A multi-objective, stochastic programming model in watershed management

Abstract

This research develops an interactive algorithm for solving a class of multi-objective decision problems. These problems are characterized by a set of objective functions to be satisfied subject to a set of nonlinear constraints with continuous policy variables and stochastic parameters. The existence of a decision situation is postulated in which there are N resources to be allocated so that P satisfactory objective levels may be attained. A probabilistic tradeoff development algorithm, labeled PROTRADE, is developed to provide a framework in which the decision maker can articulate his preferences, generate alternative solutions, develop tradeoffs among these, and eventually arrive at a satisfactory solution provided it exists. As the decision maker arrives at a vector-valued solution, with a value for each objective function, he also generates the probabilities of achieving such values. Then, as his preferences are articulated, he is able to trade-off objective function values against one another, and directly against their probabilities of achievement. A central assumption of this research is that there is not an "optimal" solution to the problem, but only "satisfactory" solutions. The reason for this is that the decision maker is allowed to have a dynamic preference structure that changes as the various tradeoffs are generated and new information is made available to him. The algorithm is developed in the context of parameters normally distributed. Several theorems are presented which extend the applicability of the algorithm to nonnormal random variables, specifically exponential, uniform, and beta random variables. A case study of the Black Mesa region in northern Arizona is provided to demonstrate the feasibility of the algorithm. This region is being strip-mined for coal and the managing agency must decide on the extent of several management practices. The practices or objective functions considered in the study are: (1) livestock production, (2) augmentation of water runoff, (3) farming of selected crops, (4) control of sedimentation rates, and (5) fish pond-harvesting. Finally, conclusions are presented and areas for future investigation are suggested.