# American Institute of Mathematical Sciences

January  2009, 5(1): 81-94. doi: 10.3934/jimo.2009.5.81

## Analysis of bullwhip effect in supply chains with heterogeneous decision models

 1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hunghom, Hong Kong, China 2 Department of Mathematics, Sun Yat-sen University, Guangzhou, China 3 Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Received  March 2008 Revised  October 2008 Published  December 2008

In modeling a supply chain, it is often assumed that agents of different echelons adopt similar inventory policies. As a result, bullwhip effect exists across different echelons up the supply chain when the product demand at the retailer level increases and decreases. However, a retailer and a manufacturer are two very different entities in a supply chain, which should employ different decision processes in managing their operations. In view of this, we study the application of heterogeneous decision models for retailers and manufacturers to analyze the bullwhip effect in a supply chain. In particular, we formulate a simple supply chain consisting of many retailers, a manufacturer and a warehouse. The inventory policy of the retailers is simply to use the inventory position to absorb variations in the demand. For the manufacturer, the demand can be met by keeping a higher inventory level or by varying the production rate more frequently. A multi-criteria objective function is formulated and analytic solutions are derived. We illustrate how the bullwhip effect varies for different selections of scaling parameters. By using optimal control theory, we show that the bullwhip effect can be suppressed if a smooth production requirement is enforced.
Citation: K. F. C. Yiu, L. L. Xie, K. L. Mak. Analysis of bullwhip effect in supply chains with heterogeneous decision models. Journal of Industrial and Management Optimization, 2009, 5 (1) : 81-94. doi: 10.3934/jimo.2009.5.81
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