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Perishable inventory control with backlogging penalties: A mixed-integer linear programming model via two-step approximation

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COMPUTERS & OPERATIONS RESEARCH 2025年 176卷

作者： Wu, Yulun Tanaka, Shunji Kyoto Univ Grad Sch Engn Dept Elect Engn Nishikyo Ku Kyoto 6158510 Japan Okayama Univ Fac Environm Life & Nat Sci & Technol 3-1-1 Tsushima NakaKita Ku Okayama 7008530 Japan

This study proposes a novel approximate mixed-integer linear programming (MILP) model for the perishable inventory control problem considering non-stationary demands and backlogging penalties. Because of the existence of the waste costs incurred by outdated products in the cost function, it is difficult to apply the linearization technique employed for the non-perishable inventory control problem directly to our problem. To address this difficulty, we develop a two-step approximation method. In the first step, we approximate each expected cost to simplify the cost function, making it easy to handle. In the second step, we apply an existing linearization technique to linearize this function and then obtain the MILP model. We evaluate the proposed model in computer simulations by comparing it with other existing methods. The results show that our model closely matches a benchmark method capable of obtaining near-optimal solutions in solution quality, and it achieves abetter trade-off between solution quality and computational efficiency than existing heuristics.

关键词： Inventory control Perishable products Non-stationary demands mixed-integer linear programming model Piecewise linearization

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Mathematical modeling and hybrid evolutionary algorithm to schedule flexible job shop with discrete operation sequence flexibility

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COMPUTERS & OPERATIONS RESEARCH 2025年 176卷

作者： Yuan, Shuai Zhu, Xiaomin Cai, Wei Gao, Jinsheng Zhang, Runtong Beijing Jiaotong Univ Sch Mech Elect & Control Engn Beijing Peoples R China North China Elect Power Univ Sch Econ & Management Beijing Peoples R China Beijing Jiaotong Univ Sch Econ & Management Beijing Peoples R China

In actual industrial production, several operations of a job may not have precedence relationships and can be placed at any point in the process route. However, traditional flexible job shop scheduling problems (FJSP) often assume that all operations of each job must be processed in strict linear order. Therefore, this research addresses the FJSP with discrete operation sequence flexibility (FJSPDS) with the objective of minimizing the makespan. Based on existing models, two novel mixed-integer linear programming (MILP) models are formulated by improving the description methods of variables and constraints, significantly enhancing the models' performance. Additionally, a hybrid evolutionary algorithm (HEA) is proposed to solve large-scale instances through the following three aspects. An improved encoding method is proposed, which makes the search space of the HEA and solution space of the problem more compatible and reduces the possibility of optimal solutions being missed. A special neighborhood structure is designed according to the characters of sequence-free operations, and an iterative local search method is introduced to improve the quality of the solution. A knowledge-driven reinitialization operator is developed, which generates new individuals based on the features of the historical elite population, guiding the evolution of populations, avoiding premature convergence while also avoiding falling into local optima. Finally, a total of 110 benchmark problem instances are utilized to verify the superior effectiveness of the MILP models and the HEA in solving FJSPDS.

关键词： Flexible job shop scheduling mixed-integer linear programming model Discrete operation sequence flexibility Hybrid evolutionary algorithm Knowledge-driven reinitialization Iterative local search

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Optimal Placement and Sizing of Distributed Generation in Electrical DC Distribution Networks Using a Stochastic mixed-integer LP model

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2025年第8期50卷 5835-5851页

作者： Valencia-Diaz, Alejandro Hincapie, Ricardo A. Gallego, Ramon A. Univ Tecnol Pereira Dept Elect Engn Pereira 660003 Risaralda Colombia

This paper presents a stochastic mixed-integer linear mathematical model for finding the optimal placement and sizing of distributed generation in a DC distribution network, considering the uncertainty of electrical demand and distributed renewable sources. The proposed model accurately represents the original mixed-integer nonlinear model, obtaining a globally optimal solution in less computational time with low errors. The mathematical model allows for considering constraints related to the maximum limits for the penetration of distributed generation, such as those specified by Resolution CREG 174 of 2021. Furthermore, the uncertainties of the electrical demand, wind energy-based distributed generation (DG), and solar energy-based DG are considered in the mathematical models using a two-stage stochastic programming approach. The accuracy and efficiency of the proposed model were tested and validated on a 21-node DC test system from the specialized literature, and the effectiveness and robustness were assessed on a 69-node DC test system. The obtained results show that the proposed stochastic mixed-integer linear mathematical model performs well.

关键词： Distributed generation DC distribution systems mixed-integer linear programming model Stochastic programming

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Optimization reverse logistics for waste plastic recycling in India: a genetic algorithm approach

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INNOVATIVE INFRASTRUCTURE SOLUTIONS 2025年第5期10卷 1-13页

作者： Kumar, Sachin Sinha, Sanjeev Ranjan, Rajesh Saurav, Samir Natl Inst Technol Civil Engn Dept Patna India

The increasing environmental and economic impacts of plastic waste necessitate efficient recycling strategies. Despite advancements in reverse logistics for materials like metals and construction waste, plastic waste recycling remains underexplored, especially in urban contexts. This study fills this gap by developing a genetic algorithm (GA) and mixed-integer linear programming (MILP) model to optimize the reverse logistics network for plastic garbage in Patna, India. The approach incorporates 23 optimally located recycling facilities, resulting in an estimated 16.3% reduction in overall costs and 19.7% improvement in transportation efficiency. By integrating collection centers, the model effectively addresses low-density and contamination challenges, leading to a 22.5% increase in material recovery rates. Sensitivity evaluations on GA parameters and transportation costs confirm the model's robustness, producing stable and convergent solutions across different scenarios. Future research might compare GA performance with other optimization methods like Ant Colony or Grey Wolf Optimization and investigate stochastic frameworks to account for uncertainty in waste generation. This study provides a scalable, cost-effective, and data-driven framework for improving urban plastic waste management. The findings offer valuable insights for policymakers, urban planners, and waste management industries, helping them design more sustainable and economically viable recycling systems.

关键词： Plastic waste recycling Reverse logistics optimization Waste management efficiency Genetic algorithm mixed-integer linear programming model

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Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management

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Engineering 2024年第5期36卷 223-239页

作者： Lu Zhen Zhiyuan Yang Gilbert Laporte Wen Yi Tianyi Fan School of Management Shanghai UniversityShanghai 200444China Department of Decision Sciences HEC MontréalMontréalQC H3T 2A7Canada School of Management University of BathBath BA27AYUK Department of Building and Real Estate The Hong Kong Polytechnic UniversityHong Kong 999077China

Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based *** engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection *** on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring *** tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging *** comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale *** overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our *** numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale *** experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency.

关键词： Engineering management Unmanned aerial vehicle Inspection routing and scheduling optimization mixed-integer linear programming model Variable neighborhood search metaheuristic

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Energy storage and transmission expansion planning: substitutes or complements?

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第8期12卷 1738-1746页

作者： Bustos, Carlos Sauma, Enzo de la Torre, Sebastian Aguado, Jose A. Contreras, Javier Pozo, David Pontificia Univ Catolica Chile Ind & Syst Engn Dept Santiago Chile Pontificia Univ Catolica Chile UC Energy Res Ctr Santiago Chile Univ Malaga Dept Elect Engn Malaga Spain Univ Castilla La Mancha Escuela Tecn Super Ingenieros Ind Ciudad Real Spain Skolkovo Inst Sci & Technol Ctr Energy Syst Moscow Russia

The massive development of energy storage systems (ESSs) may significantly help in the supply-demand balance task, especially under the existence of uncertain and intermittent sources of energy, such as solar and wind power. Using ESSs as complements of renewable generation has technical and economic consequences in both the short-term operation and the long-term expansion planning of the grid. The authors propose a transmission expansion planning model that incorporates decisions about the expansion of generic ESS units in order to study the interaction between the penetration and location of ESSs and the transmission investment decisions. The problem is formulated as a mixed-integer linear programming model and considers different demand blocks and their correlation with renewable generation, to account for the distinct features of the system over time. The authors' results show that ESSs are not only substitutes of transmission assets, but they may also be complemented with transmission assets depending on the power system characteristics. They use a 27-bus representation of the main Chilean network to illustrate the model proposed and to highlight some interesting results about the potential complementarity of ESSs and transmission expansion.

关键词： power transmission planning power transmission economics investment energy storage integer programming linear programming supply and demand transmission expansion planning energy storage systems ESSs supply-demand balance task renewable generation economic consequences long-term grid expansion planning generic ESS unit expansion transmission investment decisions mixed-integer linear programming model transmission assets power system characteristics Chilean network

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Mathematical modeling and a hybrid evolutionary algorithm for process planning

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JOURNAL OF INTELLIGENT MANUFACTURING 2021年第3期32卷 781-797页

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

Process planning is an essential part of the manufacturing system linking the designing and practical manufacturing. However, the reported process planning models are too simple to describe all characteristics because of the complexity of process planning. Therefore, a new mixed-integer linear programming (MILP) mathematical model is established based on OR-node of the network graph. In the model, the linear expression of the OR-node controlling function as well as three types of changing costs are first established. Beside, considering the OR-node selection state in the encoding and decoding method, a hybrid evolutionary algorithm (HEA) is designed to combine a genetic algorithm with a simulated annealing algorithm. The tournament selection method is adopted in the proposed HEA, and the discussion on the tournament size is conducted on the open problems to make the algorithm designing more reasonable and scientific. The HEA and the new MILP model are both tested on series of numerical experiments which are carried on the existing benchmarks as well as some randomly generated cases. The behavior of both two methods can verify their effectiveness and superiority successfully.

关键词： Process planning mixed-integer linear programming model Hybrid evolutionary algorithm Benchmark

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A robust approach to multiple vehicle location-routing problems with time windows for optimization of cross-docking under uncertainty

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017年第1期32卷 49-62页

作者： Mousavi, S. Meysam Vandani, Behnam Shahed Univ Dept Ind Engn Tehran Iran Islamic Azad Univ Qazvin Branch Fac Ind & Mech Engn Qazvin Iran

The concern about significant changes in the logistics environment, such as the diversification of demands and supply quantities in pickup and delivery processes, has spurred an interest in designing scalable and robust cross-docking planning. In this study, a robust optimization model is introduced to deal with the inherent uncertainty of input data in the location and vehicle routing scheduling problems in cross-docking distribution networks. For this purpose, a new two-phase deterministic mixed-integer linear programming (MILP) model is proposed for locating cross-docks and scheduling vehicle routing with multiple cross-docks. Then, the robust counterpart of the proposed two-phase MILP model is proposed by employing the recent developments in robust optimization theory. Finally, to evaluate the robustness of obtained solutions by the new robust optimization model, a comparison is made with the obtained solutions by the deterministic MILP model in a number of realizations based on different test problems. Moreover, a meta-heuristic algorithm, namely self-adaptive imperialist competitive algorithm (SAICA), is presented for the multiple vehicle location-routing problems. Finally, this study provides various computational test problems to demonstrate the applicability and capability of the proposed robust two-phase MILP model and meta-heuristic solution approach.

关键词： Cross-docking planning location vehicle routing scheduling robust optimization mixed-integer linear programming model meta-heuristic algorithms

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Electric bus charging scheduling on a bus network

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2024年 161卷

作者： Zhou, Yu Meng, Qiang Ong, Ghim Ping Wang, Hua Beihang Univ Sch Transportat Sci & Engn Beijing 100191 Peoples R China Beihang Univ Sch Transportat Sci & Engn Key Lab Intelligent Transportat Technol & Syst Minist Educ Beijing 100191 Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore Hefei Univ Technol Sch Automot & Transportat Engn Hefei 230009 Peoples R China

This study addresses the electric bus charging scheduling problem (EBCSP) within a bus network comprising multiple bus routes, depots, and a fleet of heterogeneous electric buses (EBs) operated by a public transport (PT) operator. The EBCSP aims to minimize total costs by concurrently determining the assignment of EBs to trips(i.e., EB-to-trip assignment) and their corresponding charging schedules. A partial charging policy allows for flexible charging durations, considering a published timetable consisting of trip tasks. We formulate the EBCSP as a mixed-integer linear programming model and a set-covering formulation. For small-scale EBCSPs, we propose a branch-and-price algorithm utilizing the set-covering formulation for exact solutions. As large-scale EBCSPs pose computational challenges, we develop an optimizationbased adaptive large neighborhood search ( opt -ALNS) method. The opt -ALNS method employs ALNS operators for EB-to-trip assignment and solves the remaining linear programming problem efficiently. To enhance the opt -ALNS process, we introduce a labeling method to assess solution feasibility and rebuild solutions. Moreover, we incorporate EB battery degradation effects into the proposed method. Finally, we assess the performance of the opt -ALNS method on real-life instances and compare it with the branch-and-price algorithm.

关键词： Electric bus charging scheduling Bus network mixed-integer linear programming model Set-covering model Branch-and-price algorithm Adaptive large neighborhood search method Battery degradation

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Liner ship fleet deployment with container transshipment operations

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2012年第2期48卷 470-484页

作者： Wang, Shuaian Meng, Qiang Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore

This paper proposes a liner ship fleet deployment (LSFD) problem with container transshipment operations. The proposed problem is formulated as a mixed-integer linear programming model which allows container transshipment operations at any port, any number of times, without explicitly defining the container transshipment variables. Experiments on the Asia-Europe-Oceania shipping network of a global liner shipping company show that more than one third (17-22 ports) of the total of 46 ports have transshipment throughputs. Computational studies based on randomly generated large-scale shipping networks demonstrate that the proposed model can be solved efficiently by CPLEX. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Fleet deployment Liner shipping Transshipment mixed-integer linear programming model

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