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Use of stochastic production coefficients in linear programming models: objective function distribution, feasibility, and dual activities

Pickens, J.B.; Dress, P.E.

Forest Science 34(3): 574-591

1988

The theoretical impact resulting from use of stochastic production coefficients on the objective function values of unconstrained and constrained linear programming problems was discussed. It was shown that the objective function value that is observed will be a biased and optimistic estimator of the true response of the natural resource system. In addition, it was shown that stochastic production estimates either have no impact or result in suboptimality when the stochastic production coefficients do not affect feasibility. The distribution of the optimal objective function value observed when stochastic production estimates are used, the objective function value of the true response of the system, and a linear combination of these random variables are hypothesized. These hypothesized distributions are then tested using a simulation approach with three error distributions and levels of variability. The simulations indicate that, when global constraints are applied, the dual activities of the global constraints in the presence of stochastic production coefficients are biased estimates of the dual activities with correct production information. In addition, truly infeasible solutions were selected nearly all of the time when feasibility could be violated. For. Sci. 34(3):574-591.

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