The dynamics of material flows in supply chains

1. The dynamics of material flows in supply chains Dr Stephen Disney Logistics Systems Dynamics Group Cardiff Business School

2. The future of bullwhip Methodological approaches to solving the bullwhip problem The bullwhip effect in supply chains Implementing a smoothing rule in Tesco Economics of the bullwhip effect Supply chain strategies for taming the bullwhip effect The golden replenishment rule Solutions to the bullwhip problem Square root law for bullwhip

3. The bullwhip effect in supply chains

4. Measures of the bullwhip effect Stochastic measures Deterministic measures

5. The bullwhip effect is important because it causes Unstable production schedules Insufficient or excessive capacities Increased lead-times Poor customer service due to unavailable products Runaway transportation and warehousing costs Excessive labour and learning costs Up to 30% of costs are due to the bullwhip effect!

6. How the bullwhip effect creates unnecessary costs + Lead-time + + + + Capacity + + Overtime / Agency work / Subcontracting + + + Stock Stock-outs - Utilisation + + + - Obsolescence + + Costs Demand Variance +

7. Methodological approaches to solving the bullwhip problem

8. Representations of time Discrete Time v Continuous Time • Inventory positions are assessed and orders are placed at discrete moments in time • At the end of every day, or the end of every week, for example • May be suitable of the way a supermarket operates, or a distribution company • In between the discrete moments of time nothing is known about the system • Inventory positions are assessed and order rates are adjusted at all moments of time • May be suitable for a petrol refinery or in a chemical plant • The system states are known at every moment of time

9. Continuous time approaches Laplace transforms Aleksandr Mikhailovich Lyapunov 1857-1918 Pierre-Simon Laplace 1749 - 1827 Differential equations Johann Heinrich Lambert 1728 – 1777 Lambert W functions Leonhard Euler 1707 - 1783

10. Discrete time approaches Stochastic processes / ARIMA George Box

11. The ARMA(1,1) demand process for 16 P&G products in their Homecare range

12. Discrete time approaches Stochastic processes / ARIMA George Box Martingales z-transforms Yakov Zalmanovitch Tsypkin 1919-1997 Joseph Leo Doob 1920-2004 State space methods Rudolfl Kalman 1930-

13. Table of transforms and their properties

14. Other useful approaches Fourier transforms Jean Baptiste Joseph Fourier (1768-1830) The beer game John Sterman Jay Forrester (1918-) System dynamics / simulation

15. Supply chain strategies for taming the bullwhip effect

16. Traditional supply chains Definition: ‘Traditional’ means that each level in the supply chain issues production orders and replenishes stock without considering the situation at either up- or downstream tiers of the supply chain. This is how most supply chains still operate; no formal collaboration between the retailer and supplier. Bullwhip increases geometrically in a traditional supply chain

17. Supply chains with information sharing Definition: Information exchange (or information sharing) means that retailer and supplier still order independently, yet exchange demand information in order to align their replenishment orders and forecasts for capacity and long-term planning. Bullwhip increases linearly in supply chains with information sharing

18. Synchronised Supply (VMI) Definition: Synchronized supply eliminates one decision point and merges the replenishment decision with the production and materials planning of the supplier. Here, the supplier takes charge of the customer’s inventory replenishment on the operational level, and uses this visibility in planning his own supply operations. Bullwhip may not increase at all in VMI supply chains

19. Integrating internal and external decision in supply chains with long lead-times RFID technologies now allow us to monitor the distribution leg

20. Solutions to the bullwhip problem

21. Replenishment rules and the bullwhip problem Set via the newsboy approach to achieve the critical fractile • Replenishment decisions influence both inventory levels & production rates. • A common replenishment decision is the “Order-Up-To” (OUT) policy…. Forecasts

22. Generating forecasts inside the OUT policy • Exponential smoothing • Moving average • Conditional expectation We will assume normally distributed i.i.d. demand & exponential smoothing forecasting from now on

23. The inventory and WIP balance equations The replenishment lead-time, Tp

24. The influence of the replenishment policy The inventory balance equation…. ….shows us that the replenishment policy influences both the orders and the net stock. Therefore, when studying bullwhip we should also consider

25. The impact of forecasting on net stock variance amplification • As then NSAmp approaches 1+Tp. • Minimising the Mean Squared Error between the forecast of demand over the lead-time and review period and its realisation will result in the minimum inventory variance. • This holds in a single echelon (Vassian 1954) and across a complete supply chain (Hosoda and Disney, 2006) when the traditional OUT policy is used

26. The impact of forecasting on bullwhip As then bullwhip approaches unity. Thus, we can see that as we make more accurate forecasts the bullwhip problem is reduced (but is not eliminated in this scenario)

27. Reducing lead-times • Reducing lead-times usually (but not always) reduces bullwhip • However, reducing lead-times will always reduce the inventory variance

28. The OUT policy through the eyes of a control engineer… WIP feedback gain (Tw) Inventory feedback gain (Ti) Unity feedback gains! • A control engineer would not be at all surprised that the OUT policy generates bullwhip as there are unit gains in the two feedback loops • Let’s add in a couple of proportional feedback controllers….

29. The first proportional controller:The Maxwell Governor

30. The golden replenishment rule

31. Matched feedback controllers • When Tw=Ti the maths becomes very much simpler • With MMSE forecasting ( ) we have…

32. The golden ratio in supply chains For i.i.d. demand, matched feedback controllers, MMSE forecasting

33. The golden ratio 1.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072...…

34. Economics of the bullwhip effect

35. Economics of inventory Inventory costs are governed by the safety stock (TNS) The Target Net Stock (TNS*) is an investment decision to be optimized In each period, when the inventory is positive a holding cost is incurred of £H per unit. In each period, if a backlog occurs (inventory is negative), a backlog cost of £B per unit is incurred

36. The economics of capacity Capacity per period = Average demand +/- slack capacity The amount of slack capacity (S*) is an investment decision to be optimized Production above capacity results in some over-time working (or sub-contracting). The cost of this type of capacity is £P per unit of over-time. Production below capacity results in some lost capacity cost of £N per unit lost.

37. Costs are a linear function of the standard deviation Inventory costs Bullwhip costs Constants Setting the amount of safety stock we need via the newsboy… … and the amount of capacity to invest in… …for a given set of costs (H, B, N, P) and lead-time, (Tp) Total costs are thus linearly related to the standard deviations

38. Sample designs for the 4 different scenarios Assuming the costs are; Holding cost, H=£1, Backlog cost, B=£9 Lost capacity cost, N=£4, Over-time cost, P=£6

39. Square root law for bullwhip

40. Distribution Network Design: Bullwhip costs 12 customers … n DC’s One manufacturer Each customer produces an i.i.d. demand, normally distributed with a mean of 5 and unit variance All lead-times in the system are one period long

41. …and it all depends on how many distribution centres we have… Each customer’s demand = N(5,1) DC demand= Factory demand=

42. … for 2 DC’s… Each customer’s demand = N(5,1) DC demand= DC demand= Factory demand=

43. … for 3 DC’s… Each customer’s demand = N(5,1) Each DC’s demand= Factory demand=

44. … for 4 DC’s… Each customer’s demand = N(5,1) Each DC’s demand= Factory demand=

45. The Square Root Law “If the inventories of a single product (or stock keeping unit) are originally maintained at a number (n) of field locations (refereed to as the decentralised system) but are then consolidated into one central inventory then the ratio exists”, Maister, (1976).

46. Proof of “the Square Root Law for bullwhip” The bullwhip (capacity) costs are given by In the decentralised supply chain the standard deviation of the orders is , In the centralised supply chain the standard deviation of the orders is Thus, which is the “Square Root Law for Bullwhip”.

47. Implementing a smoothing rule in Tesco

48. Tesco project brief • Tesco’s store replenishment algorithms were generating a variable workload on the physical delivery process • this generated unnecessary costs • The purpose of the project was to; • investigate the store replenishment rules to evaluate their dynamic performance • to identify if they generated bullwhip • offer solutions to any bullwhip problems

49. Inventory replenishment approaches

50. High volume products • Account for 65% of sales volume and 35% of product lines • Deliveries occur up to 3 times a day