THE GRADIENT NONLINEAR GOAL PROGRAMMING ALGORITHM FOR CHANCE CONSTRAINED MULTIPLE OBJECTIVE MODELS
David L. Olson · Lincoln (University of Nebraska) · 1981
Decision making is crucial to the management of organizations. Decision environments involve high degrees of uncertainty as well as multiple, conflicting objectives. Management science is concerned with providing quantitative support to managerial decision making. Previously developed management science techniques have required restrictive assumptions of certainty and/or a single criterion of value. This research seeks development of a means of decision support capable of reflecting measured uncertainty as well as multiple, conflicting objectives. A nonlinear goal programming algorithm was developed based upon the gradient method, utilizing an optimal step length. The algorithm was tested with models representative of managerial decision environments. The computer program for the algorithm was provided in the study. The gradient algorithm requires assumptions of convex solution sets, differentiable and monotonic nonlinear constraints, and normally distributed variance of stochastic parameters. The algorithm was evaluated for generality, reliability, and precision; sensitivity to parameters and data; preparational and computational effort; and convergence. While the algorithm is not a general method, it is suitable for consideration of chance constrained models. Model sensitivity to parameters was identified, as well as appropriate adjustment. The algorithm was found to require minimal preparational effort, favorable computation time, and rapid convergence to optimal solution with the exception of models containing high degrees of nonlinearity. The gradient nonlinear goal programming algorithm provides an effective method for consideration of nonlinear chance constrained models involving multiple goals. The ability to consider this class of decision model expands the quantitative support available to organization decision makers.