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A mixed integer linear programming model for optimal sovereign debt issuance

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第3期214卷 749-758页

作者： Date, P. Canepa, A. Abdel-Jawad, M. Brunel Univ Ctr Anal Risk & Optimizat Modelling Applicat Dept Math Sci Uxbridge UB8 3PH Middx England

Governments borrow funds to finance the excess of cash payments or interest payments over receipts, usually by issuing fixed income debt and index-linked debt. The goal of this work is to propose a stochastic optimization-based approach to determine the composition of the portfolio issued over a series of government auctions for the fixed income debt, to minimize the cost of servicing debt while controlling risk and maintaining market liquidity. We show that this debt issuance problem can be modeled as a mixed integer linear programming problem with a receding horizon. The stochastic model for the interest rates is calibrated using a Kalman filter and the future interest rates are represented using a recombining trinomial lattice for the purpose of scenario-based optimization. The use of a latent factor interest rate model and a recombining lattice provides us with a realistic, yet very tractable scenario generator and allows us to do a multi-stage stochastic optimization involving integer variables on an ordinary desktop in a matter of seconds. This, in turn, facilitates frequent re-calibration of the interest rate model and re-optimization of the issuance throughout the budgetary year allows us to respond to the changes in the interest rate environment. We successfully demonstrate the utility of our approach by out-of-sample back-testing on the UK debt issuance data. (C) 2011 Elsevier B.V. All rights reserved.

关键词： multistage stochastic programming Public debt management OR in government Finance

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MATHEMATICAL FOUNDATIONS OF DISTRIBUTIONALLY ROBUST multistage OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2021年第4期31卷 3044-3067页

作者： Pichler, Alois Shapiro, Alexander Tech Univ Chemnitz Fak Math D-09111 Chemnitz Germany Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in distributionally robust stochastic programming. multistage programming requires conditional versions of risk functionals to reassess future risk after partial realizations and after preceding decisions. This paper discusses a construction of the conditional counterpart of a risk functional by passing its genuine characteristics to its conditional counterparts. It turns out that the conditional risk functionals could be different from the nested analogues of the original (law invariant) risk measure. We also discuss an implication to formulations of distributionally robust stochastic programming and a relation to stochastic games.

关键词： multistage stochastic programming distributional robustness conditional risk measures dynamic equations stochastic games rectangularity

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Optimal team deployment in urban search and rescue

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2012年第8期46卷 984-999页

作者： Chen, Lichun Miller-Hooks, Elise Univ Maryland Dept Civil & Environm Engn College Pk MD 20742 USA

The problem of optimally deploying urban search and rescue (USAR) teams to disaster sites in post-disaster circumstances is formulated as a multistage stochastic program (MSP). A portion of sites requiring assistance arrive dynamically over the decision horizon and key problem characteristics are known only with uncertainty a priori. The problem seeks to identify a set of tours for USAR teams so as to maximize the total expected number of people that can be saved by attending to all or a subset of disaster sites within the disaster region. Decisions are taken dynamically over the decision horizon as situational awareness improves and survival likelihood diminishes with the aim of increasing the expected number of saved lives. To overcome the expensive computational effort associated with solving a MSP, a column generation-based strategy that consists of solving a series of interrelated two-stage stochastic programs with recourse within a shrinking time horizon is developed. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： multistage stochastic programming Two-stage stochastic program with recourse Column generation Disaster management Emergency response Dynamic routing

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Utilising demand response for distribution service restoration to achieve grid resiliency against natural disasters

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第14期13卷 2942-2950页

作者： Hafiz, Faeza Chen, Bo Chen, Chen de Queiroz, Anderson Rodrigo Husain, Iqbal North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA Argonne Natl Lab Div Energy Syst 9700 S Cass Ave Argonne IL 60439 USA North Carolina Cent Univ Sch Business Dept Decis Sci Durham NC USA North Carolina State Univ Civil Construct & Environm Engn Dept Raleigh NC USA

The increased frequency of power outages due to natural disasters in recent years has highlighted the urgency of enhancing distribution grid resilience. The effective distribution service restoration (DSR) is an important measure for a resilient distribution grid. In this work, the authors demonstrate that DSR can be significantly improved by leveraging the flexibility provided by the inclusion of demand response (DR). The authors propose a framework for this by considering integrated control of household-level flexible appliances to vary the load demand at the distribution-grid level to improve DSR. The overall framework of the proposed system is modelled as a three-step method considering three optimization problems to (i) calculate feasible controllable aggregated load range for each bus, (ii) determine candidate buses to perform DR and their target load demand, and (iii) maintain the load level in each house through home energy management during the DSR, considering uncertainties in load and solar generation sequentially. The optimization problems are formulated as linear programming, mixed-integer linear programming, and multistage stochastic programming (solved using the stochastic dual dynamic programming) models. Case studies performed in the IEEE 123-node test feeder show improvements in resilience in terms of energy restored compared to the restoration process without DR.

关键词： optimisation power grids energy management systems power distribution control power system restoration demand side management domestic appliances demand response grid resiliency power outages distribution grid resilience resilient distribution grid integrated control household-level flexible appliances distribution-grid level optimisation problems aggregated load target load demand mixed-integer linear programming distribution service restoration IEEE 123-node test feeder system stochastic dual dynamic programming multistage stochastic programming solar generation home energy management

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A mathematical model for vehicle routing problem under endogenous uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2016年第2期54卷 579-590页

作者： Khaligh, F. Hooshmand MirHassani, S. A. Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

In this study, a multistage stochastic programming (SP) model is presented for a variant of single-vehicle routing problem with stochastic demands from a dynamic viewpoint. It is assumed that the actual demand of a customer becomes known only when the customer is visited. This problem falls into the category of SP with endogenous uncertainty and hence, the scenario tree is decision-dependent. Therefore, nonanticipativity of decisions is ensured by conditional constraints making up a large portion of total constraints. Thus, a novel approach is proposed that considerably reduces the problem size without any effect on the solution space. Computational results on some test problems are reported.

关键词： multistage stochastic programming endogenous uncertainty vehicle routing problem dynamic strategy decision-dependent scenario tree nonanticipativity constraints

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An interval multistage water allocation model for crop different growth stages under inputs uncertainty

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AGRICULTURAL WATER MANAGEMENT 2017年 186卷 86-97页

作者： Chen, Shu Shao, Dongguo Gu, Wenquan Xu, Baoli Li, Haoxin Fang, Longzhang Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China

Due to different responses of crop growth stages to the water deficit, it is necessary to optimize water allocation between different growth stages to obtain the maximum food production in reservoir irrigation systems which are widely distributed throughout Southern China and India. In order to address the inputs uncertainties and dynamics existing in the above agricultural water management, an interval multistage water allocation model is developed. By incorporating multistage stochastic programming and interval parameter programming, the developed model can deal with uncertain inputs both expressed as interval parameters and probability distributions, and realize a dynamic irrigation among different growth stages from a reservoir. In the model, water requirement targets are first treated as first-stage decision variables to tackle the unique problem of agricultural water management. Additionally, given that net benefit and penalty of each growth stage are key parameters due to their determinative roles for allocation between different growth stages, a crop water production function is introduced into the calculation to make them factually reflect the competition among different growth stages. The model is then applied to the Yangshudang Irrigation District to plan rice irrigation and demonstrate its applicability. Rainfall has been divided into five levels with probability distributions in each growth stage and parameters have been characterized as interval numbers to show system uncertainty. Five scenarios that represent different initial active storage levels of the reservoir are set to acquire more detailed results. Through the parameter estimation, net benefits are [1.08,1.29], [5.04, 6.01], [11.79,14.08] and [1.61,1.92] RMB/m(3), and penalties are [2.39, 2.48], [11.13, 11.54], [26.05, 27.01] and [3.55, 3.68] RMB/m(3) for tillering stage, booting stage, heading stage and milky stage respectively. Through the model simulation, water requirement targets in booti

关键词： Crop growth stage Interval programming Irrigation water allocation multistage stochastic programming Water production function Inputs uncertainty

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A model for optimization of process integration investments under uncertainty

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ENERGY 2011年第5期36卷 2733-2746页

作者： Svensson, Elin Stromberg, Ann-Brith Patriksson, Michael Chalmers Univ Technol Environm & Energy Dept SE-41296 Gothenburg Sweden Univ Gothenburg Dept Math Sci SE-41296 Gothenburg Sweden Chalmers Univ Technol Dept Math Sci SE-41296 Gothenburg Sweden

The long-term economic outcome of energy-related industrial investment projects is difficult to evaluate because of uncertain energy market conditions. In this article, a general, multistage, stochastic programming model for the optimization of investments in process integration and industrial energy technologies is proposed. The problem is formulated as a mixed-binary linear programming model where uncertainties are modelled using a scenario-based approach. The objective is to maximize the expected net present value of the investments which enables heat savings and decreased energy imports or increased energy exports at an industrial plant. The proposed modelling approach enables a long-term planning of industrial, energy-related investments through the simultaneous optimization of immediate and later decisions. The stochastic programming approach is also suitable for modelling what is possibly complex process integration constraints. The general model formulation presented here is a suitable basis for more specialized case studies dealing with optimization of investments in energy efficiency. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Process integration multistage stochastic programming Mixed-integer linear programming Scenario-based modelling Decision support Investment planning

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Multi-Stage stochastic programming Under Endogenous Uncertainty of Integrated Sustainable Chemical Process Design and Expansion Planning

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ACS SUSTAINABLE CHEMISTRY & ENGINEERING 2024年第47期12卷 17190-17209页

作者： Xu, Yuxuan Li, Yue Zhang, Lifeng Yuan, Zhihong Tsinghua Univ Dept Chem Engn Beijing 100084 Peoples R China Imperial Coll London Sargent Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England

Effective decision-making is essential for minimizing the environmental footprint while strengthening the competitiveness of the chemical industry. This paper proposes a multistage stochastic programming (MSSP) framework to take into account the design and expansion planning simultaneously for a sustainable multinetwork that integrates the water treatment, renewable energy supply, and carbon capture, utilization and storage (CCUS) with a main chemical processing sector under endogenous uncertainty related to conversion rates arising from the possible processing steps. Both economic and environmental concerns are involved in the optimization model for the entire system. The resulting mixed-integer linear programming (MILP) model is then solved using the Lagrangean decomposition algorithm. The proposed framework is further implemented in xylitol process design problems. Four cases are established based on different combinations of uncertain parameter distributions and time horizons, with model complexity increasing sequentially. The effectiveness of the proposed framework is further validated under new randomized sampling scenarios. The results indicate that integrating multinetworks can significantly reduce carbon emissions, thereby mitigating environmental impacts while satisfying production demands. Specifically, carbon dioxide (CO2) can be fully captured and optimally utilized, wastewater can be completely treated, and economic benefits can be effectively maximized. In comparison to the deterministic model, the MSSP counterpart offers a sustainable, robust, and reliable solution for integrated design and expansion planning over the specified time horizon. Additionally, it achieves the value of stochastic solution (VSS) of 2%, potentially saving millions of dollars in long-term capacity planning, thereby underscoring the advantages of incorporating endogenous uncertainty into the problem formulation.

关键词： sustainable design expansion planning endogenousuncertainty multistage stochastic programming Lagrangean decomposition

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Heuristic solution approaches to the pharmaceutical R&D pipeline management problem

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COMPUTERS & CHEMICAL ENGINEERING 2015年 74卷 34-47页

作者： Christian, Brianna Cremaschi, Selen Univ Tulsa Dept Chem Engn Tulsa OK 74104 USA

The paper presents two heuristic approaches, a shrinking horizon multiple two-stage stochastic programming (MTSSP) decomposition algorithm and a knapsack decomposition algorithm (KDA), for solving multistage stochastic programmes (MSSPs) with endogenous uncertainty, specifically focusing on pharmaceutical research and development (R&D) pipeline management problem. The MTSSP decomposition algorithm decomposes the problem into a series of two-stage stochastic programmes, which are solved as resources become available. The KDA decomposes the MSSP into a series of knapsack problems, which are created and solved at key decision points on a rolling horizon fashion. Based on the results of the six case studies, both the MTSSP decomposition algorithm and the KDA generate implementable solutions that are within three percent of the rigorous MSSP solution obtained by CPLEX 12.51. Both methods showed several orders of magnitude decrease in the CPU times compared to ones that were required to solve the rigorous MSSP. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Endogenous uncertainty multistage stochastic programming Pharmaceutical R&D pipeline management Knapsack decomposition

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Amultistage decision-dependent stochastic bilevel programming approach for power generation investment expansion planning

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IISE TRANSACTIONS 2018年第8期50卷 720-734页

作者： Zhan, Yiduo Zheng, Qipeng P. Univ Cent Florida Dept Ind Engn & Management Syst Orlando FL 32816 USA

In this article, we study the long-term power generation investment expansion planning problem under uncertainty. We propose a bilevel optimization model that includes an upper-level multistage stochastic expansion planning problem and a collection of lower-level economic dispatch problems. This model seeks for the optimal sizing and siting for both thermal and wind power units to be built to maximize the expected profit for a profit-oriented power generation investor. To address the future uncertainties in the decision-making process, this article employs a decision-dependent stochastic programming approach. In the scenario tree, we calculate the non-stationary transition probabilities based on discrete choice theory and the economies of scale theory in electricity systems. The model is further reformulated as a single-level optimization problem and solved by decomposition algorithms. The investment decisions, computation times, and optimality of the decision-dependent model are evaluated by case studies on IEEE reliability test systems. The results show that the proposed decision-dependent model provides effective investment plans for long-term power generation expansion planning.

关键词： multistage stochastic programming bilevel optimization generation expansion decision-dependent probability decomposition algorithms

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