The Fuzzy Optimistic-Reasonable-Pessimistic Inventory Model

Abstract

In inventory and production decision problems, decision makers are interested to identify the optimal inventory and production level. In a certain decision environment, the optimal inventory level could be determined through traditional inventory methods and the optimal ptoduction level could be determined through linear programming algorithms. In an uncertain decision environment, the traditional methods and algorithms can not provide efficient and relevant solutions for these levels, due to the vague and changing parameters. In this case it is neccesary to develop new methods and models that can deal with vague variables and provide optimal levels. In this paper, the optimal inventory and production levels are determined through a single model that uses fuzzy linear programming. This new model is Fuzzy Optimistic-Reasonable-Pessimistic Inventory Model. It has three scenario: optimistic, reasonable and pessimistic, that are defined through triangular fuzzy numbers. In this way, decision makers can deal with vague parameters. These scenarios help managers to divide the Fuzzy ORP Model into three sub-models, that can be easily solved through traditional Simplex Algorithms. Each sub-model provides a crisp solution for each scenario. The solutions forms the final fuzzy optimal solution. The Fuzzy PRO Inventory Model helps managers to identify three optimal levels and to rank them according to their evaluations. This is useful, also, in predictions, where the decision makers should predict different scenarios for the production process. The limit of this model is the definition of the variables and scenarios. This model consider that all values for all variables and coefficients have the same definition: the inferior limit is related to the optimistic sceanrio, the peak is represents the reasonable limit and the superior limit is related to the pessimistic scenario. In real problem, the decision variables could have different definition than coefficients. The inferior limit of the cost is related to the optimistic scenario, but the superior limit of the production level can be related to the optimistic scenario. There are different representations for the scenarios.