Determining Optimal Level of Product Availability Optimal Matching of Supply and Demand (III) 1 蔣明晃教授 【本著作除另有註明外，採取創用 CC 「姓名標示 －非商業性－相同方式分享」台灣 3.0 版授權釋出】創用 CC 「姓名標示 －非商業性－相同方式分享」台灣 3.0 版 第 八單元 (1) ： Determining Optimal Level of Product Availability

Supply Chain Decision-Making Framework InventoryTransportationFacilitiesInformation Supply chain structure Drivers Supply chain strategy Competitive strategy EfficiencyResponsiveness 2

►D►Determining optimal level of product availability ►O►Ordering under capacity constraints ►L►Levers to improve supply chain profitability ►C►Contracts Outline 》 Single order in a season 》 Continuously stocked items 3

Mattel, Inc. & Toys “R” Us Mattel was hurt last year by inventory cutbacks at Toys “R” Us, and officials are also eager to avoid a repeat of the 1998 Thanksgiving weekend. Mattel had expected to ship a lot of merchandise after the weekend, but retailers, wary of excess inventory, stopped ordering from Mattel. That led the company to report a $500 million sales shortfall in the last weeks of the year... For the crucial holiday selling season this year, Mattel said it will require retailers to place their full orders before Thanksgiving. And, for the first time, the company will no longer take reorders in December, Ms. Barad said. This will enable Mattel to tailor production more closely to demand and avoid building inventory for orders that don't come. - Wall Street Journal, Feb. 18, 1999 barbiecollections Microsoft 。 Wikipedia stephaniefierman.com 4

►H►How much should Toys R Us order given demand uncertainty? ►H►How much should Mattel order? ►W►Will Mattel’s action help or hurt profitability? ►W►What actions can improve supply chain profitability? Key Questions 5

►C►Cost of overstocking: ►C►Cost of understocking: 》 The loss incurred for each unsold unit 》 The margin lost for each lost sale unit Factors Affecting Optimal Level of Product Availability 6

A Newsboy Problem overstockingunderstocking Microsoft 。 7

Parkas at L.L. Bean Cost per parka = $45 Sale price per parka = $100 Discount price per parka = $50 Holding and transportation cost to outlet = $10 ►Profit from selling parka (cost of understocking)= $100-$45 = $55 ►Cost of overstocking = $45+$10-$50 = $5 llbean.com 8

Cost per parka = $45 Sale price per parka = $100 Discount price per parka = $50 Holding and transportation cost to outlet = $10 ►Profit from selling parka (cost of understocking)= $100-$45 = $55 ►Cost of overstocking = $45+$10-$50 = $5 How much to order? Parkas at L.L. Bean 9

Parkas at L.L. Bean ◈ Expected profit from extra 100 parkas = ◈E◈Expected demand = 10 (‘00) parkas ◈E◈Expected profit from ordering 10 (‘00) parkas 5500  P (demand  1100) – 500  P (demand < 1100) = 5500  0.49 – 500  0.51 =

Cost per parka = $45 Sale price per parka = $100 Discount price per parka = $50 Holding and transportation cost to outlet = $10 ►Profit from selling parka (cost of understocking)= $100-$45 = $55 ►Cost of overstocking = $45+$10-$50 = $5 How much to order? Parkas at L.L. Bean 11

Parkas at L.L. Bean ◈E◈Expected profit from extra 100 parkas = ◈ Expected demand = 10 (‘00) parkas ◈ Expected profit from ordering 10 (‘00) parkas 5500  P (demand  1100) – 500  P (demand < 1100) = 5500  0.49 – 500  0.51 = 2440 = $49,900  [D i (p-c)-(1,000-D i (c-s))]P i +(1-p i )1,000(p-c) 10 i=4 12

Parkas at L.L. Bean ◈E◈Expected profit from extra 100 parkas = ◈ Expected demand = 10 (‘00) parkas ◈ Expected profit from ordering 10 (‘00) parkas 5500  P (demand  1100) – 500  P (demand < 1100) = 5500  0.49 – 500  0.51 = 2440 = $49,900  [D i (p-c)-(1,000-D i (c-s))]P i =(1-p i )1,000(p-c) 10 i=4 13

Parkas at L.L. Bean ◈E◈Expected profit from extra 100 parkas = ◈ Expected demand = 10 (‘00) parkas ◈ Expected profit from ordering 10 (‘00) parkas 5500  P (demand  1100) – 500  P (demand < 1100) = 5500  0.49 – 500  0.51 = 2440 = $49,900  [D i (p-c)-(1,000-D i (c-s))]P i =(1-p i )1,000(p-c) 10 i=4 14

Cost per parka = $45 Sale price per parka = $100 Discount price per parka = $50 Holding and transportation cost to outlet = $10 ►Profit from selling parka (cost of understocking)= $100-$45 = $55 ►Cost of overstocking = $45+$10-$50 = $5 How much to order? Parkas at L.L. Bean 15

Parkas at L.L. Bean ◈ Expected profit from extra 100 parkas = ◈ Expected demand = 10 (‘00) parkas ◈ Expected profit from ordering 10 (‘00) parkas 5500  P (demand  1100) – 500  P (demand < 1100) = 5500  0.49 – 500  0.51 = 2440 = $49,900  [D i (p-c)-(1,000-D i (c-s))]P i =(1-p i )1,000(p-c) 10 i=

Parkas at L.L. Bean 17

Parkas at L.L. Bean ◈O◈Optimal order quantity is 1300 parkas, which provides a CSL of 92% ◈T◈The fill rate achieved if 1300 parkas are ordered 18

Cost per parka = $45 Sale price per parka = $100 Discount price per parka = $50 Holding and transportation cost to outlet = $10 ►Profit from selling parka (cost of understocking)= $100-$45 = $55 ►Cost of overstocking = $45+$10-$50 = $5 How much to order? Parkas at L.L. Bean 19

Parkas at L.L. Bean ◈O◈Optimal order quantity is 1300 parkas, which provides a CSL of 92% ◈T◈The fill rate achieved if 1300 parkas are ordered 20

◈p◈p= sale price; ◈s◈s = outlet or salvage price; ◈c◈c = purchase price ◈C◈CSL = Probability that demand will be at or below reorder point At optimal order size, Expected Marginal Benefit from raising order size= (1-CSL * )(p - c) Expected Marginal Cost = CSL * (c - s). (1-CSL * )C u = CSL *  C o, CSL * = C u / (C u + C o )=1/[1+(C o /C u )] Optimal level of service 21

Parkas at L.L. Bean ◈ Expected profit from extra 100 parkas = ◈ Expected demand = 10 (‘00) parkas ◈ Expected profit from ordering 10 (‘00) parkas 5500  P (demand  1100) – 500  P (demand < 1100) = 5500  0.49 – 500  0.51 = 2440 = $49,900  [D i (p-c)-(1,000-D i (c-s))]P i =(1-p i )1,000(p-c) 10 i=4 22

◈ p= sale price; ◈ s = outlet or salvage price; ◈ c = purchase price ◈ CSL = Probability that demand will be at or below reorder point At optimal order size, Expected Marginal Benefit from raising order size= (1-CSL * )(p - c) Expected Marginal Cost = CSL * (c - s). (1-CSL * )C u = CSL *  C o, CSL * = C u / (C u + C o ) Optimal level of service C U =Under Stock. C O= Over Stock Demand<=N →p-c →c-s P-S p-c =1/[1+(C o /C u )] (1-CSL * )C u = CSL *  C o, CSL * = C u / (C u + C o ) 23

Optimal Order Size(O * ) and Fill Rate under Optimal Order Size ◈ Optimal Order Size (O*) ◈ Fill rate at O* CSL * = C u / (C u + C o ) =1/[1+(C o /C u )] 24

Order Quantity for a Single Order ► O * = Optimal order size ◈ C o = Cost of overstocking = $5 u = Profit from sale =Cost of understocking= $55 Optimal Order Quantity = Probability 25

Optimal level of product availability ►Expected profit 26

Expected Profit, Overstock and Understock under O * ►E►Expected overstock ►E►Expected understock 27

Example: Sportmart ►The manager at Sportmart has to decide on the number of skis to purchase for the winter season. Considering past demand data and weather forecasts for the year, management has forecast demand to be normal distributed with a mean 350 and a standard deviation 100. Each pair of skis costs c=$100 and retails for p=$250. Any unsold skis at the end of the season are disposed of for $85. Assume that it costs $5 to hold a pair of skis in inventory for the season. Evaluate the number of skis that the manager should order to maximize expected profits. ◈ Cu = p – c = = 150 ◈ Co = 100 – 80 = 20 ◈ CSL* = Cu / (Cu + Co) = 0.88 ◈ O* = NORMINV(0.88, 350, 100) = 468 ◈ Expected profits = $49,146 ◈ Expected overstock = 108 ◈ Expected understock = 8 28

Continuously Stocked Items: Optimal Safety Inventory Levels ◈C◈CSL = Probability of not stocking out in a cycle with current level of safety stock = Cycle Service Level ◈R◈ROP = Reorder point ◈D◈D = Average demand per unit time ◈◈ = Standard deviation of demand per unit time ◈s◈ss = Safety stock ◈C◈C u = Cost of stock out per unit ◈h◈h = Holding cost as a fraction of product cost per unit time ◈C◈C = Unit cost ◈H◈H = Cost of holding one unit for one year = hc ◈S◈S = Fixed cost associated with each order ◈Q◈Q * = Economic order quantity CSL Optimal Order Size (O*) hC DS Q 2 *  Microsoft 。 29

►C►CSL * = 1- HQ * /C u D ◈ Example: D = 100 gallons/week;  = 20; unit cost = $3; h = 0.2; H = $0.6/gal./year; L = 2 weeks; Q = 400; ROP = 300, D L = DL = 200, ◈ What is the imputed cost of stocking out? CSL=F(ROP, D L,  L ) = F(300,200,28.3) = C u = 0.6  400/[( )  5200] = Optimal Safety Inventory Levels for Backlogged 30

Optimal Safety Inventory Levels for Lost Sales ►C►CSL * = 1- HQ * /(HQ * + C u D) ►F►Follow the previous example, given C u = $2. ►What is optimal CSL? CSL =  400/(0.6   5200) = 0.98 Backlogged CSL * = 1- HQ * /C u D 31

Levers for Increasing Supply Chain Profitability ►D►Decreasing the costs of overstocking and understocking ►R►Reducing the demand uncertainty Microsoft 。 32

►Increase salvage value: sell to outlet, sell to different regions The Ways to decreasing the costs of overstocking and understocking ►Decrease margin lost from stockout : 1.backup sourcing 2.purchase from market 3.rain check 4.discount Microsoft 。 33

Impact of Co/Cu on Optimal CSL Co/Cu CSL * 1 34

The Ways to Reduce Demand Uncertainty ►I►Improved forecasting to lower uncertainty ►Q►Quick response: reduce lead time to increase number of orders per season ►P►Postponement of product differentiation ►T►Tailored sourcing 35

How to Estimate Demand Distribution? ►H►Historical data: Time series forecasting ►D►Dependent factors: Regression, causal forecasting ►E►Expert opinion: Buying committee Key: Forecast must include estimated demand and uncertainty (standard deviation) of demand 36

Impact of Improving Forecasts Example: A buyer at Bloomingdales responsible for purchasing dinnerware with X’mas pattern. Demand: Normally distributed with a mean of D = 350 and standard deviation of  D = 150 Purchase price = $100 Retail price = $250 Disposal value = $80 How many units should be ordered as  D changes? Cu = 250 – 100 = 150, Co = 100 – 80 = 20 CSL*  150/( ) = 0.88 Microsoft 。 37

Impact of Improving Forecasts Example: A buyer at Bloomingdales responsible for purchasing dinnerware with X’mas pattern. Demand: Normally distributed with a mean of D = 350 and standard deviation of  D = 150 Purchase price = $100 Retail price = $250 Disposal value = $80 How many units should be ordered as  D changes? Cu = 250 – 100 = 150, Co = 100 – 80 = 20 CSL*  150/( ) =

Variation of Profit and Inventories with Forecast Accuracy Example: A buyer at Bloomingdales responsible for purchasing dinnerware with X’mas pattern. Demand: Normally distributed with a mean of D = 350 and standard deviation of  D = 150 Purchase price = $100 Retail price = $250 Disposal value = $80 How many units should be ordered as  D changes? Cu = 250 – 100 = 150, Co = 100 – 80 = 20 CSL*  150/( ) = 0.88 Expected Overstock Expected Overstock Expected Profit Expected Profit Expected Understock Expected Understock Standard Deviation of Forecast Error 39

What’s Quick Response? ►A widely used strategy 》 By general merchandise, soft-lines retailers and manufacturers 》 To reduce retail out-of-stocks, forced markdown, merchandising system and operating costs 》 Suppliers and retailers work together to respond more rapidly to consumer needs 》 By sharing POS information to jointly forecast future demand for replenishable items, and to continuously monitor trends to detect opportunities for new items 》 Spread through the supply chain and seamlessly linked at each stage by electronic data interchange ►A partnership strategy ►A JIT strategy Microsoft 。 40

頁碼作品授權條件作者 / 來源 4 本作品轉載自 barbiecollections 網站 ( ，瀏覽日期 2012/1/11 。依據著作權法第 46 、 52 、 65 條合理使用。 4 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 4 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 4 本作品轉載自 Wikipedia ( ，瀏 覽日期 2012/5/17 ，依據著作權法第 46 、 52 、 65 條合理使用。 4 本作品轉載自 stephaniefierman 網站 ( missed-opportunity.php#comments) ，瀏覽日期 2012/2/22 。依據著作權法 第 46 、 52 、 65 條合理使用。 missed-opportunity.php#comments 7 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 8 本作品轉載自 llbean.com 網站 ( ) ，瀏覽日期 2012/1/11 。 依據著作權法第 46 、 52 、 65 條合理使用。 ( 因網站商品隨時更新，故此頁 面無永久性網址。 ) 版權聲明 41

頁碼作品授權條件作者 / 來源 29 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 29 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 32 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 33 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 37 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 37 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 40 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 版權聲明 42

頁碼作品授權條件作者 / 來源 40 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 40 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 40 本作品轉載自 Microsoft Office 2007 多媒體藝廊，依據 Microsoft 服務合約 及著作權法第 46 、 52 、 65 條合理使用。 Microsoft 服務合約 版權聲明 43