Optimal capital allocation in multi-projects portfolio based on startup level under two-period investment

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.