Determining Economic Order Quantity (EOQ) with Increase in a Known Price under Uncertainty through Parametric Non-Linear Programming Approach

Abstract

Constant unit procurement cost is one of the main assumptions in the classic inventory control policies. In the realistic world and practice, suppliers sometimes face increase in the price of a known item. In this paper, an inventory model for items with a known one-time-only price increase under fuzzy environment is presented by employing trapezoidal fuzzy numbers to find the optimal solution. We developed three different policies on the basis of methods such as α-cuts, for defuzzification of internal parameters before solving the model, and Vujosevic, for difuzzification of the external parameters after solving it. In the first policy, we integrated α-cuts method and Parametric Non-Linear Programming ( ) problems to attain the Membership Functions ( ) of external variables in the primary model for achieving the optimal solution. These variables were reached by internal parameters through two-phase maximum/minimum non-linear programming problems and the external variables were approximate fuzzy numbers. Under the other two policies, we used defuzzification techniques of Centroid of Gravity ( ), Signed Distance ( ), and the Maximum Degree of Membership ( ) to attain crisp numbers. The optimal order policies by the three methods were compared and numerical computations showed that the efficiency of the first method (i.e., the presented one) was considerably better than that of the other two methods. In fact, the first method selected the optimal and attractive strategies by allocating membership functions to different α-cuts and provided the Decision Maker ( ) with great information to decide and select the best strategies. The methods were validated by a numerical example. The main aim of this model was determining the special ordering range and net costs saving quantity (involving ordering, holding, and purchasing costs). The time of ordering for positive net costs saving was calculated.