首先，本文在已有可打断项目组合选择模型的基础上，引入了消耗性资源和可更新资源约束，构建了一个更符合实际的新模型；其次，为了达到模型简化的目的，本文给出了资金约束的现值表示，并给出了理论证明；最后，利用GAMS对模型进行了算例分析。数值实验结果表明：1）资源约束下的项目打断有时可以给企业带来积极效益，这有别于已有的研究；2）在考虑资源约束的情况下，资源消耗少且同时收益高的项目应优先执行；3）当资源的供给量较少时，资源约束是决定项目选择的关键因素。此外，通过企业实际的案例对数值实验结果进行了验证。
With the development of scientific technology and the acceleration of economic globalization, managers who own much capital face more and more projects to choose. How to invest the scarce resources such as budget, people and time. on a most profitable subset is crucial for a firm/organization. This is the main concern of project portfolio selection problem. In real world, managers note that project interruptions may happen, which come from some managerial concerns, such as the lack of cash, materials and technicians. When managers consider the project interruptions as a strategy in choosing the best execution scheduling for projects, i.e., in fact, they try to optimize the project execution by running the projects by portions, and the consideration of the project interruptions as the above strategy is manager's initial intent. These types of interruptions are called divisibility. In this paper this type of project portfolio selection problem considering divisibility is mainly concerned. To the best of our knowledge, there is yet not research about resource constraints introduced into the project portfolio selection problem considering divisibility. Therefore, based on the model of project portfolio selection considering divisibility, a new model considering consumptive and renewable resource constraints is constructed. This model is a mixed integer programming problem with a linear objective function. And then a model of project portfolio selection problem without divisibility is set up. This model is an integer programming problem. The comparison analysis of the above two models is presented.More specifically, the second model is the special case of the first model under some assumptions. Secondly, for the purpose of simplifying the above models, the capital present value presentation is introcluced and proved. Finally, one numerical example is given to illustrate the characteristic of the new model with using GAMS. The result shows that: 1) unlike the research of the past, project divisibility can bring positive influence for the enterprise under the resource constraints. 2) Those projects with more profits and less use of resources are required precedence over all others. 3) When resources are limited, resource constraints are key factors for the selection of projects. A practical case provides the proof for the above results.
[1] Markowitz H. Portfolio selection [J]. The Journal of Finance, 1952, 7(1): 77-91.
[2] 姚建伟. 资源受限项目组合选择及调度优化研究[D]. 杭州: 浙江大学, 2010.
[3] Abbassi M,Ashrafi M,Tashnizi E S. Selecting balanced portfolios of R&D projects with interdependencies: A cross-entropy based methodology [J]. Technovation, 2014, 34(1): 54-63.
[4] Weingarten H M. Capital budgeting of interrelated projects: survey and synthesis [J]. Management Science, 1966, 12(7): 485-516.
[5] Cho W,Shaw M J,Kuon H D. The effect of synergy enhancement on information technology portfolio selection [J]. Information Technology and Management, 2013, 14(2): 125-142.
[6] 谷晓燕. 基于实物期权的研发项目动态投资决策模型[J]. 中国管理科学, 2015, 23(7): 94-102.
[7] Servakh V V, Sukhikh S L. Hybrid algorithm for scheduling with regard for reinvestment of profits [J]. Automation and Remote Control, 2004, 65(3): 449-455.
[8] Stummer C,Heidenberger K. Interactive R&D portfolio analysis with project interdependencies and time profiles of multiple objectives [J]. IEEE Transactions on Engineering Management, 2003, 50(2): 175-183.
[9] Ghasemzadeh F, Archer N P. Project portfolio selection through decision support [J]. Decision Support Systems, 2000, 29(1): 73-88.
[10] Medaglia A L, Hueth D, Mendieta J C, et al. A multi-objective model for the selection and timing of public enterprise projects [J]. Socio-Economic Planning Sciences, 2008, 42(1): 31-45.
[11] 寿涌毅, 宋淳江. 复杂产品系统研发项目合作伙伴选择优化[J]. 科研管理, 2014, 35(10): 144-149.
[12] 李秉祥, 吴建祥. 管理防御视角下经理人长短期项目选择的可分离均衡[J]. 系统工程理论与实践, 2015, 35(4): 939-944.
[13] Belenky A S. A Boolean programming problem of choosing an optimal portfolio of projects and optimal schedules for them by reinvesting within the portfolio the profit from project implementation [J]. Applied Mathematics, 2012, 25(10): 1279-1284.
[14] Li Xingmei, Fang S C, Tian Ye, et al. Expanded model of the project portfolio selection problem with divisibility, time profile factors and cardinality constraints [J]. Journal of the Operational Research Society, 2015, 66(7): 1132-1139.
[15] Chen Jiaqiong, Askin R G. Project selection, scheduling and resource allocation with time dependent returns [J]. European Journal of Operational Research, 2009, 193(1): 23-34.
[16] Liu Shushun, Wang C J. Optimizing project selection and scheduling problems with time-dependent resource constraints [J]. Automation in Construction, 2011, 20(8): 1110-1119.
[17] 郭研, 董超. 基于资源约束的高新技术企业研发项目选择策略研究[J]. 项目管理技术, 2015, 13(4): 15-18.
[18] 方晨, 王凌. 资源约束项目调度研究综述[J]. 控制与决策, 2010, 25(5): 641-656.
[19] 于超, 樊治平. 考虑决策者后悔规避的风险投资项目选择方法[J]. 中国管理科学, 2016, 24(6): 29-37.
[20] 李星梅, 王雅娴, 刘再领, 等. 考虑风险因素的可打断项目组合选择问题[J]. 中国管理科学, 2015, 23(S1): 297-300.
[21] 李星梅, 刘再领, 赵秋红. 可打断项目组合选择问题局部敏感性分析[J]. 系统工程理论与实践, 2016, 36(7): 1816-1825.
