BUS606: Operations and Supply Chain Management

To distinguish the information sharing level of implementing SCM software or not, the "decentralised supply chain model" and "centralised supply chain model" should be firstly proposed for analysis. In the decentralised supply chain model, information of "average demand" and "variance of demand" of end customers are not shared for other supply chain members.

The studies on the bullwhip effect typically adopt the ratio of variances as the general measures for the bullwhip effect. Fransoo and Wouters tried to use the ratio of the coefficients of variation (CV) between the output supplier sales and the input retailer sales. The bullwhip ratio (BWR) is denoted by Equation (1). However, this formula is more suitable for two-stage supply chain and it is argued here that it is not suitable for calculation of multi-stages supply chain.

$BWR = \dfrac{ \sigma_{supplier} / \mu_{supplier}}{ \sigma_{retailer}/ \mu_{retailer} }$ (1)

In order to make sure that customer demand will be satisfied under the uncertainty, upstream suppliers will always tend to prepare higher inventory levels than really consumed. Therefore, for the upstream stages of the supply chain, the higher variance in order is faced than that in the downstream ones. The relation of faced variance in the kth stage and real demand variance can be shown as Equation (2) , where the Q stands for the placed order, D stands for average customer demand, Li stands for the lead time between stage i and i+1, and p is the number of demand observations. In contrast to decentralised supply chain model, i.e., the centralised supply chain model, the relationship of faced variance in the kth stage and real demand variance can be shown as Equation (3). It is easy to find that the variance ratio of the placed order and customer demand is lower than that in decentralised supply chain model.

$\frac{\operatorname{Var}\left(Q^{x}\right)}{\operatorname{Var}(D)} \geq \prod_{i=1}^{i}\left(1+\frac{2 L_{\bar{i}}}{p}+\frac{2 L_{\bar{i}}^{2}}{p^{2}}\right)$ (2)

$\frac{\operatorname{Var}\left(Q^{x}\right)}{\operatorname{Var}(D)} \geq 1+\frac{2 \sum_{i=1}^{k} L_{i}}{p}+\frac{2\left(\sum_{i=1}^{k} L_{i}\right)^{2}}{p^{2}}$ (3)

Meanwhile, to demonstrate the effects of implementing SCM software, the rate "R" of implementing supply chain software in the total supply chain can be shown as Equation (4), where j stands for the number of stages that has implemented the same SCM software system in entire k stages of the supply chain. Furthermore, the finally developed model that links the bullwhip effect and the implementation of SCM software in this study is modelled as Equation (5).

$R = \dfrac{}{k}$  $j= 0 \approx k$ (4)

$\frac{\operatorname{Var}\left(Q^{k}\right)}{\operatorname{Var}(D)} \geq \sqrt{R}-\left[1+\frac{2 \sum_{i=1}^{k} L_{\bar{z}}}{p}+\frac{2\left(\sum_{i-1}^{k} L_{\bar{k}}\right)^{2}}{p^{2}}\right]+(1-\sqrt{R}) \cdot\left[\prod ^ { k } \left(1+\frac{2 L_{i}}{p}+\right.\right.$ (5)