Zero-one Allocation of Substitutable Resources

Abstract

The author found a major limitation of the original zero-one programming method: it can't take into account that some resources are substitutable regarding some particular activities, i. e. the desired result is achievable by using any of them. Substitutability can be multi-level when the higher level resources are broader categories, containing every kind of resources which can be substituted regarding one or more activities. Usually substitutability is not a general feature but refers only to some particular activities. This article: -defines this kind of substitutability, - describes a tree-structured model of this special kind of hierarchical substitutability, - introduces a measure of substitutability, called 'substitutability coefficients'. The author modified the original mathematical formulas: -for calculating the constraints of higher level resources in the hierarchy, and - for determining the feasible solutions (a set of inequalities), taking the hierarchical substitutability of resources into account.