Bullwhip Entropy Analysis and Chaos Control

Conclusions

This paper constructs a supply chain model with a manufacturer and two retailers. In the sales game process, retailers forecast their sales volume based on their bounded rationality and information and replenish goods using the order-up-to inventory policy. We find the demand game system disturbed by weak noise will experience quasi-stable, quasi-periodic and quasi-chaotic state as retailers increase their sales adjustment speeds. This paper mainly analyzes these nonlinear characteristics of the supply chain with consumer returns under a sales game scenario and compares the bullwhip effect under different iteration states. The conclusions show that: the profit of the traditional retailer will be reduced with the growth of the online retailer's return rate. As the online retailer's adjusting parameter increase, the system enters a quasi-periodic state, and the bullwhip effect of both retailers increases rapidly with a slight shock. The bullwhip effect experiences intense shock when the system enters a quasi-chaotic state. The supply chain system suffers a great bullwhip effect in the quasi-periodic state and the quasi-chaotic state. For the online retailer, an adjustment parameter which maintains the system in the quasi-steady stage is an optimal sales adjustment strategy to make the supply chain avoid the greater bullwhip effect. With the help of the delayed feedback control method, the online retailer can control the system, expand the stable region and effectively mitigate the bullwhip effect.

There are a number of implications for the manufacturer and the retailers: (1) the manufacturer should help the online retailer maintain a low return rate, otherwise, the profit of the traditional retailer will be reduced, too; (2) the retailers can adopt a suitably large sales adjustment speed to obtain greater profits, but they must keep the sales game system in the stable state and their sales volume in the basin of attraction; (3) the manufacturer should pay attention to the adjustment speeds of the two retailers. Once the system falls in to chaos, the delayed feedback control method can be adopted to control the chaotic system far away from the large bullwhip effect and large entropy.

Limitations of this work include: (1) all the results are obtained from the simulations; (2) only one traditional retailer and one online retailer are considered in the supply chain model. The theoretical analysis of the bullwhip effect and multiple retailers in the game supply chain would be improvements and directions for future research.