Exam 2 Bullwhip Effect John H Vande Vate

Exam 2 Bullwhip Effect John H. Vande Vate Spring, 2006 1 1

Question 1 • Consider a situation similar to the retail game. You have 16 weeks to sell 2, 000 units of an item. You must sell the item at the full price of $100 for the first week. After that you may discount by 10%, 20%, 30% or 50%, but once you discount you cannot later raise the price. You can salvage any items that do not sell during the 16 -week season for $40 each. 2 2

Estimates 3 3

Question A • You are contemplating a pricing strategy for a new item similar to the one illustrated above. Assuming the new item enjoys essentially the same price elasticity as the item above, would it make economic sense to use a 50% discount for the new item? • No. Only makes sense if you are otherwise going to salvage. But in that case, a better strategy is to use the 30% discount. • ($70 – $40)*2. 19*Rate of Sales at Full Price = $65. 66*Rate of Sales at Full Price is the revenue you make above just salvaging • ($50 – $40)*3. 46* Rate of Sales at Full Price = $34. 55*Rate of Sales at Full Price is all you get from 4 4 a 50% discount

Question B If your answer … explain how large the lift from a discount of 50% would have to be for that discount to make sense. ($70 – $40)*2. 19*Rate of Sales at Full Price = $65. 66*Rate of Sales at Full Price < ($50 – $40)*(1+Lift)*Rate of Sales at Full Price 65. 66 < 10*(1+Lift) 6. 566 < (1 + Lift) 5. 566 < Lift or 557% 5 5

Question C Decentralized: Allocate the inventory to the stores and allow each store to optimize its revenues using the pricing model. Centralized: Allocate only a small amount of inventory to the stores, optimize the pricing using the model centrally, and then restock the stores frequently from this central stock. FOCUS YOUR ARGUMENTS ON REVENUE RATHER THAN COST. BE CERTAIN TO ADDRESS THE ADVANTAGES OF EACH APPROACH IN TERMS OF REVENUE. 6 6

Question 2 • As the company prepares to make its final scheduled shipment of the part to the Spartanburg plant it recognizes that • a. Current inventory position 1, 000 units • b. Remaining demand is uniformly distributed between 500 and 2, 500 units. • c. Any suspension systems that have to be written off cost the company $400 per unit. • d. Sending additional suspension systems after the last scheduled shipment costs the company $200 per unit. • Based only on this information, how many units would you recommend BMW include in its last 7 shipment and why? 7

Question 2 • Balance the risks: • P = Probability Demand is <= Q • The next item costs you $400 if – D <= Q so with probability P • The next item saves you $200 if – D > Q so with probability (1 -P) • Want these to be equal – 400 P = 200(1 -P) – P = 1/3 • That’s the probability D <= Q. 8 8

Question 2 • • Embarrassment from here on What Q gives this probability? 1/3 of the way from 500 to 2500. 500 + 1/3 of the difference between the two 500 + 2000/3 500 + 667 = 1167 Net out the stock already sent 167 = 1167 – 1000 9 9

Question 2 • 3. A company relies on Continuous Review policy to maintain its inventory of a component with the following characteristics: i. Annual Demand: 100, 000 units per year • ii. Std Dev in Weekly Demand: 100 units • iii. Average Lead-time: 3 weeks • iv. Std Dev in lead time: 2 days • Carry about two standard deviations in leadtime demand as safety stock. HINT: BE CAREFUL WITH UNITS HERE! • 10 10

Question A • Question A: Assuming independence in the demand from week to week and independence between the length of the lead time and the rate of demand during that time, provide an estimate of the standard deviation in lead time demand for this product. • Computing in terms of weeks or days • L= 3 weeks or 21 days (or 15 days) • D = 1923 (or 2000) per week or 274 (or 400) per day • s. D = 100 units per week or 37. 78 = 100/sqrt(7) per week • s. L = 2/7 = 0. 286 weeks (0. 20 weeks) • Should get something like 576 units as std. Dev in lead time demand s. L = Ls 2 D + D 2 s 2 L • Sqrt(3*100^2 + 1923^2*0. 286^2) = 576 11 11

Question B • Imagine that for the same cost you could improve either the Standard Deviation in Weekly Demand, the Standard Deviation in Lead Time or the Average Lead Time by 10%. You only get to improve one of them. Which will have the greatest impact on your overall inventory? • Improve Average Lead Time. This reduces safety stock AND Pipeline inventory 12 12

Question C • If the company moves to a periodic review policy for this product and orders every two weeks. What safety stock will the company need to carry to insure the same 98% in-stock performance per order cycle as before? Is this more or less than the safety stock required under the Continuous Review Policy? s = (T+L)s 2 D + D 2 s 2 L • Sqrt((2+3)*100^2 + 1923^2*0. 286^2) = 593 • Safety Stock is about 1186 vs 1152, a little larger 13 13

Sqrt(N) rule is a bad fit. Widely different “customers” Question 4 Assuming independence, variances add 14 14

Question 4 • Pipeline: – 4 weeks at $361, 000/52 = $6942 per week – That’s $27, 796 in the pipeline – Same for both proposals • Cycle: – Shipments of $6942 in value – Split between two locations or one, but same total • Safety: – A: 2*standard deviation in demand during T+L 2* (T+L)s 2 D + D 2 s 2 L = 2*Sqrt(5*1482^2) = 2*Sqrt(5)*1482 = $6, 626 15 15

Question 4 • Safety: – A: 2*standard deviation in demand during T+L 2* (T+L)s 2 D + D 2 s 2 L = 2*Sqrt(5*1482^2) = 2*Sqrt(5)*1482 = $6, 626 – B: Shanghai & Singapore • Shanghai: 2*standard deviation in demand during T+L 2* (T+L)s 2 D + D 2 s 2 L = 2*Sqrt(5*1430^2) = 2*Sqrt(5)*1430 = $6, 396 • Singapore: 2*standard deviation in demand during T+L 2* (T+L)s 2 D + D 2 s 2 L = 2*Sqrt(5*387^2) = 2*Sqrt(5)*387 = $1, 730 Total: $8, 126 16 16

Performance Average: 80 17 17

Expectation Expected Average to be between 83 and 95 Question 1: 20 – 25 (Partial credit on C) Question 2: 25 Question 3: 18 – 20 (B was tricky) Question 4: 20 – 25 18 18

The Bullwhip Effect Be Sure To Read: Chapter 4 of Simchi-Levi “The Bullwhip Effect in Supply Chains” By Hau Lee, V. Padmanabhan & Seungjin Whang 19 19

What it is… The Bullwhip Effect describes the phenomenon in which order variability is amplified as it moves up the supply chain from end-consumers through distribution and manufacturing to raw material suppliers. 20 20

Example Procter & Gamble: Pampers • Smooth consumer demand • Fluctuating sales at retail stores • Highly variable demand on distributors • Wild swings in demand on manufacturing • Greatest swings in demand on suppliers 21 21

Illustration Consumer Sales at Retailer Consumer demand 1000 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 11 9 7 5 3 0 1 100 Retailer's Orders to Distributor 1000 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 11 9 7 5 0 3 100 1 Retailer Order 900 22 22

Illustration Retailer's Orders to Distributor 1000 Retailer Order 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 9 11 7 5 3 0 1 100 Distributor's Orders to P&G 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 11 9 7 5 0 3 100 1 Distributor Order 1000 23 23

Illustration Distributor’s Orders to P&G 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 9 11 7 5 3 0 1 100 P&G's Orders with 3 M 1000 900 800 700 600 500 400 300 200 40 37 34 31 28 25 22 19 16 13 7 4 0 10 100 1 P&G Order Even worse at superabsorber suppliers like Degussa Distributor Order 1000 24 24

Illustration Consumer Sales at Retailer Consumer demand 1000 900 800 700 600 500 400 300 200 41 39 37 35 33 31 29 27 25 23 21 19 17 15 13 11 9 7 5 3 0 1 100 P&G's Orders with 3 M 1000 900 800 600 500 400 300 200 40 37 34 31 28 25 22 19 16 13 7 4 0 10 100 1 P&G Order 700 25 25

The Causes • • • Lead Times Forecasting & Inventory Models Pricing Strategies Order batching Uncertain Supply & Order Gaming 26 26

Lead Times • Long and Unreliable Lead Times make forecasts worse and supply less reliable 27 27

Forecasts • Periodic Review Inventory Models – Cost of Inventory – Cost of Expediting or Backordering – NO CONCERN FOR CHANGES IN ORDERS • The Forecast is wrong, but we will chase it in and drag our suppliers with us in futile attempt to ensure our inventories are “smooth” • BMW team on “Ship-to-Average” will talk more about that Thursday 28 28

Pricing Strategies • • Promotions Pre-announced price reductions Volume discounts Hockey stick effect 29 29

Order Batching • Driven by – Pricing strategies – Transportation rate structure (consolidate) – Transportation infrastructure (weekly sailings) • BMW team on Frequency will talk about cures for this on Thursday 30 30

Uncertain Supply & Order Gaming • Lucent in 2000 ~2. 5% of US GDP 31 31

Reducing the Bullwhip • Increase frequency • Ship-to-Average • Reduce variability – Risk Pooling, Postponement, contracts, … – Reduce lead time and lead time variability • Strategic partnerships • Less frequent financial reporting (? ) – Coca Cola 32 32

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