A Stochastic Programming Model for Agricultural Planning under Uncertain Supply -demand Relations

A STOCHASTIC PROGRAMMING MODEL FOR AGRICULTURAL PLANNING UNDER UNCERTAIN SUPPLY -DEMAND RELATIONS Teruaki Nanseki NatiolUlI Agriculture Research Center (Received April 15,1988; Revised October 28, 1988) The main purpose of this paper is to present a stochastic programming model for agricultural planning under uncertain supply-demand relations and to propose an algorithm for the model. We first illustrate that several economic problems under undertaint~ must be formulated as a quadratic programming model in which the linear coefficients are stochastic variables. The model is considered as an extension of the linear stochastic programming model reported by Freund (1956) and Kataoka (1963, 1967). The following alternative criteria for optimization are introduced to complete the model: (1) maximizing the expected value of utility; (2) maximizing aspiration level; (3) maximizing probability. The deterministic equivalents are then derived with the mathematical characteristics of the solutions. The equivalence relations among the eqUivalents are also clarified. We propose an iteration algorithm for the equivalents by taking advantage of the relations. The algorithm is based on lhe secant method and the convex quadratic programming method. Finally, an application of the model is illustrated with a procedure for application.