Fuzzy non-linear programming: Theory and application in manufacturing

Due to the complexity of the manufacturing environment, problems that can be solved by mathematical programming techniques are usually represented with non-linear programming (NP) models instead of linear programming (LP) models. When non-stochastic vagueness exists between the problem description and its corresponding NP model, fuzzy set theory can be applied to the mathematical model for the purpose of vividly representing the problem. This paper discusses the idea of the fuzzy NP model. Fuzzy set concepts are adapted to the NP objective function and constraints. An identical crisp NP model is derived from the fuzzy NP model for solving the problem numerically. Kuhn-Tucker conditions are addressed to determine the existence of a global optimal solution. A fuzzy machining economics model, which attempts to find optimal manufacturing parameters under vague elements of influence, is used to demonstrate the theory of the fuzzy NP model. © 1988 Taylor and Francis Ltd.