An Application ofZ-Matrices to a Class of Resource Allocation Problems

Abstract

This study focuses on allocation problems that have some of their constraints defined in terms of Leontief input-output matrices, known as Z-matrices. A few properties of these matrices are discussed and then applied to achieve a possible reduction in the dimensionality of the resource allocation models. An allocation problem of the above nature is the subject of the recent work of Luss and Gupta [Luss, M., S. K. Gupta. 1974. Allocation of marketing effort among P substitutional products in N territories. Oper. Res. Quart. 25 77–88.], who were concerned about optimal allocation of marketing efforts among substitutional products distributed in different sales territories. The reduction procedure is then applied to their model to yield several extensions.