Substitutes and Complements in Constrained Linear Models
J. Scott Provan · SIAM Journal on Algebraic and Discrete Methods · 1987
We consider the problem of when two variables in a linear programming model can be considered to be substitutes (self-interfering) or complements (self-reinforcing). Several definitions proposed in the economic and mathematical literature are investigated in the context of linear programming models. The concept of determinacy is used to formalize and classify these definitions. Determinacy is studied for a class of network flow models, where graph-theoretic characterizations of substitutes and complements are given.