The bullwhip effect under different information-sharing settings: a perspective on price-sensitive demand that incorporates price dynamics

Abstract

Information sharing has been shown previously in the literature to be effective in reducing the magnitude of the bullwhip effect. Most of these studies have focused on a particular information-sharing setting that assumes demand follows an autoregressive process. In this paper, we contribute to the literature by presenting a price-sensitive demand model and a first-order autoregressive pricing process that is coupled to the optimal order-up-to inventory policy and the optimal minimum mean-squared error forecasting technique. We compare a no information-sharing setting – in which only the first stage of the supply chain observes end-customer demands and market prices, and upstream echelons must base their forecasts on downstream incoming orders – with two information-sharing settings, end-demand and order information and end-demand information. In the case of end-demand and order information, upstream echelons develop their forecasts and plan their inventories based on the end-customer demand, price information, and downstream orders. With end-demand information, upstream echelons use only end-customer demands and market prices to conduct their forecasting and planning. We derive the analytical expressions of the bullwhip effect with and without information sharing, quantify the impact of information sharing on the reduction of the bullwhip effect associated with end-demand and order information and end-demand information, and explore the optimal information setting that could most significantly restrain the bullwhip effect. Our analysis suggests that the value of these two information-sharing settings can be high, especially when the pricing process is highly correlated over time or when the product price sensitivity coefficient is small. Moreover, we find that the value of adopting end-demand and order information is always greater than that of end-demand information.

Keywords:

• information sharing
• bullwhip effect
• order-up-to inventory policy
• minimum mean-squared error forecasting technique

Acknowledgements

The research presented in this paper was supported by the Natural Science Foundation Project of Shaanxi Province (2010JM9003), the National Social Science Foundation Project of China (06CJY019), the National Natural Science Foundation Project of China (70602017, 71071126, 70971105, and 70433003), the Specialized Research Fund for the Doctoral Program of Higher Education (NCET-10–0934), and the Fundamental Research Funds for the Central Universities. We express our gratitude to the anonymous referees for their valuable comments, which have improved this paper considerably.

Notes

1. Zhang and Burke (2011) considered an AR (1) pricing process to investigate compound causes of the bullwhip effect by analysing an inventory system with multiple price-sensitive demand streams. However, this paper uses the AR (1) pricing process to study the impact of information sharing on the bullwhip effect.

2. Note that is the function of two types of error terms, the demand shocks that are specific to the retailer, , and overall market shocks, . The reduced demand model is not an AR (1) or more general ARMA demand process.

3. We use the stationary AR (1) pricing process to simplify our exposition. However, when the pricing process is nonstationary due to its increasing (or decreasing) trend or business cycle, the mean price, , may vary over time. However, if the nonstationarity is as simple as the mean price varying in a known way ( = constant), e.g., because of the business cycle, then we can use the same approach to analyse when the pricing process is nonstationary, i.e., . The results presented in this paper remain unchanged. The demand model with the AR (1) demand process also used this approach to deal with a nonstationary situation (Sodhi and Tang 2011).

4. Our model can be extended to when . However, it can be shown that the estimation of the standard deviation of the L_i period forecasting error is independent of time, and the results in this paper remain unchanged. For a better understanding, we refer readers to read through this paper and then see Appendix B for a more detailed discussion of these contents.

5. The assumption that is presented here can be extended to analyse different forecasting techniques, such as the MA or ES techniques. However, because our intent is to analyse the value of information sharing on the bullwhip effect, we shall restrict our attention to only the optimal forecasting technique, i.e., the MMSE technique. A similar assumption has also been made by Lee, So, and Tang (2000), Hosoda and Disney (2006), and Sodhi and Tang (2011).

6. The retailer’s order quantity can also be written as when using Equations (1) and (11), and where . Thus, the wholesaler can utilise this equation to estimate the actual value of d_t and then utilise Equation (1) to estimate the actual value of p_t . However, because it is complicated to conduct a theoretical analysis on the value of information sharing when the wholesaler utilises historical order quantities to estimate the actual demand and price, we shall limit the scope of our paper by assuming that the wholesaler would not utilise these equations to estimate the actual value of d_t and p_t . A similar assumption has also been adopted by Lee, So, and Tang (2000) and Ali and Boylan (2011).

7. In reality, neither the retailer nor the wholesaler knows the exact values of the parameters of the demand process. However, the retailer can use the statistical software and the historical demand and price data to estimate the parameters of the demand process with sufficient accuracy. In addition, as shown in Lee, So, and Tang (2000), it is also reasonable that the wholesaler knows the demand process parameters, as information about the underlying demand process can be communicated to the wholesaler by discussing periodically with the retailer, or the wholesaler can be provided with historic demand and price data from which the demand process parameters can be readily deduced. A similar assumption has also been adopted by Gaur, Giloni, and Seshadri (2005).

8. We can rewrite Equations (1) and (2) as and . Thus, can be given as and can be given as .

9. The assumption presented here can be extended to analyse when ; however, the analysis would become more complex. Because our intent is to obtain basic managerial insight, we shall restrict our attention to the assumption that L ₁ = 0. We will analyse the influence of b, L ₁, L ₂, , and on the value of information sharing using the numerical analysis in Section 7, when .

10. We did not conduct a theoretical analysis on the impact of the price correlation coefficient, , on the value of information sharing. However, it can be shown that the value of information sharing reaches a maximum value at a certain value, and we will conduct a numerical analysis in Section 7 to understand this point.

11. Note, there is one special case in our numerical example where V_{NIS–IS 2} decreases when L ₁ increases from 2 to 4; see the scenario for b = 1 and for when comparing the values in Table 4 with those in Table 5. However, for the other cases, V_{NIS–IS 2} increases with L ₁.

12. For large values of L ₁ and L ₂, is close to one under the two information-sharing settings. Numerical results for these cases are not given in this paper as tabular forms. For example, V_{NIS–IS 1} reaches its maximum when , and V_{NIS–IS 2} reaches its maximum when when b = 1, L ₁ = L ₂ = 10, and .

13. Also note that increases when the lead times L ₁ and L ₂ are increased. For example, reaches its minimum value, i.e., the savings reach their highest value when when b = 1, L ₁ = L ₂ = 10, and .