Supply Chain (CSC) design and integration in deterministic and stochastic environments by providing a family of models for the optimization of a dynamic, multi-product, multi-site contractor-led CSC. With the objective of minimizing the total CSC cost, optimal decisions are made on network design, production, inventory holding and transportation, while also considering discounts for bulk purchases, logistics centers, on-site shortages and an inventory-preparation phase. The models integrate the operations of temporal and project-based supply chains into a sustainable network with repetitive flows, large scope contracts and economies of scale to provide the main contractor with a versatile optimization framework which can account for different levels of uncertainty. The novelty of this paper lies in providing a flexible integrative optimization CSC tool that accounts for multiple CSC actors (suppliers and/or logistics centers), projects, products, time periods, operations, and different decision-making environments depending on the nature of the problem and the risk-attitude of the decision maker. This paper contributes to the fast-growing research field of stochastic CSC optimization showcasing stochastic transitions of a mixed-integer linear programming model to chance-constrained programming and two-stage programming and incorporating uncertainties with different types of probability distributions or scenarios, and even interdependent uncertainties-approaches that have not been explored extensively in the CSC context. The results reveal that the stochastic approaches sacrifice the minimum cost of deterministic solutions having average settings to obtain robust well-hedged solutions over the possible parameter variations and that the selection of a suitable method for modeling uncertainty is context-dependent.

关键词： Construction supply chain management Construction supply chain network design and integration Stochastic optimization mixed-integer linear programming Chance-constrained programming Two-stage programming

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