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A mixed-integer linear programming approach for the T-row and the multi-bay facility layout problem

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期295卷 443-462页

作者： Dahlbeck, Mirko TU Dortmund Univ Fac Business & Econ Vogelpothsweg 87 D-44227 Dortmund Germany Georg August Univ Gottingen Inst Numer & Appl Math Lotzestr 16-18 D-37083 Gottingen Germany

We introduce a new facility layout problem, the so-called T-Row Facility Layout Problem (TRFLP). The TRFLP consists of a set of one-dimensional departments with pairwise transport weights between them and two orthogonal rows which form a T such that departments in different rows cannot overlap. The aim is to find a non-overlapping assignment of the departments to the rows such that the sum of the weighted center-to-center distances measured in rectilinear directions is minimized. The TRFLP is a generalization of the well-known Multi-Bay Facility Layout Problem with three rows (3-BFLP). Both problems, the TRFLP and the 3-BFLP, have wide applications, e.g., factory planning, semiconductor fabrication and arranging rooms in hospitals. In this work we present a mixed-integer linear programming approach for the TRFLP and the 3-BFLP based on an extension of the well-known betweenness variables which now can be equal to one if the corresponding departments lie in different rows. One advantage of our formulation is the calculation of inter-row distances without big-M-type constraints. We provide cutting planes exploiting the crossroad structure in the layout, and hence T-row (3-Bay) instances with up to 18 (17) departments are solved to optimality in less than 7 h. The best known approach for the 3-BFLP is clearly outperformed. Additionally, tight lower bounds for larger instances are calculated to evaluate our heuristically determined layouts. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Facilities planning and design mixed-integer linear programming Row layout problem

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Optimal override policy for chemotherapy scheduling template via mixed-integer linear programming

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OPTIMIZATION LETTERS 2022年第5期16卷 1549-1562页

作者： Huang, Yu-Li Sikder, Ishtiak Xu, Guanglin Mayo Clin Robert & Patricia E Kern Ctr Sci Hlth Care Delive Rochester MN USA Univ N Carolina Dept Syst Engn & Engn Management Charlotte NC 28223 USA

Owing to treatment complexity in chemotherapy administration, nurses are usually required at the beginning, end, and at certain times during the treatment period to ensure high-quality infusion. It is, thus, critical for an outpatient chemotherapy unit to design a scheduling template that can effectively match nursing resources with treatment requirements. The template contains appointment slots of different lengths and thus allows schedulers to place patients into these slots according to the provider's order. As the template is often used over a period of several months, there usually exists a mismatch between the daily patient mix and the fixed structure of the given template. Hence, override policies must be employed to adjust to demand. However, these policies are often manually performed by schedulers. We propose a mixed-integer linear programming model to systematically develop optimal override policies in place of the manual process to improve template utilization while maintaining template stability. Numerical experiments based on real-life data from a chemotherapy unit are conducted to demonstrate the effectiveness of the proposed approach.

关键词： Chemotherapy Scheduling template Override policy mixed-integer linear programming

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A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2013年第Apr.期97卷 133-143页

作者： Rueda-Medina, Augusto C. Franco, John F. Rider, Marcos J. Padilha-Feltrin, Antonio Romero, Ruben Univ Estadual Paulista Fac Engn Ilha Solteira Ilha Solteira SP Brazil

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions;(b) different types of DGs are represented by their capability curves;(c) the short-circuit current capacity of the circuits is modeled through linear expressions;and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Radial distribution system Distributed generation Optimal allocation mixed-integer linear programming Short-circuit currents

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Simultaneous line planning and timetabling based on a combinational travel network for both trains and passengers: a mixed-integer linear programming approach

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2020年第3期16卷 1333-1374页

作者： Zhou, Wenliang Li, Xiang Xue, Lijuan Deng, Lianbo Yang, Xia Cent South Univ Sch Traff & Transportat Engn Changsha 410075 Peoples R China Cent South Univ Rail Data Res & Applicat Key Lab Hunan Prov Changsha 410075 Peoples R China SUNY Polytech Inst Dept Civil Engn Utica NY USA

This paper is devoted to designing a mixed-integer linear programming to solve the simultaneous line planning and timetabling problem. A directed graph is first constructed to represent the combinational travel network for both candidate trains and passengers. Through this graph, it is easy to simultaneously describe trains' operation choices, passengers' travel choices, and their restrictive relations. Based on it, a mixed-integer linear programming model with many binary and non-negative integer decision variables is built to simultaneously optimize the line plan, timetable, and passenger travel choices, which can be efficiently solved using commercial solver CPLEX for small-scale network, while a decomposition strategy is required to combine with CPLEX for large-scale network. A set of numerical experiments are carried out to analyse the impacts of flow sub-units, number of candidate trains, and weight factors. Finally, we conduct two case studies for testing the practicability of our proposed method.

关键词： Timetabling line planning rail network combinational travel network mixed-integer linear programming

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A mixed-integer linear programming model with multi-unit strategy for distributed biorefinery superstructures with economic and social benefits

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2022年第6期24卷 1903-1925页

作者： Maharana, Debasis Kommadath, Remya Kotecha, Prakash Indian Inst Technol Guwahati Dept Chem Engn Gauhati 781039 Assam India Indian Inst Technol Guwahati Sch Business Gauhati 781039 India

Biofuels have emerged as a promising alternative for depleting fossil fuels. Efficient biofuel production requires the optimal supply chain design and the planning of complex production operations in biorefineries. The biomass processing is capacity constrained due to design restrictions. The limitation on the production capacity corresponding to a selected technology restricts the maximum production from the most profitable process. In such a scenario, the production plan involves the use of less profitable processes to satisfy the demand, resulting in a sub-optimal solution. This article proposes a multi-unit, multi-period supply chain model to overcome the restriction in plant capacity by establishing multiple units of a profitable process. The multi-objective optimization study of the proposed model has been demonstrated on a case study from the literature that requires the design of supply chain for bioenergy. The proposed formulation leads to solutions with better economic and social benefits than those reported in the literature. The multi-unit model provides a solution which has a 4.73% increase in profit and generates 78 additional jobs for a horizon of 12 months. The optimal network design has contributed to several key findings, such as the breakeven point of the raw materials with respect to the profit and the dual relationship between profit and the number of jobs generated. The study also analyzes the effect of multiple units and variations of demand on the proposed model. The multi-unit model is able to determine a solution with 3.96% improvement in profit even with a reduction in the demand by 50%. [GRAPHICS] .

关键词： Biofuel supply chain Facility location Capacity planning Social impact Economic optimization mixed-integer linear programming

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Design of grounding systems in substations using a mixed-integer linear programming formulation

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ELECTRIC POWER SYSTEMS RESEARCH 2009年第1期79卷 126-133页

作者： Khodr, H. M. Salloum, G. A. Saraiva, J. T. Matos, M. A. Polytech Inst Porto GECAD Knowledge Engn & Decis Support Res Ctr P-4200072 Oporto Portugal INELECTRA CA Caracas Venezuela Univ Porto Fac Engn INESC Porto Oporto Portugal

The main purpose of this paper is the development of an optimization model to design grounding grids in electrical substations. The design of a grounding grid in a substation is formulated as a mixed-integer linear programming problem. The developed optimization model incorporates the constructive Characteristics, as well as the technical and security requirements inherent to the construction, installation and operation of these grids. The model includes variables defining the grid characteristics according to the configurations admitted by the designer, which are selected amongst a set of pie-selected grounding designs. The definition of these configurations includes the geometry of the grid, the depth at Which the conductors will be installed and the radius of the conductor. A finite number of configurations can be generated before running the optimization process by considering all the variables in accordance with the IEEE Std 80-2000. The optimization problem also includes safety constraints related with the maximum allowed touching and step voltages, which are defined according to the fibrillation discharge limits. These fibrillation discharge limits are defined by IEEE Std 80-2000 for low frequencies for high frequencies. the limits are not the same as in 50 Hz). The model also includes the equivalent impedance of the transmission line supplying the substation where it will be located the grounding grid to be designed. As a result, the problem outputs define the most adequate grounding grid among the possible pre-selected configurations. This selection is driven by the total investment and installation costs, corresponding to the objective of the optimization model. To illustrate the interest of this research, the paper includes a case study based oil a real Situation, as all example of a potential application of this approach for engineering grounding design. Finally, it should also be referred that the scope of application of this methodology is potentially

关键词： Engineering design Grounding system Substation design Optimization mixed-integer linear programming

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Optimal scheduling algorithm in point merge system including holding pattern based on mixed-integer linear programming

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2020年第10期234卷 1638-1647页

作者： Lee, Somang Hong, Youkyung Kim, Youdan Seoul Natl Univ Dept Aerosp Engn Seoul 08826 South Korea Seoul Natl Univ Inst Adv Aerosp Technol Seoul 08826 South Korea

An optimal scheduling algorithm of the point merge system that considers a holding pattern is presented based on mixed-integer linear programming. The route structure of the point merge system is constructed by adopting virtual fixes, and appropriate constraints are included to integrate a holding pattern into the formulation of point merge system. The performance of the proposed point merge system holding algorithm is demonstrated by comparing with the point merge system and first-come first-served algorithms via Monte Carlo simulation. Simulation reveals that the point merge system holding algorithm shows the best performance in terms of delay reduction and intervention rate by air traffic controllers. The proposed point merge system holding algorithm is expected to assist human air traffic controllers as a decision support tool.

关键词： Air traffic management point merge system holding pattern mixed-integer linear programming sequencing and scheduling

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A mixed-integer linear programming formulation for the modular layout of three-dimensional connected systems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2022年第0期201卷 739-754页

作者： O'Neill, Sam Wrigley, Paul Bagdasar, Ovidiu Univ Derby Dept Elect Comp & Math Kedleston Rd Derby DE22 1GB England

Given the considerable complexity of process plants, there has been a great deal of research focused on aiding the design of plant layout through mathematical optimisation, i.e. optimising the positioning of the equipment in the plant for space and cost efficiency. Recently, the use of modular approaches within the construction industry, whereby work is performed off-site before being assembled on-site, has become a popular and powerful way of reducing build schedules and costs. Modular approaches have many other real applications where items must be packed to minimise the connections between them (e.g. piping, wiring, modular office and factory layouts) and consider the modular layout of the system. In this paper, we provide a formulation of the problem that, in addition to the standard layout problem, considers a modular block layout to allow modular construction and transportation of the plant. The problem is represented as a directed network, with the aim to pack the items into predefined containers and minimise the rectilinear distance between the connected items. We propose mixed-integer linear programming (MILP) models for the 2-dimensional and 3-dimensional problems and solve them using the state-of-the-art mathematical programming solver, Gurobi. Because of the combinatorial nature of the problem, solutions involving a large number of items may not converge and a suboptimal solution must be considered. However, our results suggest that even in the case of optimising a large number of items, the suboptimal solutions found after a reasonable number of iterations where deemed, by a domain expert, to be a good enough starting point to continue the design process, especially in the early concept phase. (c) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Floor packing Bin packing Facility layout mixed-integer linear programming MILP Process plant design

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Parallel Domain-Decomposition Algorithms for Complexity Certification of Branch-and-Bound Algorithms for mixed-integer linear and Quadratic programming

arXiv

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arXiv 2025年

作者： Shoja, Shamisa Arnström, Daniel Axehill, Daniel Division of Automatic Control Department of Electrical Engineering Linköping University Sweden Division of Systems and Control Department of Information Technology Uppsala University Sweden

When implementing model predictive control (MPC) for hybrid systems with a linear or a quadratic performance measure, a mixed-integer linear program (MILP) or a mixed-integer quadratic program (MIQP) needs to be solved, respectively, at each sampling instant. Recent work has introduced the possibility to certify the computational complexity of branch-and-bound (B&B) algorithms when solving MILP and MIQP problems formulated as multi-parametric MILPs (mp-MILPs) and mp-MIQPs. Such a framework allows for computing the worst-case computational complexity of standard B&B-based MILP and MIQP solvers, quantified by metrics such as the total number of LP/QP iterations and B&B nodes. These results are highly relevant for real-time hybrid MPC applications. In this paper, we extend this framework by developing parallel, domain-decomposition versions of the previously proposed algorithm, allowing it to scale to larger problem sizes and enable the use of high-performance computing (HPC) resources. Furthermore, to reduce peak memory consumption, we introduce two modifications to the existing (serial) complexity certification framework, integrating them into the proposed parallel algorithms. Numerical experiments show that the parallel algorithms significantly reduce computation time while maintaining the correctness of the original framework. © 2025, CC BY.

关键词： mixed-integer linear programming

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A Unifying Complexity-Certification Framework for Branch-and-Bound Algorithms for mixed-integer linear and Quadratic programming

arXiv

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arXiv 2025年

In model predictive control (MPC) for hybrid systems, solving optimization problems efficiently and with guarantees on worst-case computational complexity is critical, particularly in real-time applications. These optimization problems often take the form of mixed-integer linear programs (MILPs) or mixed-integer quadratic programs (MIQPs) that depend on system parameters. A common approach for solving such problems is the branch-and-bound (B&B) method. This paper extends existing complexity certification methods by presenting a unified complexity-certification framework for B&B-based MILP and MIQP solvers, specifically for the family of multi-parametric MILP and MIQP problems that arise in, e.g., hybrid MPC applications. The framework provides guarantees on worst-case computational metrics, including the maximum number of iterations or relaxations B&B algorithms require to reach optimality. It systematically accounts for different branching and node selection strategies, as well as heuristics integrated into B&B, ensuring a comprehensive certification framework. By offering theoretical guarantees and practical insights for solver customization, the proposed framework enhances the reliability of B&B for real-time application. The usefulness of the proposed framework is demonstrated through numerical experiments on both random MILPs and MIQPs, as well as on MIQPs arising from a hybrid MPC problem. © 2025, CC BY.

关键词： mixed-integer linear programming

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