两阶段资金投入条件下多项目组合中基于项目启动水平的资金分配问题研究

Optimal Capital Allocation in Multi-projects Portfolio based on Startup Level under Two-period Investment

对两阶段资金投入条件下多项目组合中基于项目启动水平的资金分配问题进行了研究.由于已启动项目的资金不能按预算全额投入,因此文中引入了项目启动水平的概念,低于最低启动水平则项目不能启动.假设每个项目的净收益值与资金投入值可表示为与启动水平有关的线性函数,据此对两阶段投资过程分别建立了数学模型,分析认为它们分别属于0/1背包问题和连续背包问题,且都为NP难题.在建立了相关定理及定义的基础上,基于连续松弛条件下的价值密度贪婪准则,分别应用分枝定界算法、动态规划算法得到了该问题的资金分配最优策略.

It intends to study a problem of capital allocation in the case of enterprise determines to activate multi- projects simultaneously for portfolio with two stage of investment. Because the funding capital amount is limited, it introduces the notion of the project＇s startup level, which means that the project would be rejected if its capital invested is lower than this level. It suppose that the amounts of each project＇s profit as well as the amounts of project＇ s capital invested can be described as a linear function of the project＇s startup level. Moreover, it build the models for multi-projects portfolio of two stage of investment, and analyzes they are 0-1 knapsack problem and a continuous knapsack problem respectively, which are both shown to be NP-hard. On the basis of constructing theorem, lemma and definition for the portfolio, it obtains an optimal strategy for the problem with dynamic programming algorithm, branch and bound algorithm and greedy principle of valuable density.