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Two novel MILP models with different flexibilities for solving integrated process planning and scheduling problems

JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2023年第9期74卷 1955-1967页

作者： Liu, Qihao Li, Xinyu Gao, Liang Fan, Jiaxin Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

Process planning and shop scheduling are considered two independent subsystems in traditional flexible manufacturing systems. For correlation and complementarity, integrated process planning and scheduling (IPPS), which has become the main focus of production research, is investigated. The commonly used approaches, intelligent algorithms and their variants, can efficiently find high-quality solutions but cannot guarantee their optimality and stability. To address these shortcomings, based on the OR-nodes of a process network, this paper establishes a mixed-integer linear programming (MILP) model with full-flexibility to solve small-scale IPPS problems. Additionally, for larger-scale problems, another model with semi-flexibility is generated by decomposing the flexibilities into two layers to simplify the original solution space of IPPS. Based on the semi-finished process routes generated by level-1 models, level-2 can search and obtain satisfactory results. The two proposed MILP models are coded in the optimisation programming language and solved by the linear solver CPLEX on 35 benchmark problems with different degrees of flexibility. Extensive experimental results successfully show the superiority of the two proposed models to the other state-of-the-art algorithms and MILP models.

关键词： Scheduling integrated process planning and scheduling mixed-integer linear programming mathematical model benchmark

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Proactive Frequency Stability Scheme Based on Bayesian Filters and Spectral Clustering

IEEE OPEN ACCESS JOURNAL OF POWER AND ENERGY

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IEEE OPEN ACCESS JOURNAL OF POWER AND ENERGY 2025年 12卷 100-110页

作者： Paramo, Gian Baquedano-Aguilar, Mario D. Bretas, Arturo Meyn, Sean Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Sandia Natl Labs Elect Grid Secur Albuquerque NM 87185 USA Univ Grenoble Alpes Grenoble INP CNRS G2Elab F-38000 Grenoble France

This work presents a proactive distributed model for power system frequency stability. High-level penetration of renewable energy sources into the grid have introduced unforeseen and unmodeled system dynamics. Underfrequency load shedding state-of-the-art solutions are reactive in design, with efficiency constrained by the modeling error. Being able to detect unstable conditions early makes it possible to generate optimized corrective actions. In this work, phasor measurement units are used to predict frequency values. When a disturbance is detected, the state of frequency is predicted a few seconds into the future via a particle filter algorithm. Corrective actions are modeled through a mixed integer linear programming algorithm within system areas established through spectral clustering. The solution is implemented on Matlab, considering IEEE test systems. The proactive design of the method combined with its multiple layers of optimization deliver results that outperform state-of-the-art solutions. Easy-to-implement model, without hard-to-derive parameters, highlights potential aspects towards real-life implementation.

关键词： Mathematical models Power system dynamics Particle measurements Filters Clustering algorithms Atmospheric measurements Power system stability Phasor measurement units Weight measurement Time-frequency analysis spectral clustering dynamic state estimation mixed-integer linear programming particle filter frequency stability

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Efficient real-time rail traffic optimization: Decomposition of rerouting, reordering, and rescheduling problems

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JOURNAL OF RAIL TRANSPORT PLANNING & MANAGEMENT 2025年 33卷

作者： Lovetei, Istvan Ferenc Lindenmaier, Laszlo Aradi, Szilard Budapest Univ Technol & Econ Fac Transportat Engn & Vehicle Engn Dept Control Transportat & Vehicle Syst Muegyetemrkp 3 H-1111 Budapest Hungary

The real-time railway traffic management problem occurs when the pre-planned timetable cannot be kept due to various disturbances;therefore, the trains must be rerouted, reordered, and rescheduled. Optimizing the real-time railway traffic management aims to resolve conflicts, minimizing the delay propagation or energy consumption. In one of our previous works, the existing mixed-integer linear programming optimization models are extended considering a safety-relevant issue of railway traffic management, the overlaps. However, solving the extended model can be time-consuming in complex control areas and traffic situations involving numerous trains. Therefore, we propose different computationally efficient multi-stage models by decomposing the problem according to the rerouting, reordering, and rescheduling subproblems. First, a lightweight heuristic MILP model that provides a fast but sub-optimal solution is given by reformulating the train delays into pair-wise interpretation. Second, we extend the heuristic model to grant an optimal solution to the original problem faster than the existing MILP formulations. The impact of the model decomposition is investigated mathematically and experimentally in various realistic simulated traffic scenarios concerning the optimization's objective value and computational demand. The proposed multi-stage models significantly decrease the optimization runtime of both the original and the extended railway traffic management problems.

关键词： Rail transportation Real-time traffic management Railway traffic optimization mixed-integer linear programming Runtime performance Problem decomposition Rerouting and rescheduling

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Optimizing Transmission Network Expansion Planning Using Search Space Reduction

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IEEE ACCESS 2025年 13卷 68773-68784页

作者： Meneses, Marco Zamora, Harol Macedo, Leonardo H. Romero, Ruben Sao Paulo State Univ UNESP Sch Engn Dept Elect Engn BR-15385007 Ilha Solteira SP Brazil Sao Paulo State Univ UNESP Sch Engn & Sci Dept Engn BR-19272100 Rosana SP Brazil

Transmission network expansion planning is a critical and complex problem related to the operation and development of electrical power systems. It is typically formulated as a mixed-integer nonlinear programming (MINLP) problem with combinatorial characteristics. Various mathematical models have been proposed to better approximate real-world system behavior, but even the most relaxed formulations remain computationally challenging. This paper introduces a search space reduction strategy to reduce the gap between the optimal solution of the MINLP model and its relaxed counterpart by strategically considering surrogate constraints. This approach enhances computational efficiency, significantly reducing processing time when using an optimization solver. By applying this method, we successfully determined the previously unknown optimal solution for the Brazilian north-northeast system.

关键词： Mathematical models Optimization Search problems Planning Transportation Load flow Complexity theory linear programming Heuristic algorithms Power generation mixed-integer linear programming nonlinear programming optimization of power systems transmission network expansion planning

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Energy-efficient train timetable optimization for tram system under multi-signal priority strategies

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SCIENTIFIC REPORTS 2025年第1期15卷 1-20页

作者： He, Jing Wang, Fengyuan Duan, Yuting Yang, Zhoulou Yang, Jian Kunming Univ Sci & Technol Sch Fac Transportat Engn Kunming 650500 Peoples R China Lijiang Xueshan Rail Transit Co Ltd Lijiang 674100 Peoples R China West Yunnan Univ Appl Sci Dali 671000 Peoples R China

Energy-efficient operation is an effective approach for diminishing the operational expenses and carbon emissions of the tram system. Tram operation strategies and signal priority play a vital role in energy-efficient train timetable optimization. However, the impact of trams on road traffic efficiency has limited consideration in traditional optimization methods. This paper develops a bi-objective mixed-integer linear programming (MILP) model incorporating multi-signal priority strategies (e.g., active signal priority strategy, no-signal priority strategy) and road traffic flow to obtain an energy-saving operation scheme. First, the signal priority strategy that trams should adopt based on the intersection traffic flow is determined to improve road traffic efficiency. Second, the speed profiles and stop plans of trams at the intersections are considered to reduce energy consumption and improve passenger comfort. The bi-objective MILP model can be solved by a commercial solver like CPLEX. A variety of comparative experiments using Lijiang Tram Line 1 in China are able to verify the effectiveness of the model. Compared with the timetable obtained by the active signal priority strategy (initial timetable), the proposed model could achieve the total energy consumption reduced by 5.01%, passenger comfort improved by 8.23%, and the number of vehicles delayed reduced by 27.21%.

关键词： Energy-efficient train timetable mixed-integer linear programming Signal priority strategies Tram system

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Optimization of machine configuration and scheduling in the hybrid flow shop using a linear programming-driven evolutionary approach

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ROBOTICS AND COMPUTER-INTEGRATED MANUFACTURING 2025年 95卷

作者： Zhang, Mengya Wang, Cuiyu Li, Xinyu Gao, Liang Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Intelligent Mfg Equipment & Technol Wuhan 430074 Peoples R China Wenhua Coll Fac Mech & Elect Engn Wuhan 430074 Peoples R China

The growing demand for flexible production systems is driven by product diversity and fluctuating order volumes. Seasonal variations can lead to imbalances between available machines and order demands, making efficient resource configuration critical before production begins. This paper addresses the optimization of machine configuration and scheduling in the hybrid flow shop, incorporating the order delivery time window. Most previous studies have focused on fixed machine numbers, while this study considers uncertain machine availability. This paper presents the mixed-integer linear programming model of the problem, and a linear programming (LP)-driven variable strategies evolutionary approach. The proposed approach combines an evolutionary algorithm with LP-driven neighborhood search for sequence optimization. Three strategies are constructed by narrowing down the search scope, which effectively reduces the algorithm's stagnation time and speeds up the convergence. To evaluate the effectiveness of the approach, the scales of application of the three LP strategies are first tested. Then ablation and comparison experiments are conducted, which show that the proposed approach generally agrees with the MILP results on small-scale problems and with smaller time resources. Experiments on 60 sets of large-scale problems show that the proposed approach has significant advantages over 5 state-of-the-art evolutionary algorithms and the MILP model. Additionally, the experiments show that the LPdriven strategy can improve the algorithm efficiency by about 13.32 % compared with the conventional strategy. These results demonstrate the potential of the LP-driven evolutionary approach for solving the complex scheduling problem.

关键词： Hybrid flow-shop scheduling Machine configuration Evolutionary algorithm linear programming strategy mixed-integer linear programming

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A matheuristic-based solution approach for integrated stock selection and sizing problem with a case study in a corrugated box-production company

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 195卷

作者： Baykasoglu, Adil Subulan, Kemal Karaman, Ilkim Dokuz Eylul Univ Fac Engn Dept Ind Engn Buca Izmir Turkiye Dokuz Eylul Univ Grad Sch Nat & Appl Sci Buca Izmir Turkiye

The majority of former research has concentrated on different variants of the cutting stock problems with fixedsized stocks only, and there is a scarcity of studies in the literature on variable-sized cutting stock problems, where dimensions of stocks (width and length) also need to be determined. In this research topic, a few studies have been published in recent years. Based on this motivation, this paper addressed a case-oriented twodimensional cutting stock problem with variable-sized stocks of a carton box manufacturing company to determine optimal dimensions, production requirements, and the purchasing amounts of the corrugated boards. A novel mathematical programming model of the problem is first developed that formally defines the problem. Due to the complex nature of the proposed model and difficulties in its optimal solution, a matheuristic-based solution approach is also proposed. The proposed approach incorporates a mixed-integer linear program (MILP) into a Simulated Annealing (SA) algorithm. By using the proposed matheuristic approach, the dimension values of the purchased corrugated boards are selected from the combinations of zero-waste dimensions of the demanded carton boxes and supplied at each iteration of the SA algorithm as inputs to MILP. Then, MILP is easily solved within reasonable computation times by making use of the Gurobi MIP solver in each SA iteration. The performance of the matheuristic approach is first tested on a real-life application study for the towel radiator box products of a manufacturing company in Turkey. Thereafter, a comprehensive computational study is also performed. Computational results have demonstrated that the proposed approach can generate promising results, which necessitate minimal stock diversity and impose minimum waste costs when compared to the existing cutting and purchasing plans of the company as well as the results of some greedy search heuristics embedded in the proposed MILP model.

关键词： Stock selection and sizing problem Matheuristic mixed-integer linear programming Simulated annealing Corrugated carton box production industry

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Using a Just-In-Time Approach in the Green Supply Chain, Taking Into Account CO2 Emissions, Under Uncertainty in the Pre- and Post-COVID-19 Situation

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DISCRETE DYNAMICS IN NATURE AND SOCIETY 2025年第1期2025卷

作者： Abbasi, Sina Jabari, Sobhan Mirzaei, Akram Azimi Azad, Ashkan Zamanian, Saba Islamic Azad Univ Dept Ind Engn Lahijan Iran Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Islamic Azad Univ Fac Skills & Entrepreneurship Tehran Iran Kish Int Campus Univ Tehran Fac Ind Engn Kish Iran

The main objective of this study is to develop a fuzzy-based approach for building a multistage, multiproduct, and multiperiod supply chain network (SCN) after and before the COVID-19 pandemic. The proposed model optimizes production and distribution planning under uncertainty in a multiperiod stochastic process network. The model is designed to help decision-makers manage the green supply chain (GSC) of their organizations. It was developed using the mixed-integer linear programming (MILP) approach. The model aims to maximize customer satisfaction in the pre- and post-COVID-19 era by reducing the total cost and delivery time they face. The model also estimates production, asset locations, order allocation, and inventory levels. Under uncertain conditions, a new probabilistic MILP model addresses the multiproduct, multiperiod SCN design (SCND) problem. The two objectives of this model are to maximize time and cost by using the concepts of total cost of ownership, activity-based costing, and just-in-time (JIT) production. The model's outputs include the quantity of goods purchased, produced, inventoried, delivered, and transported and the selection of suppliers before and after the COVID situation. A numerical example solved using the above technique is given to evaluate and validate the model and the proposed solution approach. Finally, the results of the study are presented.

关键词： distribution requirements fuzzy set green supply chain management mixed-integer linear programming optimal models

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Quantitative insights into the integrated push and pull production problem for lean supply chain planning 4.0

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第17期62卷 6251-6275页

作者： Reyes, John Mula, Josefa Diaz-Madronero, Manuel Univ Politecn Valencia Res Ctr Prod Management & Engn CIGIP Alcoy Alicante Spain Univ Tecn Ambato Fac Syst Engn Ambato Ecuador

Validated quantitative models for lean supply chain planning (LSCP) are still scarce in the literature, particularly because conventional push systems have not been widely integrated and tested with pull systems in sustainable and resilient environments in the Industry 4.0 context. Hence the main contribution of this paper is to develop an optimisation model that is able to contribute to the LSCP with the combination of push and pull strategies. Here we present an integrated just-in-time (JIT) production system with material requirement planning (MRP) for a SC that takes a traditional five-level structure based on a mixed-integer linear programming model (MILP) dubbed as LSCP 4.0. The model is able to simultaneously plan the production and inventory of materials and finished goods to satisfy demand from forecasts and firm orders. The selection of alternative suppliers as a proactive measure to face disruptive events is also considered. Furthermore, sustainable practices are included in the objective function for profit maximisation by considering CO2 emissions. This proposal is tested in the footwear sector. The results demonstrate that the combined use of JIT and MRP through a quantitative approach improve performance in leanness, sustainability and resilience by decreasing the bullwhip effect at different SC levels.

关键词： Lean manufacturing sustainability supply chain resilience mixed-integer linear programming industry 4.0

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Proximity results in convex mixed-integer programming

arXiv

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arXiv 2024年

作者： Kocuk, Burak Morán, R. Diego A. Industrial Engineering Program Sabanci University Istanbul34956 Turkey Industrial and Systems Engineering Department Rensselaer Polytechnic Institute TroyNY12180-3590 United States

We study proximity (resp. integrality gap), that is, the distance (resp. difference) between the optimal solutions (resp. optimal values) of convex integer programs (IP) and the optimal solutions (resp. optimal values) of their continuous relaxations. We show that these values can be upper bounded in terms of the recession cone of the feasible region of the continuous relaxation when the recession cone is fulldimensional. If the recession cone is not full-dimensional we give sufficient conditions to obtain a finite integrality gap. We then specialize our analysis to second-order conic IPs. In the case the feasible region is defined by a single Lorentz cone constraint, we give upper bounds on proximity and integrality gap in terms of the data of the problem (the objective function vector, the matrix defining the conic constraint, the right-hand side, and the covering radius of a related lattice). We also give conditions for these bounds to be independent of the right-hand side, akin to the linear IP case. Finally, in the case the feasible region is defined by multiple Lorentz cone constraints, we show that, in general, we cannot give bounds that are independent of the corresponding right-hand side. Although our results are presented for the integer lattice Zn, the bounds can be easily adapted to work for any general lattice, including the usual mixed-integer lattice Zn1 × Rn2 , by considering the appropriate covering radius when needed. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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