The Design of Inverse Network DEA Model for Measuring the Bullwhip Effect in Supply Chains with Uncertain Demands

Two different bullwhip effects with equal scores may have different sensitivities and production patterns. As a result, the difference between these two seemingly equal scores has been ignored in previous methods (such as frequency response and moving average). So, the present study constructs a model of Inverse Network Data Envelopment Analysis, to introduce the relative and interval scores of the bullwhip effect magnitude, when a series of uncertain demands are made in a specific time interval. In the first stage of the proposed network, the uncertain demands and the forecasted uncertain data are regarded respectively as the model’s inputs and outputs. These output data constitute the intermediate variables and consequently the inputs of the second stage of the study model. In the second stage, after considering the ordering policies, the uncertain orders are sent. Due to utilizing both the optimistic and pessimistic perspectives, the study methodology includes an interval value for measuring the bullwhip effect with relative attitude. In the optimistic perspective, the analyzed decision making unit has the optimal status in comparison with other decision making units. In the pessimistic perspective, the analyzed decision making unit has the worst status in comparison with other decision making units. The results show that time is an unfair factor in the size of the bullwhip effect. The impact of uncertainties on the bullwhip effect in the demand forecasting stage is greater than the ordering stage. According to the research findings, cross-sectional planning is possible at different times according to different conditions. Therefore, using the results of the research, a fair score of the bullwhip effect can be obtained by considering all perspectives.