Calibration of objective functions in stochastic linear models of production networks

In our study we concentrated on the random aspects of a network production problem in the context of Stochastic Linear Programming. Based on the philosophy of the 2-Stage Method we estimated the feasible region [set of decisions that complies with all linear and random restrictions]; we took into account the Historical Production Record which includes ‘optimal’ policies or decisions implemented in L previous periods, and then we established a weight system for decision making [the most logical has the lowest weight]. Minkowski’s functional was the tool of choice because of its continuous nature and because it is differentiable in convex and polyhedral regions as it is in our case. After a discrete approach to the problem, we focused on a second aspect of the problem in which we described primal and dual formats for the stochastic linear model. Complementarity Slackness Conditions were evaluated and a sequence of Primal–Dual programs was thus generated; each pair is different by a parameter value and their ‘optimal’ solutions yield a Primal–Dual Central Path which is also extremely useful for estimating [calibrating] the cost of adopted policies and/or decisions.