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Dynamic programming algorithms are developed for optimal capital allocation subject to budget constraints. We extend the work of Weingartner Weingartner, H. M. 1966. Capital budgeting of interrelated projects: Survey and synthesis. Management Sci. 12(7, March) 485–516. and Weingartner and Ness Weingartner, H. M., D. N. Ness. 1967. Methods for the solution of the multi-dimensional 0/1 knapsack problem. Oper. Res. 15(1, January–February) 83–108. by including multilevel projects, reinvesting returns, borrowing and lending, capital deferrals, and project interactions. We are able to handle dynamic programming models with several state variables because the optimal returns are monotone non-decreasing step functions. Computational experience with a variety of problems is reported.
Nemhauser et al. (Thu,) studied this question.