A New Model for Stochastic Linear Programming

The linear programming formulation with random variation in the coefficient matrix is considered. A new model is proposed in which the random variation in the constraints is removed and terms dependent upon the distributions associated with the random constraints introduced into the objective function. The new objective function may be interpreted quite naturally as the sum of the original costs, the expected shortage (or overage) and the set-up cost.

Comparisons made between the solutions of the linear program using the mean values of the distributions and the solution using the model show it is sometimes extremely costly to tacitly set the elements of the linear program at their mean values.