Application of Mathematical Programming to the Productivity Investment Fund Program: A Capital Rationing Problem

摘要

This study explores the potential applications of mathematical programming (MP) to a capital rationing problem of the Department of Defense. It demonstrates that the current method of selecting projects for funding results in a suboptimal economic mix of capital investment projects. Based on data from the Fiscal Year 1985 Productivity Investment Fund (PIF) program, substantial dollar savings are likely if PIF projects are selected using MP instead of ranking. Using a single-criterion MP model, the opportunity cost of ranking (defined as the difference between the net present value (NPV) the mix found by MP and the NPV of the mix actually funded by the DoD) was $205.6 million. The economic superiority of the MP-selected mix was demonstrated over broad ranges of budget ceilings and discount rates. The average opportunity cost of ranking ranged from $23 million to $242 million, depending on the ranking criterion or method used. Two multiple-criteria MP models were also developed and tested using the FY85 PIF data. The mixes found by these models were economically superior to those found by ranking, when pre-specified objectives (involving minimum levels of return on investment and labor savings) were set for the solution mix.