Optimization of a machining economics model with fuzzy exponents and coefficients

The primary objective of a machining economics model is to determine the optimal cutting parameters that minimize production costs while satisfying some design constraints. This paper develops a solution method that can derive the fuzzy unit production cost of a fuzzy machining economic model when the exponents of decision variables in the objective function, the cost and the constraint coefficients are fuzzy numbers. A pair of two-level machining economics problems is formulated to calculate the upper and lower bounds of the fuzzy unit production cost at possibility level a. Based on the duality theorem and by using a variable substitution technique, the two-level machining economics problem is transformed into the one-level conventional geometric program. Solving the corresponding pair of geometric programs produces the interval of the unit production cost. The examples show that the interval of unit production cost contains more information when the parameters in machining economics problems are fuzzy numbers.