项目组合选择优化建模研究
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摘要
项目组合选择问题是指在一定资源约束条件下,从候选项目中,选出-组项目,以实现企业一个或者多个战略目标的要求。项目组合选择问题是一类涉及组合优化、约束优化、多目标优化等运筹学建模和决策技术的综合问题,且有着广阔的应用领域,比如投资项目组合选择,IT项目组合选择,工程建设项目组合选择,研发项目组合选择等。并且随着问题规模的扩大,需要采用智能优化算法进行求解。具有较强的理论研究价值和实践应用价值。
项目组合选择问题随着社会的发展,在经典项目管理优化问题的基础上发展起来的。经典的项目管理优化问题有项目时间-成本置换问题,项目调度问题,项目调度鲁棒性问题等。这些问题的研究多是在单项目环境下进行的,近年来才逐渐扩展到多项目领域,比如多项目的调度。总体来讲,这些优化问题的研究还停留在如何“做好项目”的层面上,仍然没有从企业的战略高度去考虑怎样“做好的项目”。项目组合选择问题则兼顾了企业的宏观和微观要素,呈现出更高的复杂性,具有更强的生命力,正成为项目管理领域新的研究热点。
通过对国内外相关文献的研阅和分析,本文对项目组合选择问题的研究考虑在不确定性的宏观大背景下进行。在研究方法上选择运筹学优化方式进行建模研究。对于所建优化模型的求解,由于组合选择问题本身就是NP-Hard的。因此,本文采用智能优化算法进行模型求解,在较复杂的模型求解中,引入路径再连接方法进行局部爬山搜索,以获得更高质量的解。实际的仿真结果也验证了算法的有效性和正确性。通过对各领域项目组合选择现象共性特点的分析,得出了研究的主要切入点。并对所应用的基本理论知识进行了汇总和梳理。
主要研究内容包括：
(1)研究了资源可转换情况下的项目组合选择问题。构建了资源转换理论框架,提出了约束假违反和约束真违反的概念。仿真测试表明在存在资源转换条件下,资源可以得到充分的整合和利用,能够获得更高的项目组合选择收益。
(2)研究了考虑多技能人技能合成的项目组合选择问题,构建多技能人技能非线性合成函数,建立了多技能人数量受限情况下,最大化选择项目的价值的非线性混合整数优化模型,并结合项目的技能需求,为所选项目构建多技能人工作团队。由于技能合成的非线性,设计了三阶段求解方法,仿真测试验证了设计算法的有效性。
(3)研究了两期双情景项目组合选择整体优化问题,建立了双层0-1整数规划模型,上层模型为确定性情景,以两期所选项目整体价值最大为优化目标；下层为不确定性情景,以下层选择项目期望值最大为优化目标,并采用方差与期望值比值作为风险约束条件。实验得出了不同风险系数下的优化结果,并通过分析获得了较为鲁棒的核心选择项目。
(4)研究了不确定条件下多期滚动项目组合选择问题,以各期获利最大为优化目标,以企业战略需求与所选项目的合成战略贡献之间的均衡匹配性和资源动态增益性为关联约束条件,构建了优化模型。进行了十期的仿真测试研究,发现在5期以内可以保证获利的稳定性,获利波动期在第6-8期,可以帮助企业确定最佳战略调整期。各期不同类型的项目选择数量也具有较明显的周期性变化规律,研究结果具有实践指导意义。
(5)构建了模糊情景下最小-最大遗憾值(Min-Max Regret, MMR)和最小-最大相对遗憾值(Min-Max Relative Regret, MMRR)两种项目组合选择鲁棒优化(Robust Optimization,RO)模型。并根据决策者风险偏好的不同,组合形成四种确定性转换模式。在求解中综合考虑了解鲁棒和模型鲁棒的协调问题。通过仿真测试得出了一些有益的研究结论和管理建议。
结合上述研究内容,本文的创新研究工作主要可以归结为两个创新点,一是约束视角的创新,包括：可转换资源约束；多技能人资源约束；模糊情景约束；战略均衡约束四个具体的约束内容的创新；二是项目组合内部结构创新,包括：多期整体项目组合结构和多期混合项目组合结构两种结构创新。主要的研究成果体现在：探讨了资源可转换条件下的转换机制和约束违反的判别机制,并将其应用于不确定情况下的项目组合选择问题；在模糊理论的基础上构建了战略均衡匹配的理论体系,并给出了相关的公式组,将之与资源的增益性共同形成关联约束；同时,对模糊理论中贴近度的概念进行了发展,提出了上方模糊度和下方模糊度的概念,丰富了模糊理论的内容。通过建模和仿真研究,也得出了一些有益的研究成果,比如：企业战略变更的最佳调整时期；项目到达与项目选择之间的周期性规律；人力技能对组选结果和人员分配的影响等。
Project Portfolio Selection Problem (PPSP) is to select a set of projects from candidate projects under certain resources constraints in order to realize enterprise's one or more strategic objectives. PPSP is a sort of synthetical problem which involves operational research and decision-making technology such as combinatorial optimization, constrained optimization, multi-objective optimization, etc. PPSP has been widely used in many fields, such as investment project portfolio selection, IT project portfolio selection, Research and Development(R&D) project portfolio selection, etc. With the expansion of the PPSP, intelligent optimization algorithm is then adopted to solving the problem. PPSP has important theoretical and practical value.
With the development of society, PPSP has developed on the basis of classical project management optimization problem. The classical project management optimization problem includes time-cost trade-off problem、Resource-constrained Project Scheduling Problem (RCPSP), robust resource-constrained project scheduling, etc. These problems were often researched in single project environment. Only in recent years, they have expanded to multi-project area, such as multi-project scheduling. Generally speaking, researches of these optimization problems only consider how to do a good job in projects, but not considering do good projects from enterprise's strategic height. PPSP considers both enterprise's macro and micro factors, it is more complex and has more vitality, so it is becoming one of hot topics in project management area.
On the basis of a comprehensive overview on the research of project management at home and abroad, the PPSP is researched in the macro context. The modee of operation optimization is selected to set up the research model.PPSP is NP-Hard, therefore intelligent optimization algorithm is adopted to solve the constructed model. For solving the more complex models, Path Relinking (PR) is adopted to hill-climbing search, which ensures more accurate solutions. Simulation results show the effectiveness of the proposed algorithm. Thought systeming of characteristics of project portfolio in several fields, Combining with related literatures of home and abroad and characteristics of projects, we get the main breakthrough point, and the basic related theoretical knowledge about problem were collected and carded.
The main achievements of this dissertation are as follows:
(1) Project Portfolio Selection Problem considering Resources Conversion was researched. Resources conversion theoretical framework was proposed. Further, the concepts of constraint false violation and constraint true violation were put forward. Simulation test show, with considering resources conversion condition, resources can be integrated and utilized sufficiently, and more benefit of project portfolio selection be obtained,
(2) Project Portfolio Selection Problem considering skill synthesis about multi-skilled workforce was researched. A function of skill nonlinear synthesis about multi-skilled workforce was constructed. A nonlinear mixed integer programming model was established, and the objective was maximum of the value of projects, which has been selected with constraint of numbers of multi-skilled workforce. Work team of multi-skilled workforce was built up for each project that has been selected, with considering skilled requirement of the project. Because nonlinear synthesis of skill, a three stages algorithm was designed to solve the problem. Simulation test showed the algorithm was effective.
(3) Project Portfolio Selection Problem considering two-stage and double scenarios was researched under the whole portfolio constrction. A model of bi-level0-1integer programming model was established. Upper-level model was in deterministic scenario, optimization objective was maximization all of the value of projects, which have been selected within two stages. Lower layer model was in uncertain sense, optimization objective was maximization of expected value of projects that have been selected at the second stage, and the ratio of variance and expected value was adopted as risk constraint. Through test analysis, we get the optimization result with different risk index, and some robust core projects were presented.
(4) Project Portfolio Selection Problem considering Multi-phase Rolling portfolio constrction was researched under uncertain condition. The optimization objective was maximization of benefits of each phase. Related constraints were builded relying both matching of strategy equilibrium between enterprise strategy requirement and synthesis of strategy contribution of projects which were selected, and the enhancement effect of resources. With this,we built a optimization model. Simulation test of ten phases show that enterprise can get benefits steadily during five phases, and benefits is differentiate about6-8phases. This conclusion can help enterprise adjust its strategy periods. Statistics about numbers of project are selected in every phase show the periodic regularity. Research resultion can give a guidance to execution of project portfolio selection.
(5) Two models of Robust Optimization of project portfolio selection with fuzzy scenario was proposed, which objective function was Min-Max Regret or Min-Max Relative Regret. Combining risk preference of decision-maker, four deterministic modes about the models were formed. At the same time, the balance of the robust solutions feasibility and optimality was considered. Simulation test get lots of favorable conclusion, and some useful management advices are proposed.
This paper has two main innovations, the first is the innovation of optimization constraint form, including the innovation of resources conversion constraint, multi-skilled workforce constraint, fuzzy scenario constraint, and strategy equilibrium constraint.the second is the innovation of project portfolio structure, including the innovation of Multi-phase whole project portfolio structure and Multi-phase rolling project portfolio structure. The main research achievements of this paper are: Resources Conversion mechanism and discriminant mechanism of constraint violation are discussed and applied to PPSP under uncertainty, the theoretical system of matching of strategy equilibrium is constructed based on fuzzy theory and relative formulas are given, matching of strategy equilibrium and enhancement effect of resources are used as association constraint. the concept of nearness in fuzzy theory is extended, the concepts of Upper-side and down-side nearness are proposed which enriches the contents of fuzzy theory. Some positive achievements are also attained through simulations, for example, optimum adjustment periods of enterprise strategy alteration.; periodic regularity between project arriving and project selection; the effect of personnel skill for project portfolio results and personnel assignment,etc.
项目组合选择问题随着社会的发展,在经典项目管理优化问题的基础上发展起来的。经典的项目管理优化问题有项目时间-成本置换问题,项目调度问题,项目调度鲁棒性问题等。这些问题的研究多是在单项目环境下进行的,近年来才逐渐扩展到多项目领域,比如多项目的调度。总体来讲,这些优化问题的研究还停留在如何“做好项目”的层面上,仍然没有从企业的战略高度去考虑怎样“做好的项目”。项目组合选择问题则兼顾了企业的宏观和微观要素,呈现出更高的复杂性,具有更强的生命力,正成为项目管理领域新的研究热点。
通过对国内外相关文献的研阅和分析,本文对项目组合选择问题的研究考虑在不确定性的宏观大背景下进行。在研究方法上选择运筹学优化方式进行建模研究。对于所建优化模型的求解,由于组合选择问题本身就是NP-Hard的。因此,本文采用智能优化算法进行模型求解,在较复杂的模型求解中,引入路径再连接方法进行局部爬山搜索,以获得更高质量的解。实际的仿真结果也验证了算法的有效性和正确性。通过对各领域项目组合选择现象共性特点的分析,得出了研究的主要切入点。并对所应用的基本理论知识进行了汇总和梳理。
主要研究内容包括：
(1)研究了资源可转换情况下的项目组合选择问题。构建了资源转换理论框架,提出了约束假违反和约束真违反的概念。仿真测试表明在存在资源转换条件下,资源可以得到充分的整合和利用,能够获得更高的项目组合选择收益。
(2)研究了考虑多技能人技能合成的项目组合选择问题,构建多技能人技能非线性合成函数,建立了多技能人数量受限情况下,最大化选择项目的价值的非线性混合整数优化模型,并结合项目的技能需求,为所选项目构建多技能人工作团队。由于技能合成的非线性,设计了三阶段求解方法,仿真测试验证了设计算法的有效性。
(3)研究了两期双情景项目组合选择整体优化问题,建立了双层0-1整数规划模型,上层模型为确定性情景,以两期所选项目整体价值最大为优化目标；下层为不确定性情景,以下层选择项目期望值最大为优化目标,并采用方差与期望值比值作为风险约束条件。实验得出了不同风险系数下的优化结果,并通过分析获得了较为鲁棒的核心选择项目。
(4)研究了不确定条件下多期滚动项目组合选择问题,以各期获利最大为优化目标,以企业战略需求与所选项目的合成战略贡献之间的均衡匹配性和资源动态增益性为关联约束条件,构建了优化模型。进行了十期的仿真测试研究,发现在5期以内可以保证获利的稳定性,获利波动期在第6-8期,可以帮助企业确定最佳战略调整期。各期不同类型的项目选择数量也具有较明显的周期性变化规律,研究结果具有实践指导意义。
(5)构建了模糊情景下最小-最大遗憾值(Min-Max Regret, MMR)和最小-最大相对遗憾值(Min-Max Relative Regret, MMRR)两种项目组合选择鲁棒优化(Robust Optimization,RO)模型。并根据决策者风险偏好的不同,组合形成四种确定性转换模式。在求解中综合考虑了解鲁棒和模型鲁棒的协调问题。通过仿真测试得出了一些有益的研究结论和管理建议。
结合上述研究内容,本文的创新研究工作主要可以归结为两个创新点,一是约束视角的创新,包括：可转换资源约束；多技能人资源约束；模糊情景约束；战略均衡约束四个具体的约束内容的创新；二是项目组合内部结构创新,包括：多期整体项目组合结构和多期混合项目组合结构两种结构创新。主要的研究成果体现在：探讨了资源可转换条件下的转换机制和约束违反的判别机制,并将其应用于不确定情况下的项目组合选择问题；在模糊理论的基础上构建了战略均衡匹配的理论体系,并给出了相关的公式组,将之与资源的增益性共同形成关联约束；同时,对模糊理论中贴近度的概念进行了发展,提出了上方模糊度和下方模糊度的概念,丰富了模糊理论的内容。通过建模和仿真研究,也得出了一些有益的研究成果,比如：企业战略变更的最佳调整时期；项目到达与项目选择之间的周期性规律；人力技能对组选结果和人员分配的影响等。
Project Portfolio Selection Problem (PPSP) is to select a set of projects from candidate projects under certain resources constraints in order to realize enterprise's one or more strategic objectives. PPSP is a sort of synthetical problem which involves operational research and decision-making technology such as combinatorial optimization, constrained optimization, multi-objective optimization, etc. PPSP has been widely used in many fields, such as investment project portfolio selection, IT project portfolio selection, Research and Development(R&D) project portfolio selection, etc. With the expansion of the PPSP, intelligent optimization algorithm is then adopted to solving the problem. PPSP has important theoretical and practical value.
With the development of society, PPSP has developed on the basis of classical project management optimization problem. The classical project management optimization problem includes time-cost trade-off problem、Resource-constrained Project Scheduling Problem (RCPSP), robust resource-constrained project scheduling, etc. These problems were often researched in single project environment. Only in recent years, they have expanded to multi-project area, such as multi-project scheduling. Generally speaking, researches of these optimization problems only consider how to do a good job in projects, but not considering do good projects from enterprise's strategic height. PPSP considers both enterprise's macro and micro factors, it is more complex and has more vitality, so it is becoming one of hot topics in project management area.
On the basis of a comprehensive overview on the research of project management at home and abroad, the PPSP is researched in the macro context. The modee of operation optimization is selected to set up the research model.PPSP is NP-Hard, therefore intelligent optimization algorithm is adopted to solve the constructed model. For solving the more complex models, Path Relinking (PR) is adopted to hill-climbing search, which ensures more accurate solutions. Simulation results show the effectiveness of the proposed algorithm. Thought systeming of characteristics of project portfolio in several fields, Combining with related literatures of home and abroad and characteristics of projects, we get the main breakthrough point, and the basic related theoretical knowledge about problem were collected and carded.
The main achievements of this dissertation are as follows:
(1) Project Portfolio Selection Problem considering Resources Conversion was researched. Resources conversion theoretical framework was proposed. Further, the concepts of constraint false violation and constraint true violation were put forward. Simulation test show, with considering resources conversion condition, resources can be integrated and utilized sufficiently, and more benefit of project portfolio selection be obtained,
(2) Project Portfolio Selection Problem considering skill synthesis about multi-skilled workforce was researched. A function of skill nonlinear synthesis about multi-skilled workforce was constructed. A nonlinear mixed integer programming model was established, and the objective was maximum of the value of projects, which has been selected with constraint of numbers of multi-skilled workforce. Work team of multi-skilled workforce was built up for each project that has been selected, with considering skilled requirement of the project. Because nonlinear synthesis of skill, a three stages algorithm was designed to solve the problem. Simulation test showed the algorithm was effective.
(3) Project Portfolio Selection Problem considering two-stage and double scenarios was researched under the whole portfolio constrction. A model of bi-level0-1integer programming model was established. Upper-level model was in deterministic scenario, optimization objective was maximization all of the value of projects, which have been selected within two stages. Lower layer model was in uncertain sense, optimization objective was maximization of expected value of projects that have been selected at the second stage, and the ratio of variance and expected value was adopted as risk constraint. Through test analysis, we get the optimization result with different risk index, and some robust core projects were presented.
(4) Project Portfolio Selection Problem considering Multi-phase Rolling portfolio constrction was researched under uncertain condition. The optimization objective was maximization of benefits of each phase. Related constraints were builded relying both matching of strategy equilibrium between enterprise strategy requirement and synthesis of strategy contribution of projects which were selected, and the enhancement effect of resources. With this,we built a optimization model. Simulation test of ten phases show that enterprise can get benefits steadily during five phases, and benefits is differentiate about6-8phases. This conclusion can help enterprise adjust its strategy periods. Statistics about numbers of project are selected in every phase show the periodic regularity. Research resultion can give a guidance to execution of project portfolio selection.
(5) Two models of Robust Optimization of project portfolio selection with fuzzy scenario was proposed, which objective function was Min-Max Regret or Min-Max Relative Regret. Combining risk preference of decision-maker, four deterministic modes about the models were formed. At the same time, the balance of the robust solutions feasibility and optimality was considered. Simulation test get lots of favorable conclusion, and some useful management advices are proposed.
This paper has two main innovations, the first is the innovation of optimization constraint form, including the innovation of resources conversion constraint, multi-skilled workforce constraint, fuzzy scenario constraint, and strategy equilibrium constraint.the second is the innovation of project portfolio structure, including the innovation of Multi-phase whole project portfolio structure and Multi-phase rolling project portfolio structure. The main research achievements of this paper are: Resources Conversion mechanism and discriminant mechanism of constraint violation are discussed and applied to PPSP under uncertainty, the theoretical system of matching of strategy equilibrium is constructed based on fuzzy theory and relative formulas are given, matching of strategy equilibrium and enhancement effect of resources are used as association constraint. the concept of nearness in fuzzy theory is extended, the concepts of Upper-side and down-side nearness are proposed which enriches the contents of fuzzy theory. Some positive achievements are also attained through simulations, for example, optimum adjustment periods of enterprise strategy alteration.; periodic regularity between project arriving and project selection; the effect of personnel skill for project portfolio results and personnel assignment,etc.
引文
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