The Subdivided Investment Scheduling Problem with Market Lives

We consider an investment problem where n possible entries are to be selected by a single investment company.There is a capital resource limition C for the company.For every possibly selected entry i ∈ {1, 2, ··· , n},there is a required operation capital O_i, a market life L_i,a required operation finished time T_i and a currently potential profit P_i which could be only obtained by the company P_i {(1 - S_j/L_j),S_j is the start time of operation entry i, because human resource is limited for the company, the next entry could be operated only when the privous entry has finished its operation. The objective is to find an ordered entry subset of {1, 2, ···,n} S = {i₁,i₂, ··· ,i_k} which satisfied Σ_j∈s O_j ≤ C and Σ_j∈s P_j (1 -S_j/L_j) is maximized. We define this problem as the subdivided investment sequencing problem with market lives, analyze its NP-hardness, and give an efficient heuristic algorithm for it.