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Sequencing mixed-model assembly lines with risk-averse stochastic mixed-integer programming

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2022年第12期60卷 3774-3791页

作者： Guo, Ge Ryan, Sarah M. Univ Baltimore Dept Informat Syst & Decis Sci 1420 N Charles St Baltimore MD 21201 USA Iowa State Univ Dept Ind & Mfg Syst Engn Ames IA USA

Sequencing decisions in mixed-model assembly lines are complicated by various uncertainty factors. This paper addresses a real-life uncertainty factor identified in a manufacturer of large vehicles, by modelling unreliable part delivery and quality. stochastic optimisation is applied to find sequencing policies that improve the on-time performance of its mixed-model assembly lines. As schedulers have different levels of risk aversion, a risk-averse programme is further presented to protect against the decision maker's chosen fraction of worst scenarios. Computational studies with Progressive Hedging as the solution method, and its lower bounding approach, demonstrate the high quality of resulting sequencing decisions and the time efficiency of the solution method.

关键词： mixed-model assembly line sequencing part unavailability stochastic mixed-integer programming risk-averse optimisation Progressive Hedging algorithm

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The C³ theorem and a D² algorithm for large scale stochastic mixed-integer programming:: Set convexification

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MATHEMATICAL programming 2005年第1期104卷 1-20页

作者： Sen, S Higle, JL Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA

This paper considers the two-stage stochastic integer programming problem, with an emphasis on instances in which integer variables appear in the second stage. Drawing heavily on the theory of disjunctive programming, we characterize convexifications of the second stage problem and develop a decomposition-based algorithm for the solution of such problems. In particular, we verify that problems with fixed recourse are characterized by scenario-dependent second stage convexifications that have a great deal in common. We refer to this characterization as the C-3 (Common Cut Coefficients) Theorem. Based on the C-3 Theorem, we develop a decomposition algorithm which we refer to as Disjunctive Decomposition (D-2). In this new class of algorithms, we work with master and subproblems that result from convexifications of two coupled disjunctive programs. We show that when the second stage consists of 0-1 MILP problems, we can obtain accurate second stage objective function estimates after finitely many steps. This result implies the convergence of the D2 algorithm.

关键词： stochastic mixed-integer programming disjunctive programming cutting plane algorithms

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Scalable branching on dual decomposition of stochastic mixed-integer programming problems

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MATHEMATICAL programming COMPUTATION 2022年第1期14卷 1-41页

作者： Kim, Kibaek Dandurand, Brian Argonne Natl Lab Math & Comp Sci Div 9700 South Cass Ave Lemont IL 60439 USA

We present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caroe and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including (1) branching on the optimal solutions of the Dantzig-Wolfe reformulation of the restricted master problem and (2) using a more comprehensive (yet simple) measure for the dispersions associated with subproblem solution infeasibility. We prove that the proposed branching process leads to an algorithm that terminates finitely, and we provide conditions under which globally optimal solutions can be identified after termination. We have implemented our new branching method, as well as the Caroe-Schultz method and a branch-and-price method, in the open-source software package DSP. Using SIPLIB test instances, we present extensive numerical results to demonstrate that the proposed branching method significantly reduces the number of node subproblems and solution times.

关键词： stochastic mixed-integer programming Branch-and-bound Dual decomposition Parallel computing

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Generation Capacity Expansion Planning under Demand Uncertainty Using stochastic mixed-integer programming

Generation Capacity Expansion Planning under Demand Uncertai...

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IEEE PES General Meeting

作者： Gandulfo, William Gil, Esteban Aravena, Ignacio Univ Tecn Federico Santa Maria Valparaiso Chile

ISBN: (纸本)9781479964154

Generation Capacity Expansion Planning (GCEP) decides about generation capacity investments to adequately supply the future loads, while minimizing investment and operation costs satisfying a set of technical and security constraints. This paper presents a stochastic mixed-integer programming formulation (SMIP) for suggesting future generation investments considering demand uncertainty. The method was applied to the Chilean Northern Interconnected System (SING) with a planning horizon of 14 years considering uncertainty on the possible future connection of large industrial and mining loads. The computational challenges posed by GCEP under uncertainty required compromising between the detail of the stochastic demand representation and the detail of the transmission system. Thus, scenario-reduction was applied to keep the problem of a manageable size without losing too much transmission detail. Our results for the SING showed that use of SMIP can bring expected savings of about 1.1% on the total investment plus expected operational cost with respect to optimization using an average demand scenario. Furthermore, the stochastic plan showed less variability across scenarios and proved to be more resilient to changes in the modeling assumptions than the other plans.

关键词： generation planning capacity expansion planning stochastic optimization stochastic mixed-integer programming

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Ensemble Variance Reduction Methods for stochastic mixed-integer programming and their Application to the stochastic Facility Location Problem

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INFORMS JOURNAL ON COMPUTING 2024年第2期36卷 305-704, C2页

作者： Xu, Jiajun Sen, Suvrajeet Univ Southern Calif Ming Hsieh Dept Elect & Comp Engn Los Angeles CA 90089 USA Univ Southern Calif Daniel J Epstein Dept Ind & Syst Engn Los Angeles CA 90089 USA

Sample average approximation (SAA), the standard approach to stochastic mixed-integer programming, does not provide guidance for cases with limited computational budgets. In such settings, variance reduction is critical in identifying good decisions. This paper explores two closely related ensemble methods to determine effective decisions with a probabilistic guarantee. (a) The first approach recommends a decision by coordinating aggregation in the space of decisions as well as aggregation of objective values. This combination of aggregation methods generalizes the bagging method and the "compromise decision" of stochastic linear programming. Combining these concepts, we propose a stopping rule that provides an upper bound on the probability of early termination. (b) The second approach applies efficient computational budget allocation for objective function evaluation and contributes to identifying the best solution with a predicted lower bound on the probability of correct selection. It also reduces the variance of the upper bound estimate at optimality. Furthermore, it adaptively selects the evaluation sample size. Both approaches provide approximately optimal solutions even in cases with a huge number of scenarios, especially when scenarios are generated by using oracles/simulators. Finally, we demonstrate the effectiveness of these methods via extensive computational results for "megascale" (extremely large scale) stochastic facility location problems.

关键词： stochastic mixed-integer programming sample average approximation variance reduction bagging compromise decisions facility location problem

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Generation Capacity Expansion Planning Under Hydro Uncertainty Using stochastic mixed integer programming and Scenario Reduction

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IEEE TRANSACTIONS ON POWER SYSTEMS 2015年第4期30卷 1838-1847页

作者： Gil, Esteban Aravena, Ignacio Cardenas, Raul UTFSM Dept Elect Engn Valparaiso Chile

Generation capacity expansion planning (GCEP) is the process of deciding on a set of optimal new investments in generation capacity to adequately supply future loads, while satisfying technical and reliability constraints. This paper shows the application of stochastic mixed-integer programming (SMIP) to account for hydrological uncertainty in GCEP for the Chilean Central Interconnected System, using a two-stage SMIP multi-period model with investments and optimal power flow (OPF). The substantial computational challenges posed by GCEP imply compromising between the detail of the stochastic hydrological variables and the detail of the OPF. We selected a subset of hydrological scenarios to represent the historical hydro variability using moment-based scenario reduction techniques. The tradeoff between modeling accuracy and computational complexity was explored both regarding the simplification of the MIP problem and the differences in the variables of interest. Using a simplified OPF model, we found the difference of using a subset of hydro scenarios to be small when compared with using a full representation of the stochastic variable. Overall, SMIP with scenario reduction provided optimal capacity expansion plans whose investment plus expected operational costs were between 1.3% and 1.9% cheaper than using a deterministic approach and proved to be more robust to hydro variability.

关键词： Generation expansion planning mathematical programming optimization methods scenario reduction stochastic mixed-integer programming uncertainty

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Generation Capacity Expansion Planning under Demand Uncertainty Using stochastic mixed-integer programming

Generation Capacity Expansion Planning under Demand Uncertai...

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IEEE Power and Energy Society General Meeting

作者： William Gandulfo Esteban Gil Ignacio Aravena Universidad Tecnica Federico Santa Maria

ISBN: (纸本)9781479964161

关键词： Generation planning Capacity expansion planning stochastic optimization stochastic mixed-integer programming

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Improving efficiency and sustainability of the waste-economy-environment nexus in isolated island communities: A stochastic inexact mixed-integer fractional optimization model

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PROCESS SAFETY AND ENVIRONMENTAL PROTECTION 2025年 197卷

作者： Wang, Ziyu Lu, Zehua Chen, Xiujuan Huang, Guohe An, Chunjiang Concordia Univ Dept Bldg Civil & Environm Engn Montreal PQ H3G 1M8 Canada Univ Victoria Dept Civil Engn POB 1700 STN CSC Victoria BC V8W 2Y2 Canada Univ Texas Arlington Dept Civil Engn Arlington TX 76019 USA Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada

This study develops a stochastic inexact mixed-integer fractional optimization (SIMFO) model to enhance solid waste management (SWM) systems in isolated island communities. The model integrates inexact optimization, chance-constrained optimization, linear fractional programming, and mixed integer linear programming. It aims to maximize waste flow diversion from landfills, minimize system costs, and adhere to environmental emission caps. According to the analysis of a case study in British Columbia, Canada, by optimizing waste flows, implementing a reasonable facility expansion plan, and fully involving transfer stations, the island SWM system is expected to achieve a waste diversion rate of more than 75 %. In the future scenario, the daily amount of waste transported outside the island is reduced from 62 tonnes to zero, thereby reducing costs and environmental burdens. Compared with the present scenario (62.02 billion CO2e) and optimization programming focusing on cost reduction (69.29 billion CO2e), the upper limit result of the five-year cycle under the future scenario is 54.92 billion CO2e, representing reductions of 12 % and 21 %, respectively. The proposed SIMFO framework addresses uncertainties, optimizes facility capacity, and supports dynamic decision-making processes. This research offers a robust tool for policymakers, promoting sustainable SWM practices and long-term environmental stewardship in isolated island regions.

关键词： Indigenous communities Island practices stochastic mixed-integer programming Uncertainty Waste-environment-economy nexus Waste management

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Optimizing strategic and operational decisions of car sharing systems under demand uncertainty and substitution

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COMPUTERS & OPERATIONS RESEARCH 2025年 180卷

作者： Basciftci, Beste Koca, Esra Kosunda, Sinan Emre Univ Iowa Tippie Coll Business Dept Business Analyt Iowa City IA 52242 USA Sabanci Univ Ind Engn Program Istanbul Turkiye

Car sharing is an efficient way to improve mobility, reduce the use of personal vehicles, and lessen the associated carbon emissions. Due to increasing environmental awareness of customers and government regulations, car sharing providers must be careful about the composition of their vehicle fleet to meet diverse customer demand through vehicle types with different carbon emission levels. In this study, for a car sharing company, we consider the problems of determining service regions and purchasing decisions with a mixed fleet of vehicles under budget and carbon emission constraints, and the deployment of these vehicles to service regions under uncertain one-way and round-trip rental requests over a multi-period planning horizon. We further introduce the concept of "substitution" to the car sharing operations that provides customers with alternative vehicle options when their preferred type is unavailable. To address this complex problem, we propose a novel two-stage stochastic mixed-integer program leveraging spatial-temporal networks and multicommodity flows to capture these strategic and operational decisions of this system over the planning horizon while allowing substitution in operations. We further prove that the corresponding second-stage problem of the proposed program has a totally unimodular constraint matrix. Taking advantage of this result, we develop a branch-and-cut-based decomposition algorithm with various computational enhancements. We present an extensive computational study that highlights the value of the proposed models from different perspectives and demonstrates the performance of the proposed solution algorithm with significant speedups. Our case study provides insights for region opening and fleet allocation plans under demand uncertainty and demonstrates the value of introducing substitution to car sharing operations and the importance of integrating strategic and operational decisions and obtaining stochastic solutions.

关键词： Car sharing Substitution stochastic mixed-integer programming Decomposition algorithms Sustainable operations

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Supply Resilience Constrained Scheduling of MEGs for Distribution System Restoration: A stochastic Model and FW-PH Algorithm

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IEEE TRANSACTIONS ON SMART GRID 2025年第1期16卷 194-208页

作者： Zhang, Menglin Cai, Sheng Xie, Yunyun Zhou, Bo Zheng, Weiye Wu, Qiuwei Wen, Jinyu China Univ Geosci Sch Automat Hubei Key Lab Adv Control & Intelligent Automat Co Minist Educ Wuhan 430074 Peoples R China China Univ Geosci Engn Res Ctr Intelligent Technol Geoexplorat Minist Educ Wuhan 430074 Peoples R China Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA South China Univ Technol Sch Elect Engn Guangzhou 510641 Peoples R China Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT8 5BN North Ireland Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 430074 Peoples R China

Mobile emergency generators (MEGs) are critical resources for distribution system restoration after disaster- induced outages. However, insufficient fuel storage can cause MEGs to cease operation, leading to secondary interruptions of restored services. To enhance supply resilience, we include fuel tank (FT) dispatch as part of the MEG-aid restoration strategy. An integrated sequential service restoration model is developed to optimize the spatiotemporal travel behavior of MEGs and FTs, restoration paths, and load pickup sequences in the distribution network. To account for uncertain distribution line faults and traffic congestion, a stochastic programming approach is used. The proposed method optimally prepositions MEGs and routes them to target locations to restore critical loads by gradually forming microgrids. Moreover, the FTs in the transportation network are scheduled to ensure adequate fuel for the uninterrupted and reliable operation of MEGs. The presence of both uncertainty and discreteness presents computational challenges to the stochastic mixed-integer programming model. Thus, a distributed algorithm that combines the progressive hedging and Frank-Wolfe methods is applied to enhance computational efficiency while ensuring global convergence. Simulation results showed the effectiveness of the proposed method in improving the reliability of restoration schemes and computational efficiency.

关键词： Fuels Resilience stochastic processes Generators Convergence Fuel storage Disasters Mobile emergency generator sequential service restoration supply resilience distributed algorithm stochastic mixed-integer programming

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