Minimum risk criterion for uncertain production planning problems

Abstract

This paper considers a new class of multi-product source and multi-period fuzzy random production planning problems with minimum risk and service levels where both the demands and the production costs are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The proposed problems are formulated as a fuzzy random production planning (FRPP) model by maximizing the mean chance of the total costs less than a given allowable investment level. Because the exact value of the objective function for a given decision variable cannot be easily obtained, we adopt an approximation approach (AA) to evaluate the objective value and then discuss the convergence of the AA, including the convergence of the objective value, the convergence of the optimal solutions and the convergence of the optimal value. Since the approximating multi-product source multi-period FRPP model is neither linear nor convex, an approximation-based hybrid monkey algorithm (MA) which combines the AA, stochastic simulation (SS), neural network (NN) and MA is designed to solve the proposed model. Finally, numerical examples are provided to illustrate the effectiveness of the hybrid monkey algorithm.