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Path Flow Estimator in an Entropy Model Using a Nonlinear l-shaped algorithm

NETWORKS & SPATIAl ECONOMICS 2017年第1期17卷 293-315页

作者： Abareshi, Maryam Zaferanieh, Mehdi Keramati, Bagher Semnan Univ Dept Math Semnan Iran Hakim Sabzevari Univ Dept Appl Math Sabzevar Iran

The general problem of estimating origin-destination matrices in congested traffic networks is formulated as a mathematical program with equilibrium constraints. In this paper a path flow entropy model based on an equilibrium assignment approach is presented. It is assumed the flows on links are disaggregated due to some external reasons. Using the l-shaped algorithm the problem is transformed into a problem with less constraints. Then applying the lagrangian dual function the original problem is reduced to a nonlinear convex problem with only one linear constraint.

关键词： Origin-destination matrix Path flow estimation Traffic count Entropy model l-shaped algorithm

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Dynamic nested column and row generation for the Skiving Stock Problem under uncertain demand

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COMPUTERS & INDUSTRIAl ENGINEERING 2025年 201卷

作者： Karaca, Tolga Kudret Istanbul TopkapiUniv Dept Comp Engn TR-34087 Istanbul Turkiye

The pure Skiving Stock Problem aims to maximize the number of products with a threshold width by joining smaller items (e.g., production leftovers) through an optimal production plan. This study addresses the stochastic version of the problem under uncertain demand by proposing a two-stage stochastic programming model with recourse. The first-stage decision variable is the production quantity of the product by using each pattern of the skiving process, followed by the second-stage variables: the overproduction and underproduction quantities. The objective is to minimize the total expected cost, including the first and second-stage costs due to waste and holding or back-ordering costs. A novel solution methodology, incorporating a column generation procedure and the Integer l-shaped algorithm with Branch and Cut technique, is proposed to effectively solve this stochastic problem. We implement these two algorithms in a nested structure to combine column and row generation to obtain the optimal integer solution. To assess the efficacy and behavior of the proposed method, various experiments have been conducted on problems of escalating complexity, ranging from low to high. We further analyze and compare our solution approach with two benchmark algorithms, namely, the Progressive Hedging algorithm and the Two-Phase algorithm, which are the most pertinent in the literature. The proposed method demonstrates superiority over the Two-Phase algorithm, exhibiting a relative gap of 2.97% for the benchmark problem. Finally, we present the value of the stochastic solution and the expected value of perfect information, offering a comprehensive view of decision-making under uncertainty.

关键词： Stochastic programming Skiving stock problem Column generation l-shaped algorithm

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A stochastic hub location and fleet assignment problem for the design of reconfigurable park-and-ride systems

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TRANSPORTATION RESEARCH PART E-lOGISTICS AND TRANSPORTATION REVIEW 2024年 184卷

作者： Guillot, Matthieu Rey, David Furno, Angelo El Faouzi, Nour-Eddin Univ Gustave Eiffel ENTPE LICIT ECO7 Champs Sur Marne France Univ Cote dAzur SKEMA Business Sch Sophia Antipolis France

Park -and -ride systems have the potential to improve the efficiency of transportation networks by providing targeted shared mobility services. The design of a park -and -ride system depends on its role in regards to the broader transportation network. Reconfigurable park -and -ride systems aim to provide complementary shared mobility services in the context of varying travel demand scenarios, such as special events, network maintenance operations or non -recurrent perturbations. The design of reconfigurable park -and -ride systems involves the location of access and egress hubs for shared mobility services. We study an extended version of this hub location problem with integrated fleet assignment decisions. We consider stochastic scenarios representative of varying travel demand and traffic conditions on the network and propose a two -stage stochastic integer programming hub location formulation for this problem. First -stage variables represent hub location decision while second -stage variables represent both scenariobased transportation flows and fleet assignment decisions. The latter represent shared mobility service vehicles and they are modeled as integer variables. We develop solution methods to solve this two -stage stochastic integer programming hub location formulation. Exact approaches based on the l-shaped method are proposed with single- and multi -cut configurations. Valid inequalities along with a tight lower bound for the generation of optimality cuts are presented. We also develop a matheuristic to solve larger problem instances. We report numerical results on problem instances based on real data of the city of lyon, France. We show how stochastic scenarios representative of varying demand and traffic conditions can be generated from such data. Our experiments demonstrate the benefits of this integrated modeling approach for designing efficient reconfigurable park -and -ride systems while considering fleet assignment decisions.

关键词： Two-stage stochastic integer programming l-shaped algorithm Decomposition Matheuristic Hub location Fleet assignment Park-and-ride

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Two-stage risk-averse stochastic programming approach for multi-item single source ordering problem: CVaR minimisation with transportation cost

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INTERNATIONAl JOURNAl OF PRODUCTION RESEARCH 2023年第7期61卷 2129-2146页

作者： Taghizadeh, Elham Venkatachalam, Saravanan Wayne State Univ Dept Ind & Syst Engn 4815 Fourth St Detroit MI 48202 USA

Integrating inventory and transportation decisions is vital in supply chain management and can enable decision-makers to achieve competitive advantages. This study considers a multi-item replenishment problem (MIRP) with a piece-wise linear transportation cost under demand uncertainty, which usually occurs both in retail and production environment when several items must be ordered from a single supplier. Conventionally, two-stage stochastic programming formulation is risk-neutral, and it lacks robustness in the presence of high data variability. Hence, we introduce the Conditional Value at Risk (CVaR) approach for MIRP. Additionally, we deploy both single and multi-cut l-shaped and the sample average approximation method to circumvent the computational complexity to solve large-scale instances. The data-driven simulation study is used to benchmark the results from deterministic, risk-neutral, and risk-averse stochastic models. The results indicate that under higher data variations, the risk-averse model provides better perspectives for a decision-maker. The results show a 40-50% reduction in lost sales with marginal growth in total cost while considering CVaR instead of a risk-neutral approach.

关键词： Replenishment transportation conditional-value-at-risk (CVaR) l-shaped algorithm multi-cuts sample average algorithm

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Multiple allocation hub covering flow problem under uncertainty

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ANNAlS OF OPERATIONS RESEARCH 2023年第2期320卷 975-997页

作者： Sener, Nazmi Feyzioglu, Orhan Galatasaray Univ Grad Sch Sci & Engn Istanbul Turkey Galatasaray Univ Dept Ind Engn Istanbul Turkey

The hub covering problem can be viewed as a combination of the set covering and the hub location problem. In a traditional hub covering problem, all parameters are assumed to be deterministic. However, neglecting uncertainties associated with demand and transportation costs may lead to inferior solutions. Thus, we introduce three novel stochastic optimization models to formulate amultiple allocation hub covering problem in which deterministic transportation cost and demand assumptions are relaxed. Further, we also reflect scale economy to the models via inter-hub transportation cost discount factor. The l-shaped algorithm is applied to solve the sculpted problems. To test the efficiency of the proposed models, several test instances are generated and solved based on simulated data. The effects of the change of coverage radius, inter-hub discount factor, and hub opening cost are also examined. Results of this study validate that modeling the hub covering problem as a stochastic optimization model yields up 13.05% efficiency when compared to the expectation of the expected value method.

关键词： Hub location Network design Inter-hub discount factor l-shaped algorithm Simulated data Stochastic optimization

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Risk-Averse Two-Stage Stochastic Minimum Cost Consensus Models with Asymmetric Adjustment Cost

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GROUP DECISION AND NEGOTIATION 2022年第2期31卷 261-291页

作者： Ji, Ying li, Huanhuan Zhang, Huijie Shanghai Univ Sch Management Shanghai 200444 Peoples R China Univ Shanghai Sci & Technol Business Sch Shanghai 200093 Peoples R China

In the process of reaching consensus, it is necessary to coordinate different views to form a general group opinion. However, there are many uncertain factors in this process, which has brought different degrees of influence in group decision-making. Besides, these uncertain elements bring the risk of loss to the whole process of consensus building. Currently available models not account for these two aspects. To deal with these issues, three different modeling methods for constructing the two-stage mean-risk stochastic minimum cost consensus models (MCCMs) with asymmetric adjustment cost are investigated. Due to the complexity of the resulting models, the l-shaped algorithm is applied to achieve an optimal solution. In addition, a numerical example of a peer-to-peer online lending platform demonstrated the utility of the proposed modeling approach. To verify the result obtained by the l-shaped algorithm, it is compared with the CPlEX solver. Moreover, the comparison results show the accuracy and efficiency of the given method. Sensitivity analyses are undertaken to assess the impact of risk on results. And in the presence of asymmetric cost, the comparisons between the new proposed risk-averse MCCMs and the two-stage stochastic MCCMs and robust consensus models are also given.

关键词： Two-stage mean-risk stochastic programming Minimum cost consensus model Directional constraints l-shaped algorithm

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Two-stage stochastic integrated adjustment deviations and consensus models in an asymmetric costs context

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JOURNAl OF INTEllIGENT & FUZZY SYSTEMS 2021年第6期40卷 12301-12319页

作者： li, Huanhuan Ji, Ying Qu, Shaojian Univ Shanghai Sci & Technol Business Sch Shanghai Peoples R China Shanghai Univ Sch Management Shanghai Peoples R China Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing Peoples R China

Decision-makers usually have a variety of unsure situations in the environment of group decision-making. In this paper, we resolve this difficulty by constructing two-stage stochastic integrated adjustment deviations and consensus models (iADCMs). By introducing the minimum cost consensus models (MCCMs) with costs direction constraints and stochastic programming, we develop three types of iADCMs with an uncertainty of asymmetric costs and initial opinions. The factors of directional constraints, compromise limits and free adjustment thresholds previously thought to affect consensus separately are considered in the proposed models. Different from the previous consensus models, the resulting iADCMs are solved by designing an appropriate l-shaped algorithm. On the application in the negotiations on Grains to Green Programs (GTGP) in China, the proposed models are demonstrated to be more robust. The proposed iADCMs are compared to the MCCMs in an asymmetric costs context. The contrasting outcomes show that the two-stage stochastic iADCMs with no-cost threshold have the smallest total costs. Moreover, based on the case study, we give a sensitivity analysis of the uncertainty of asymmetric adjustment cost. Finally, conclusion and future research prospects are provided.

关键词： Two-stage stochastic integrated adjustment deviations and consensus model directional constraints uncertain adjustment costs uncertainty initial opinions l-shaped algorithm

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Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design

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TRANSPORTATION SCIENCE 2021年第2期55卷 414-435页

作者： Crainic, Teodor Gabriel Hewitt, Mike Maggioni, Francesca Rei, Walter Univ Quebec Montreal Ecole Sci Gest Dept Analyt Operat & Technol Informat Montreal PQ H2X 3X2 Canada Ctr Interuniv Rech Reseaux Entreprise Logist & Tr Montreal PQ H3T 1J4 Canada Loyola Univ Quinlan Sch Business Dept Informat Syst & Supply Chain Management Chicago IL 60611 USA Univ Bergamo Dept Econ I-24127 Bergamo Italy

Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.

关键词： partial Benders decomposition l-shaped algorithm stochastic network design models

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Two-stage stochastic minimum cost consensus models with asymmetric adjustment costs

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INFORMATION FUSION 2021年 71卷 77-96页

作者： li, Huanhuan Ji, Ying Gong, Zaiwu Qu, Shaojian Univ Shanghai Sci & Technol Business Sch Shanghai Peoples R China Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing Peoples R China

When dealing with consensus cost problems with asymmetric adjustment costs, the uncertain scenarios with certain probabilities which are becoming a serious problem decision-makers have to face. However, existing optimization-based consensus models have failed to consider uncertain factors that could influence the final consensus and total consensus cost. In order to better deal with these issues, it is necessary to develop practical consensus optimal models. Thus, we establish three two-stage stochastic minimum cost consensus models with asymmetric adjustment costs that may eventually lead the way to better consensus outcomes. The impact of uncertain parameters (such as individual opinions, unit asymmetric adjustment costs, compromise limits, costfree thresholds) are investigated by modeling three kinds of uncertain consensus models. We solve the proposed two-stage stochastic consensus problem iteratively using the l-shaped algorithm and show the convergence of the algorithm. Furthermore, a case of pollution control negotiations verifies the practicability of the proposed models. Moreover, the comparison of results with the l-shaped algorithm and CPlEX shows that the l-shaped algorithm is more effective in solving time. Some discussions and comparisons on local and global sensitivity analysis of the uncertain parameters are presented to reveal the features of the proposed models. Finally, the relationships between the minimum cost consensus model and minimum cost consensus models with asymmetric adjustment costs and the proposed models are also provided.

关键词： Two-stage stochastic programming Minimum cost consensus model Directional constraints l-shaped algorithm Sensitivity analysis

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Stochastic regional-based profit-maximizing hub location problem: A sustainable overview

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OMEGA-INTERNATIONAl JOURNAl OF MANAGEMENT SCIENCE 2023年 121卷

作者： Rahmati, Reza Neghabi, Hossein Bashiri, Mahdi Salari, Majid Ferdowsi Univ Mashhad Dept Ind Engn Mashhad Iran Coventry Univ Ctr Business Soc Coventry England

Climate change is one of the most important concerns globally, and countries need to improve their transportation infrastructure to handle flows with the least air pollution. In specific cities and regions, carbon emissions may cause in future many issues for people and societies. Although transportation hubs are very helpful in the reduction of transportation costs, they may cause an increase in carbon emissions in some regions, leading to long-term environmental problems. In this study, a model is developed for the profit-maximizing hub location problem that incorporates three pillars of sustainability. The proposed model is not only designed to maximize profit but also to control carbon emissions using a carbon cap policy and to reduce differences in emissions between regions with consideration of population density. This scheme will lead to achieving a sustainable transportation network. A two-stage stochastic programming approach is employed to cope with demand uncertainty. An enhanced sampling based on the self organizing map method was utilized to cluster scenarios that lead to dealing with small-sized problems. Furthermore, classical Benders decomposition, Pareto-optimal cut Benders decomposition, and l-shaped algorithms are employed to solve the proposed models more efficiently. The proposed models are analyzed using the well-known Turkish Network (TR) data set. Computational results demonstrate that the proposed models help to achieve sustainability. Factors of sustainability such as environmental and social can be achieved by slightly reducing the amount of profit in the economic factor. Furthermore, results show that the l-shaped algorithm with a multi-cut scheme outperforms the commercial solver, classical Benders decomposition, and Pareto-optimal cut Benders decomposition algorithms in large-size instances.& COPY;2023 Elsevier ltd. All rights reserved.

关键词： Profit-maximizing hub location Stochastic programming Sustainability l-shaped algorithm Carbon policy

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