Frequency response analysis of demand information sharing and production smoothing in a two echelon supply chain

Transcription

1 Frequency response analysis of demand information sharing and production smoothing in a two echelon supply chain Qinyun Li and Stephen Disney Logistics Systems Dynamics Group, Logistics and Operations Management Section, Cardiff Business School, Cardiff University

2 Information sharing is an important supply chain strategy (Lee et al. 1997). Production smoothing has an even longer history at improving the dynamics of supply chains (Deziel and Eilon 1967). We relax the assumptions of demand and study the impact of information sharing and production smoothing on order forecasting accuracy.

3 Models and Assumptions Unbiased exponential smoothing forecasts. Lead-time is 1 (consists of only the sequence of events delay, so physical lead-time is zero). Production Smoothing (PS) Information Sharing (IS) X t = D t No Production Smoothing (NPS) β = 1 No Information Sharing (NIS) X t = O t ( ) Oˆ = Oˆ + α X Oˆ t+ 1, t tt, 1 t tt, 1

4 All demand series can be broken down into their harmonics Jean-Baptiste Joseph Fourier Born: 21 March 1768, Auxerre, France Died: 16 May 1830, Paris, France

5 Frequency response σ 1 FE( e ) D( e ) 2 π De ( ) ε( e ) iω iω π 2 FE = π iω iω = 2 2 iω 2 iω 1 π FE( e ) D( e ) iω iω 2 π π De ( ) ε( e ) dω dω Fast Fourier Transform Amplitude Ratio (AR) Forecasting performance, see examples in McClain, 1974* Impact of IS and PS on the accuracy of order forecasts. * McClain, J.O Dynamics of exponential smoothing with trend and seasonal terms. Management Science 20(9).

6 Understanding the frequency response AR = iω Oe ( ) iω De ( ) Orders Demand

7 Result 1 In a NISNPS supply chain, the manufacturer s capacity and inventory performance are always worse than the retailer s performance.

8 Result 2 For high frequency demand (i.e. with significant noise), IS is able to improve order forecasting accuracy. Proof: This reduction mitigates the bullwhip effect at the manufacturer.

9 Result 3 For demand that is dominated by low frequency harmonics, for example S-shaped demand pattern, IS may amplify the variance of order forecast error, resulting in more variability in production and inventory control. Proof: This is a formal proof to the experiments in Steckel et al. (2004)**. ** Steckel, J.H. et al Supply chain decision making: will shorter cycle times and shared point-of-sale information necessarily help? Management Science 50(4).

10 Result 3 cont.

11 Result 4 When only PS is implemented, for high frequency demand, the variance of order forecast error can be less than the demand variance. This performance cannot be achieved by IS. Proof: AR ISNPS 21 ( + α ) 2 ( 2 α ) respectively. In other words, σ AR ω= π NISPS ω= π = = is increasing in α, therefore, the upper and lower boundaries are 4 and 1 ( α( β) + β) 2 ( 2 α) ( 2 β) σ 2 2 OFE D in a ISNPS supply chain.. By tuning β, however, we are able to achieve AR 1. NISPS < ω= π

12 Result 4 cont. ARNISPS < ω= π 1 holds when 0 α < 3 5 (0.764) < β < α 2 α σ < 2 σ 2 OFE D

13 Result 5 PS is more effective than IS at improving order forecast accuracy. The effect works across frequencies. 1.5 AR AR ISNPS 1.0 AR NISPS 0.5 α = 0.3, β =

14 Result 6 In ISPS supply chain, for high frequency demand, the variance of the order forecast error can be easily reduced to below both the demand variance and the variance of demand forecast error σ < σ 2 2α 2 α 2 2 OFE DFE

15 Result 7 However, when PS is present, the sharing of demand information is not necessarily useful. Whether or not IS is beneficial depends on the nature of demand patterns, forecasting and production smoothing.

16 IS ineffective IS ineffective σ < σ 2 2α 2 α 2 2 OFE DFE

17 Summary PS is more effective than IS for any demand patterns. With IS, order forecasting accuracy improves for high-frequency harmonics, but deteriorates for low-frequency harmonics. When PS is implemented, the effectiveness of IS depends on the nature of demand patterns, forecasting and PS.

18 Future research Fast Fourier Transform How forecast errors are transformed into orders? Forecasting performance, see examples in McClain, 1974* * McClain, J.O Dynamics of exponential smoothing with trend and seasonal terms. Management Science 20(9).

19 Thanks!

20 We also find that in a supply chain without production smoothing, smaller exponential smoothing forecasting constants lead to more accurate order forecasts when demand is dominated by high frequency harmonics. For trended or seasonal demand patterns, smaller smoothing constants are not always desirable. In both the production smoothing scenarios, smaller exponential smoothing constants result in a slight increase in the amplification of low frequencies harmonics, but lead to a decrease over the remaining frequencies.