A linear vector duality theory for decision support in joint venture planning

Abstract

Duality for linear vector optimum problems is often just a mathematical construct (l’art pour l’art). We define a family of dual problems to support decision-makers in a concrete economic situation. Entrepreneurs generally want to participate in initiatives for producing new products with similar technologies in a unique production setting. Each of them provides resources relative to the others’ consideration of their economic objective. They all agree to aggregate their different interests through a new duality concept. This paper first presents the duality concept and shows under which conditions a satisfying aggregation of the entrepreneurs’ varying objectives is possible. Numerical examples are used to make this aggregation transparent. An application is then presented to demonstrate the applicability and efficacy of the new concept.