A mathematical model for managing price fluctuations in bullwhip effect

It is assumed that by augmenting the price of goods, their demand will be diminished. But in a short interval of time, the price of different types of rice in September 2008 in Iran rise suddenly and simultaneously the demand of rice rises with a considerable speed. Our studies show that the demand is not only dependent to the price, but also it is a considerable dependence to the elevation speed of price. A new function is defined to simulate the relation between demands, price and the speed of price elevation. When the price elevation speed is low or zero, our function behaviour’s is like the classical iso-elastic function and when the price rises, the demand is diminished. But when the speed is high enough, by augmenting the price, the demand also rises. This phenomenon causes a secondary event that is the bullwhip effect. The reverse pricing effect firstly takes place and then, the bullwhip effect occurs in the supply chain. In this paper the conditions that generate the bullwhip effect are analysed by using the Lyapunov exponent