Knapsack allocation of multiple resources in benefit-cost analysis by way of the Analytic Hierarchy Process

James Bennett
Department of Political Science
Maxwell School of Citizenship and Public Affairs Syracuse University Syracuse
United States
Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States

Publication date: Feb, 1993

Journal: Mathematical and computer modelling
Vol.: 17- Issue: 4-5- Pages: 55-72

Abstract: Benefit-cost analysis has traditionally required monetary measures of benefits and costs of candidate projects. This paper demonstrates that priorities of both tangible and intangible attributes can be used in a benefit-cost setting to address the long standing problem of allocating multiple resources to projects. Although it is widely accepted that proper structuring of analytic hierarchies can achieve aggregation of a number of small projects so that their cumulative benefits are comparable to that of a large project, it frequently happens in budgetary allocation that large sums of money are allocated to a project whose intangible benefits are stretched out over much larger time horizons than other urgent projects with short term benefits. Here, the two hierarchies used to set priorities on benefits and on costs need to consider different time horizons. The Analytic Hierarchy Process and knapsack optimization are used to formulate problems in which a number of projects might be implemented by judicious distribution of resources available. For many applications, one seeks to maximize a function of net benefit, subject only to the constraints imposed by resource limitations. In others, benefit to cost ratios of projects obtained from two separate hierarchies are used. Our knapsack or recursive knapsack formulation is a complex combinatorial problem that would require approximate heuristic methods for its solution. Several realistic variants of the knapsack problem are illustrated. The computational tractability of practical knapsack problems is discussed. This paper contributes to our ability to make strategic allocation decision—where the diversity of benefits and costs demands inclusive measurement, and where optimal resource allocation is demanded by the importance of the decisions.

Keywords: BOCR, Benefits-Opportunities-Costs-Risks, Analytic Hierarchy Process, AHP