Support prices of activities in linear programming1,2
Adi Ben-Israel, Sjur Didrik Flåm · Optimization · 1989
Consider the primal LP with activities x and a resource endowment b The optimal solutions of the dual program have a well known economic interpretation as shadow prices of resources. It is possible to pose the dual problem in space of activities, by rewriting (D) as where [xtilde] is any solution of Ax = b The primal and dual Simplex methods can then be unified using certain canonical bases of the subspaces N(A) and R(AT) e.g, [3]. In this note the optimal sets of (P) and ([Dtilde]) are given concise symmetric representations using canonical bases, and the optimal y * in ([Dtilde]) are interpreted in terms of support prices of the activities in (P), related to changes in activity levels. These results are applied to activation prices of unused activities and de-activation prices of those in use.