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Global optimization of trusses with constraints on number of different cross-sections: a mixed-integer second-order cone programming approach

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第1期63卷 203-236页

作者： Kanno, Yoshihiro Tokyo Inst Technol Mat & Struct Lab Yokohama Kanagawa 2268503 Japan Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Tokyo 1138656 Japan

In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented in this paper is a new modeling of the design constraints for obtaining the minimum compliance truss design in which only a limited number of different cross-section sizes are employed. The member cross-sectional areas are considered either discrete design variables that can take only predetermined values or continuous design variables. In both cases it is shown that the compliance minimization problem can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of this optimization problem is then computed by using an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to show that the proposed approach is applicable to moderately large-scale problems.

关键词： Topology optimization Global optimization mixed-integer programming Second-order cone programming Optimal standardization

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integer programming models versus advanced planning business software for a multi-level mixed-model assembly line problem

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2020年第3期28卷 1141-1177页

作者： Kreiter, Tobias Pferschy, Ulrich Karl Franzens Univ Graz Dept Stat & Operat Res Univ Str 15 A-8010 Graz Austria

Many manufactures are shifting from classical production environments with large batch sizes towards mixed-model assembly lines due to increasing product variations and highly individual customer requests. However, an assembly line should still be run with constant speed and cycle time. Clearly, the consecutive production of different models will cause a highly unbalanced temporal distribution of workload. This can be avoided by moving some assembly steps to pre-levels thus smoothing out the utilization of the main line. In the resulting multi-level assembly line the sequencing decision on the main line has to take into account the balancing of workload for all pre-levels. Otherwise, the modules or parts delivered from the pre-levels would cause congestion of the main line. One planning strategy aims at mixing the models on the main line to avoid blocks of identical units. In this contribution we compare two different realizations for this approach. On one hand we present a mixed-integer programming model (MIP), strengthen it by adding valid inequalities and enrich it with a number of relevant practical extensions. Also the actual objective of explicitly balancing pre-level workloads is considered. On the other hand, we illustrate how this strategy could be realized in an advanced planning system linked to an enterprise resource planning system, namely SAP APO. Finally, we perform a computational study to investigate the possibilities and limitations of MIP models and the realization in SAP APO. The experiments rely on a real-world production planning problem of a company producing engines and gearboxes.

关键词： Multi-level production system Load balancing Model-mix planning mixed-integer programming SAP APO

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mixed-integer second-order cone programming for global optimization of compliance of frame structure with discrete design variables

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2016年第2期54卷 301-316页

作者： Kanno, Yoshihiro Tokyo Inst Technol Mat & Struct Lab Yokohama Kanagawa 2268503 Japan Univ Tokyo Dept Math Informat Tokyo 1138656 Japan

Frame structures are extensively used in mechanical, civil, and aerospace engineering. Besides generating reasonable designs of frame structures themselves, frame topology optimization may serve as a tool providing us with conceptual designs of diverse engineering structures. Due to its nonconvexity, however, most of existing approaches to frame topology optimization are local optimization methods based on nonlinear programming with continuous design variables or (meta)heuristics allowing some discrete design variables. Presented in this paper is a new global optimization approach to the frame topology optimization with discrete design variables. It is shown that the compliance minimization problem with predetermined candidate cross-sections can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution is then computed with an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to examine computational efficiency of the proposed approach.

关键词： Frame topology optimization Global optimization Discrete optimization mixed-integer programming Second-order cone programming

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A multi-parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems

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COMPUTERS & CHEMICAL ENGINEERING 2019年 125卷 98-113页

作者： Avraamidou, Styliani Pistikopoulos, Efstratios N. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX USA

Optimization problems involving two decision makers at two different decision levels are referred to as bi-level programming problems. In this work, we present novel algorithms for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer convex quadratic programming problems (B-MIQP) containing both integer and bounded continuous variables at both optimization levels. Based on multi-parametric programming theory, the main idea is to recast the lower level problem as a multiparametric programming problem, in which the optimization variables of the upper level problem are considered as bounded parameters for the lower level. The resulting exact multi-parametric mixed-integer linear or quadratic solutions are then substituted into the upper level problem, which can be solved as a set of single-level, independent, deterministic mixed-integer optimization problems. Extensions to problems including right-hand-side uncertainty on both lower and upper levels are also discussed. Finally, computational implementation and studies are presented through test problems. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Bilevel programming Multi parametric programming mixed-integer programming

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Damper placement optimization in a shear building model with discrete design variables: a mixed-integer second-order cone programming approach

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EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2013年第11期42卷 1657-1676页

作者： Kanno, Yoshihiro Univ Tokyo Dept Math Informat Tokyo 1138656 Japan

Supplemental damping is known as an efficient and practical means to improve seismic response of building structures. Presented in this paper is a mixed-integer programming approach to find the optimal placement of supplemental dampers in a given shear building model. The damping coefficients of dampers are treated as discrete design variables. It is shown that a minimization problem of the sum of the transfer function amplitudes of the interstory drifts can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of the optimization problem is then found by using a solver based on a branch-and-cut algorithm. Two numerical examples in literature are solved with discrete design variables. In one of these examples, the proposed method finds a better solution than an existing method in literature developed for the continuous optimal damper placement problem. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： optimal damper placement aseismic design transfer function structural control mixed-integer programming global optimization

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Integrated system dynamics modeling and optimization for artisanal and small-scale gold supply chains

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IISE TRANSACTIONS 2025年第3期57卷 322-335页

作者： Aranoglu, Fatih Flamand, Tuelay Duzgun, Sebnem Martinez, Gerardo Smith, Nicole Colorado Sch Mines Dept Min Engn Golden CO USA Univ Colorado Business Sch Denver CO 80202 USA

We address artisanal and small-scale gold mining in Peru. Using the data collected through field visits, we develop a System Dynamics (SD) model to examine the current operations of the gold supply chain, and its interplay with mercury and gas suppliers. The current mining operations cause potential health and environmental issues, due to high mercury usage, and other issues (e.g., safety issues). As a potential solution to overcome such problems, we consider incorporating a cyanide processing facility into the SD model, where we examine the amount of ore that a miner would be willing to sell to the facility under several payback scenarios. We formulate a mixed-integer programming model that prescribes the optimal transition plan of a miner from local production to selling their ore to the facility within a time horizon that maximizes a miner's profit. The optimal solution provides a 22% improvement in the miners' profit over that of their current operations. We also conduct a sensitivity analysis to test the sensitivity of the optimal solution to the changes in several input parameters. We discuss that the solution is most sensitive to the gold price changes and the least sensitive to the local production cost changes.

关键词： Small-scale gold supply chain system dynamics modeling mixed-integer programming

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An integrated approach to the optimal design of sustainably efficient biorefinery supply chains

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COMPUTERS & CHEMICAL ENGINEERING 2025年 198卷

作者： Ferrero, Lucas M. Machin Jimenez, Richard Cabrera Wheeler, Jonathan Pozo, Carlos Mele, Fernando D. Univ Nacl Tucuman Dept Ingn Proc & Gest Ind FACET Av Independencia 1800T4002BLR San Miguel De Tucuman Tucuman Argentina Consejo Nacl Invest Cient & Tecn Consejo Nacl Invest Cient & Tecn Juan Crisostomo Alvarez 722AR T4000 San Miguel De Tucuman Tucuman Argentina Swiss Fed Inst Technol Inst Chem & Bioengn Dept Chem & Appl Biosci Vladimir Prelog Weg 1 CH-8093 Zurich Switzerland Univ Rovira i Virgili Dept Engn Quim Av Paisos Catalans 26 Tarragona 43007 Spain

The agribusiness sector needs to strategically align its activities with the 2030 Sustainable Development Goals. Biorefineries offer a solution for regions rich in natural resources, allowing them to utilize available biomass and progressively reduce dependence on fossil fuels. To ensure the sustainable design and management of biorefinery supply chains, key decisions need to be carefully assessed, taking into account economic, environmental and social impacts. This study proposes a purpose-driven strategy for the multi-criteria design of sustainable biorefinery supply chains, combining a multi-scenario MILP optimization approach with an efficiency (and superefficiency) ranking using Data Envelopment Analysis (DEA) to address economic, environmental, and social trade-offs. The capabilities of the approach are demonstrated through a real case study in Argentina, using sugarcane and lemon derivatives as feedstocks for bioproducts such as ethanol, citric acid, methanol and lactic acid. The results show the production of bioethanol from sugarcane juice, together with the production of other bioproducts from sugarcane bagasse, as the optimal and sustainably efficient scenario.

关键词： Biomass Bioproducts mixed-integer programming Life cycle assessment Data envelopment analysis Multi-criteria decision-making

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Integrated multi-plant collaborative production, inventory, and hub-spoke delivery of make-to-order products

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IISE TRANSACTIONS 2025年第1期57卷 60-74页

作者： Liu, Kefei Jiang, Zhibin Zhou, Liping Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai Peoples R China Shanghai Jiao Tong Univ Sino US Global Logist Inst Antai Coll Econ & Management Shanghai Peoples R China Shanghai Jiao Tong Univ Data Driven Management Decis Making Lab Shanghai Peoples R China

Motivated by make-to-order applications with committed delivery dates in a variety of industries, we investigate the integrated multi-plant collaborative production, inventory, and hub-spoke delivery problem in a complex production-distribution network. This network includes multi-location heterogeneous plants, distribution centers, and customers, for producing customized and splittable orders with one or more general-size multi-type jobs. Completed jobs are transported from plants to distribution centers, and then the orders whose all constituent jobs have arrived are delivered from distribution centers to customer sites. The objective is to make integrated scheduling decisions for production, inventory, and delivery, for minimizing total cost composed of production, transportation, tardiness, and inventory. We first formulate this problem as a mixed-integer programming model, and analyze its intractability by proving that the problem is NP-hard and no approximation algorithms exist with a constant worst-case ratio. We then reformulate this problem as a binary integer linear programming model to select a feasible schedule for each job, and propose a combined column generation and two-layer column enumeration algorithm to solve it. Through extensive numerical experiments, we demonstrate that our proposed algorithm is capable of generating optimal or near-optimal solutions expeditiously and outperforms four benchmark approaches, and gain valuable managerial insights for practitioners.

关键词： Customized and splittable orders integrated scheduling multi-plant production and hub-spoke delivery mixed-integer programming column generation and column enumeration

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A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis

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INFORMS JOURNAL ON COMPUTING 2025年第1期37卷 1-196, C2页

作者： Jung, Jihye Choi, In-Chan Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Korea Univ Div Ind Management Engn Seoul 02841 South Korea

This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost-the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper.

关键词： mixed-integer programming multicommodity network branch and cut quantum computing circuit synthesis

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Resource allocation for Hyphantria cunea invasive management:a novel simulation-based optimization model

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APPLIED MATHEMATICAL MODELLING 2025年 138卷

作者： Zhang, Shuhua Liu, Ming Wang, Peng Nanjing Univ Sci & Technol Sch Econ & Management Nanjing 210094 Peoples R China Jiangsu Prov & Chinese Acad Sci Inst Bot Jiangsu Key Lab Res & Utilizat Plant Resources Nanjing 210014 Peoples R China

In this study, we propose an integrated mixed-integer programming (MIP) model for allocating a limited budget to control a destructive invasive insect endangering the forest vegetation, Hyphantria cunea (H. cunea). Our model seeks to minimize the number of infected and dead trees within a preset planning period, factoring in various infestation scenarios, migration behaviors, resource limitations, intervention timing, and monitoring capabilities. Our modeling framework is novel in the sense that it depicts the transmission process of H. cunea as an infectious compartmental model. Our optimization model is also meaningful because it innovatively bridges the spread dynamics of H. cunea and the optimal resource allocation by using the time-varying number of infected trees that can be accepted in testing and surveillance. Our numerical test data and parameter settings have been collected from large-scale field surveys on H. cunea in Jiangsu Province over the past three years. The scenarios-based method offers significant computational advantages in searching for the best alternatives to real-world size problems in a rational time. Furthermore, our test results specify that the proposed model can not only aid in controlling H. cunea, but also can be adopted as a potential tool for managing other invasive species in the future.

关键词： Invasive species management Resources allocation Evolutionary dynamics Scenarios-based optimization mixed-integer programming

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