基于风险控制的供应链鲁棒优化问题研究
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摘要
各种不确定性因素的存在是供应链风险的主要来源，针对不确定因素引起的风险，对供应链实施有效的风险控制是供应链风险管理的重要内容。由于不同风险因素发生的概率以及产生的影响往往各不相同，本文以供应链中最普遍同时也是影响最广泛的需求不确定性因素为研究对象，并根据需求的不确定性特点，利用鲁棒优化方法，通过建立相应的鲁棒优化模型以及对模型的相关问题的分析，研究供应链风险管理中的风险分担和风险偏好控制问题。论文的主要研究内容涉及：
1.对国内外有关供应链风险控制和鲁棒优化的发展及应用进行综述。通过对供应链风险的定性和定量研究成果进行分析和总结，提出了分散供应链下的风险分担策略和集成供应链下的风险偏好度控制策略。同时，介绍了鲁棒优化方法的基本思想，阐述了各种鲁棒优化模型的优势与应用范畴。
2.考虑到数量弹性契约可实现风险在供应链成员间按比例分担，解决需求不确定情况下的线性鲁棒优化问题。通过对历史数据的分析和预测，可以确定商品需求量的波动区间，考虑到鲁棒优化处理不确定性优化问题的优势及数量弹性契约机制的风险分担功能，研究了包含制造商和销售商的二级供应链绩效优化问题。根据Stackelberg博弈理论，建立了基于数量弹性契约鲁棒线性优化模型，提出了区间性需求分布下的分散供应链系统鲁棒契约策略和集成供应链的鲁棒订货决策，研究了鲁棒决策对供应链各成员以及整体收益的影响。
3.根据集成供应链中决策者的风险偏好度差异，研究以风险偏好控制为目的的动态生产库存管理线性鲁棒优化问题。建立以I个生产者企业，一个库存点和一个废物处理基地为核心的供应链动态生产库存框架，考虑需求不确定情况下决策者的风险偏好，将区间型不确定需求集转化为对应的椭球不确定集，以供应链整体收益最大化为目标建立不确定优化模型，运用鲁棒优化思想转化得到数据确定性线性鲁棒对应模型，并通过分析该模型的解在更一般的区间型需求不确定集下违背约束条件的概率上限讨论该鲁棒对应模型解的可靠性和有效性。
4.考虑到动态生产管理问题中决策者的计划往往与往期多期需求密切相关，进一步解决了以风险偏好控制为目的的仿射可调整鲁棒优化问题。考虑仿射可调整鲁棒优化模型（AARC）在处理动态背景下不确定问题的优势，从另一角度讨论了需求不确定情况下考虑决策者风险偏好和废物处理的供应链动态生产库存管理问题。运用仿射可调整鲁棒优化方法，建立了追求整体收益最大化的不确定优化模型，并通过等价变换获得了计算上可处理的鲁棒对应问题。
以上建立的两种鲁棒线性优化模型和仿射可调整鲁棒优化模型的解或近似解都可转化为对应的计算上可处理的确定性数学规划问题，可以通过Lingo、Matlab、Cplex、GAMS等一些常用的商业软件求解，因此，实际决策者只需要关注于实际问题的模型化过程从而忽略模型求解算法的设计。最后，针对两种鲁棒线性优化模型分别进行了数值算例分析，验证了鲁棒优化方法的有效性及鲁棒策略对供应链风险控制目标的影响。
The presence of a variety of uncertainties is the main source of supply chain risk, so thatit is an important issue of the supply chain risk management to implement effective supplychain risk control. However, different risk factors always have different probability ofoccurrence and therefore have different impact, thus, this thesis selects the demanduncertainty which is most common and also with the most extensive influence as the researchbackground. By the method of robust optimization, the risk-sharing and risk appetite controlproblems in the supply chain risk management will be considered in this thesis throughestablishing corresponding robust optimization model and the analysis of the related problems.Specific studies are as follows:
1. This thesis introduces the relevant research of supply chain risk control, and reviewsthe development and application of robust optimization. A risk-sharing strategy for thedecentralized supply chain and a risk appetite control strategy for the integrated supply chainare put forward through qualitative and quantitative research on supply chain risk.Simultaneously, it introduces the basic idea of robust optimization method and describes theadvantages and scope of application of the various robust optimization models.
2. A linear robust optimization problem subjected to demand uncertainty is consideredwhen taking into account the quantity flexibility contract which can achieve risk sharingamong supply chain members in proportion. Trough the analysis of the historical data, afluctuation range of demand for commodity can be determined. Given the nice performanceof robust optimization in handling problems with uncertainties, and the advantages of quantityflexibility contract with respect to risk-sharing mechanism, this thesis studies a two-stagesupply chain system, establishes a robust operation model based on the quantity flexibilitycontract, using the stackelberg game theory, gives the robust strategies and discusses theinfluence on the supply chain members’and the overall revenue.
3. Considering the risk preference of the integrated manager, we study the dynamicproduction and inventory management problem for the purpose of risk preference control. Asupply chain framework with I producer enterprises, one warehouse and one waste treatmentbase is constructed to describe the T-stage production and inventory management problem ,then we get one joint ellipsoid uncertainty set when taking the risk preference of decisionmakers into account, and set up one uncertain optimization model with the pursuit ofmaximizing the overall revenue. By using the robust idea, we translate the uncertainoptimization model into one deterministic linear robust counterpart, and discusses therobustness of the solution corresponding to the reliability and validity of the model.
4. For the plans made by the decision makers are often closely related to the demands ofprior periods in the dynamic production management issues, further, an affine adjustablerobust optimization problem is resolved. Considering the advantage of affinely adjustablerobust counterpart method in dealing with problems with uncertainties in the dynamic context,we develop an uncertain optimization model in pursuit of maximizing the overall revenue through adaptively controlling multi-period production policies, and equivalently convert it toone deterministic robust counterpart which is in fact a tractable second order cone problem.
The solutions or approximate solutions of above two linear robust optimization modelsand the affine adjustable robust optimization model can be obtained by translating thesemodels into the corresponding deterministic mathematical programming which arecomputationally tractable by Lingo, Matlab, Cplex, GAMS and some other commonlycommercial software, so that the actual decision makers only need to focus on the modelconstruction with neglect of the model solution algorithm design. Finally, according to twokind of linear robust optimization model, the numerical example is analyzed to show theeffectiveness of robust optimization method and describe the influence of robust strategies onthe supply chain risk control objectives.
1.对国内外有关供应链风险控制和鲁棒优化的发展及应用进行综述。通过对供应链风险的定性和定量研究成果进行分析和总结，提出了分散供应链下的风险分担策略和集成供应链下的风险偏好度控制策略。同时，介绍了鲁棒优化方法的基本思想，阐述了各种鲁棒优化模型的优势与应用范畴。
2.考虑到数量弹性契约可实现风险在供应链成员间按比例分担，解决需求不确定情况下的线性鲁棒优化问题。通过对历史数据的分析和预测，可以确定商品需求量的波动区间，考虑到鲁棒优化处理不确定性优化问题的优势及数量弹性契约机制的风险分担功能，研究了包含制造商和销售商的二级供应链绩效优化问题。根据Stackelberg博弈理论，建立了基于数量弹性契约鲁棒线性优化模型，提出了区间性需求分布下的分散供应链系统鲁棒契约策略和集成供应链的鲁棒订货决策，研究了鲁棒决策对供应链各成员以及整体收益的影响。
3.根据集成供应链中决策者的风险偏好度差异，研究以风险偏好控制为目的的动态生产库存管理线性鲁棒优化问题。建立以I个生产者企业，一个库存点和一个废物处理基地为核心的供应链动态生产库存框架，考虑需求不确定情况下决策者的风险偏好，将区间型不确定需求集转化为对应的椭球不确定集，以供应链整体收益最大化为目标建立不确定优化模型，运用鲁棒优化思想转化得到数据确定性线性鲁棒对应模型，并通过分析该模型的解在更一般的区间型需求不确定集下违背约束条件的概率上限讨论该鲁棒对应模型解的可靠性和有效性。
4.考虑到动态生产管理问题中决策者的计划往往与往期多期需求密切相关，进一步解决了以风险偏好控制为目的的仿射可调整鲁棒优化问题。考虑仿射可调整鲁棒优化模型（AARC）在处理动态背景下不确定问题的优势，从另一角度讨论了需求不确定情况下考虑决策者风险偏好和废物处理的供应链动态生产库存管理问题。运用仿射可调整鲁棒优化方法，建立了追求整体收益最大化的不确定优化模型，并通过等价变换获得了计算上可处理的鲁棒对应问题。
以上建立的两种鲁棒线性优化模型和仿射可调整鲁棒优化模型的解或近似解都可转化为对应的计算上可处理的确定性数学规划问题，可以通过Lingo、Matlab、Cplex、GAMS等一些常用的商业软件求解，因此，实际决策者只需要关注于实际问题的模型化过程从而忽略模型求解算法的设计。最后，针对两种鲁棒线性优化模型分别进行了数值算例分析，验证了鲁棒优化方法的有效性及鲁棒策略对供应链风险控制目标的影响。
The presence of a variety of uncertainties is the main source of supply chain risk, so thatit is an important issue of the supply chain risk management to implement effective supplychain risk control. However, different risk factors always have different probability ofoccurrence and therefore have different impact, thus, this thesis selects the demanduncertainty which is most common and also with the most extensive influence as the researchbackground. By the method of robust optimization, the risk-sharing and risk appetite controlproblems in the supply chain risk management will be considered in this thesis throughestablishing corresponding robust optimization model and the analysis of the related problems.Specific studies are as follows:
1. This thesis introduces the relevant research of supply chain risk control, and reviewsthe development and application of robust optimization. A risk-sharing strategy for thedecentralized supply chain and a risk appetite control strategy for the integrated supply chainare put forward through qualitative and quantitative research on supply chain risk.Simultaneously, it introduces the basic idea of robust optimization method and describes theadvantages and scope of application of the various robust optimization models.
2. A linear robust optimization problem subjected to demand uncertainty is consideredwhen taking into account the quantity flexibility contract which can achieve risk sharingamong supply chain members in proportion. Trough the analysis of the historical data, afluctuation range of demand for commodity can be determined. Given the nice performanceof robust optimization in handling problems with uncertainties, and the advantages of quantityflexibility contract with respect to risk-sharing mechanism, this thesis studies a two-stagesupply chain system, establishes a robust operation model based on the quantity flexibilitycontract, using the stackelberg game theory, gives the robust strategies and discusses theinfluence on the supply chain members’and the overall revenue.
3. Considering the risk preference of the integrated manager, we study the dynamicproduction and inventory management problem for the purpose of risk preference control. Asupply chain framework with I producer enterprises, one warehouse and one waste treatmentbase is constructed to describe the T-stage production and inventory management problem ,then we get one joint ellipsoid uncertainty set when taking the risk preference of decisionmakers into account, and set up one uncertain optimization model with the pursuit ofmaximizing the overall revenue. By using the robust idea, we translate the uncertainoptimization model into one deterministic linear robust counterpart, and discusses therobustness of the solution corresponding to the reliability and validity of the model.
4. For the plans made by the decision makers are often closely related to the demands ofprior periods in the dynamic production management issues, further, an affine adjustablerobust optimization problem is resolved. Considering the advantage of affinely adjustablerobust counterpart method in dealing with problems with uncertainties in the dynamic context,we develop an uncertain optimization model in pursuit of maximizing the overall revenue through adaptively controlling multi-period production policies, and equivalently convert it toone deterministic robust counterpart which is in fact a tractable second order cone problem.
The solutions or approximate solutions of above two linear robust optimization modelsand the affine adjustable robust optimization model can be obtained by translating thesemodels into the corresponding deterministic mathematical programming which arecomputationally tractable by Lingo, Matlab, Cplex, GAMS and some other commonlycommercial software, so that the actual decision makers only need to focus on the modelconstruction with neglect of the model solution algorithm design. Finally, according to twokind of linear robust optimization model, the numerical example is analyzed to show theeffectiveness of robust optimization method and describe the influence of robust strategies onthe supply chain risk control objectives.
引文
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[3] A. Ben-Tal, A. Nemirovski. Robust solution of uncertain linear programs[J]. Operations Research Letter,1999, 25(1): 1-13.
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