Microsoft PowerPoint - OM_Betting_on_Uncertain_Demand_2015.pptx

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1 News Vendor: Betting on Uncertainty The Newsvendor Problem Managing Fashion Goods Profit Maximizing Order Quantity Fill Rate and In Stock Probability Case: Managing Style Goods 不 能 依 賴 歷 史 銷 售 數 據 來 預 測 需 求 委 外 代 工 的 流 行 性 商 品 必 須 在 銷 售 季 節 開 始 前 數 個 月 決 定 採 購 量 銷 售 季 節 短, 少 有 再 補 貨 的 機 會 單 一 機 會 的 採 購 經 常 因 進 貨 不 足 而 提 前 結 束 銷 售 單 一 機 會 的 採 購 經 常 因 庫 存 過 剩 而 必 須 mark down Zara 利 用 限 量 款 式 的 行 銷 消 除 預 測 與 存 貨 管 理 的 需 要 1

2 1. The Newsvendor Problem Only one procurement opportunity. Stochastic demand leads to lost sales or leftover. There are losses of profit and goodwill for each unsatisfied customer. There is no salvage value for any leftover. How to balance cost of ordering too much vs. cost of ordering too little? 3 Single Period Inventory Control 適 用 於 無 庫 存 價 值 之 商 品 採 購 航 空 超 額 訂 位 1. 報 紙 需 求 D 為 常 態 分 布 平 均 值 =90 papers 標 準 差 =10 papers D~N(E(D), s d 2 ) 進 貨 90 papers P(stockout)=P(D>90)=P(D>E(D))=50% x Goal: P(stockout)<20% P(no stockout)>80% P(D<x)>80% P(D<E(D)+z s d )>80% Decision: 進 貨 (10)=99 papers 4 2

3 Optimal Quantity for Newspaper Problem 進 貨 高 估 需 求 的 單 位 成 本 =C o 報 紙 的 進 價 =0.20 進 貨 低 估 需 求 的 單 位 成 本 =C u 報 紙 的 銷 售 利 潤 =0.30 Question: 目 前 進 貨 90 份 報 紙, 提 高 進 貨 量 是 否 能 增 加 利 潤? 不 缺 貨 機 率 P =P( 增 加 進 貨 後 不 會 賣 光 )=P( 需 求 <90)=0.5 潛 在 利 潤 (1 P) C u =0.5(0.30) > 潛 在 損 失 P C o =0.5(0.20) Key: 增 加 進 貨 量 直 到 Cu P C C o u Optimal service level 如 果 C u << C o, 我 們 應 如 何 調 整 進 貨 量? 5 Case : Order Management at Sport Obermeyer Klaus Obermeyer founded Obermeyer in 1947, when he was among the first ski instructors on Aspen Mountain. Customer service, marketing, design & research, accounting in Colorado Rockies. Contract manufacturers in Hong Kong and China. Long lead time, short sales period Increasing product variety, more marked downs 3

4 Case: Forecasting at Sport Obermeyer Demands depend on weather, fashion trend, economy. Forecasts based on Panel Consensus. Dominant members have stronger influence on the outcome of a consensus forecast. Independent forecasts can provide an indicator of the forecast accuracy for each style. 7 Case: Collaborating with Retailers Obermeyer invites key customers to place early orders (20% of total sales) to get market information. Forecasts are updated based on those early orders. 8 4

5 Case: Order Planning at Sport Obermeyer Panel forecasts Early bird orders Revised forecasts 1st shipment 2nd shipment Phase 1 min. orders Phase 2 revised orders Summer extra orders and expensive styles Selling season 9 2. Forecast and Single Period Inventory Control Two selling seasons: Spring and Fall. Surf suits are fashion products. Production in Taiwan requires a three month lead time. Order quantity based on past sales of similar products and human judgment. Cost=110, price=180, salvage value=90 O Neill s Hammer 3/2 wetsuit 10 5

6 Ordering Timeline and Economics Half of the actual demands deviate from initial forecasts by at least 25%. 兩 個 月 後 的 更 新 預 測 較 為 準 確, 但 是 來 不 及 修 改 訂 單 Generate forecast of demand and submit an order to TEC Spring selling season Nov Dec Jan Feb Mar Apr May Jun Jul Aug Receive order from TEC at the end of the month Left over units are discounted 11 Creating a Demand Forecast 因 為 設 計 不 同, 前 幾 季 舊 款 式 的 銷 售 不 適 合 用 來 預 測 新 款 式 的 需 求 O Neill surveyed individuals in the organization and took the average (=3200) as the initial forecast. 決 定 進 貨 量 時, 不 能 只 考 慮 需 求 的 預 測 值, 還 要 評 估 需 求 的 變 異 程 度 設 進 貨 量 為 Q, 需 要 評 估 需 求 低 於 或 超 過 Q 的 可 能 性 F(Q)=Prob{Demand Q} 12 6

7 3. How to Estimate Demand Uncertainty? 預 測 誤 差 預 測 能 力 不 足? 需 求 的 不 確 定 性? 7000 上 一 季 各 款 式 的 預 測 與 實 際 銷 售 之 對 比 Actual demand Forecast 13 Forecasts vs. Actual Demand (Previous Season) A/Fratio actualdemand forecast Product description Forecast Actual demand Error* A/F Ratio** JR ZEN FL 3/ EPIC 5/3 W/HD JR ZEN 3/ WMS ZEN-ZIP 4/ HEATWAVE 3/ JR EPIC 3/ WMS ZEN 3/ ZEN-ZIP 5/4/3 W/HOOD WMS EPIC 5/3 W/HD EVO 3/ JR EPIC 4/ WMS EPIC 2MM FULL HEATWAVE 4/ average A/F ratio 1 過 去 預 測 沒 有 普 遍 高 估 或 低 估 14 7

8 Sorted A/F Ratios 假 設 今 年 預 測 的 準 確 度 與 去 年 相 當, 而 去 年 的 預 測 誤 差 可 用 來 評 估 今 年 需 求 的 變 異 程 度 去 年 共 有 33 種 款 式,A/F ratio 最 小 值 為 % chance that the demand is only 25% of the forecast. Product description Forecast Actual demand A/F Ratio* Rank Percentile** ZEN-ZIP 2MM FULL % ZEN 3/ % ZEN 4/ % WMS ELITE 3/ % WMS EPIC 4/ % JR EPIC 4/ % EVO 3/ % JR ZEN FL 3/ % EPIC 3/ % 15 Empirical Distribution Function for the Hammer 3/2 預 測 值 =3200, 利 用 過 去 的 預 測 誤 差 估 計 今 年 需 求 的 可 能 變 化 A/F Ratio Q F(Q ) A/F Ratio Q F(Q ) A/F Ratio Q F(Q ) Q = A/F ratio times the initial sales forecast, 3200 units F (Q ) = the probability demand is less than or equal to the quantity Q 16 8

9 Using A/F Ratios to Estimate Demand Uncertainty Empirical Distribution Initial forecast is % chance that the demand is no more than % chance that the demand is at least Note. If average A/F ratio < 1, reduce the current forecast. Normal Distribution Expected demand = average A/F ratio forecast = = 3192 Std. deviation of demand = S.D. of A/F ratio forecast = = Empirical vs. Normal Demand Distribution Probability N(3192, ) Quantity 18 9

10 Using Distribution to Estimate Demand Uncertainty O Neill 可 假 設 Hammer 3/2 的 需 求 ~N(3192, ) If the order quantity is increased to 4000, probability of not stocking out is z 0.68 ( z) x z Forecast vs. Order Quantity 由 於 預 測 不 會 百 分 百 準 確, 訂 購 量 不 必 等 於 預 測 值, 應 根 據 利 潤 殘 值 需 求 變 異 進 行 調 整 If the profit is good, there is an incentive to order more. If the salvage value is low, we order less to control losses

11 The Profit-Maximizing Order Quantity 80 Expected gain or loss Expected gain Expected loss Q th unit ordered 21 Too much and Too little Costs C o = overage cost 產 品 賣 不 完 而 賠 本 出 清 的 損 失 For Hammer 3/2 C o = cost salvage value = c v = = 20 C u = underage cost 產 品 不 夠 賣 而 損 失 的 潛 在 利 潤 For Hammer 3/2 C u = price cost = p c = =

12 Finding Optimal Order Quantity F(Q) = P(D<Q) = in stock probability ( 期 末 仍 有 庫 存 ) To maximize expected profit, order Q units so that expected loss on the Q th unit equals expected gain on the Q th unit: C F( Q) C 1 F Rearrange the above equation C u / (C o +C u ) is called the critical ratio. o Q 最 佳 訂 購 量 Q* : 使 不 缺 貨 機 率 P(D< Q*) critical ratio. u Cu F( Q) C C o u 23 Hammer 3/2 s Optimal Order Quantity p = 180; c = 110; v = 90; C u = ; C o = Evaluate the critical ratio: Cu C C Lookup in the empirical distribution table o u Product description Forecast Actual demand A/F Ratio Rank Percentile HEATWAVE 3/ % HEAT 3/ % HAMMER 3/ % Convert A/F ratio into the order quantity Q Forecast * A / F 3200 *

13 5. Performance Measures D ~ N(3192, ) 假 設 訂 購 量 為 3456 expected demand expected sales = expected lost sales 3192 expected left over inventory = Q expected sales 3456 expected profit (price cost) expected sales (cost salvage value) expected left over expected fill rate = fraction of demand that is satisfied = expected sales / expected demand in stock probability: P(demand < Q) 25 Order Quantity and Expected Lost Sales Expected Lost Sales If 0 units are ordered, all sales are lost, so expected lost sales equals mean demand, Order quantity If 5000 units are ordered, expected lost sales will be nearly zero

14 Example: How to Calculate Expected Lost Sales Demand > Order quantity= (Loss = 10) x (Prob D = 130) (Loss = 20) x (Prob D = 140) (Loss = 80) x (Prob D = 200) expected lost sales = 10 x P{D=130} + 20 x P{D=140} x P{D=200} 27 Hammer 3/2 s Expected Loss Sales Table Assume the demand follows the empirical distribution function: Q F (Q ) L (Q ) Q F (Q ) L (Q ) Q F (Q ) L (Q ) Q = order quantity F (Q ) = probability demand is less than or equal to the order quantity L (Q ) = loss function (the expected amount demand exceeds Q ) 28 14

15 Measures Based on Empirical Distribution expected sales = expected demand expected lost sales = = 2816 expected left Over Inventory = Order Quantity Expected Sales = = 640 expected profit = (price cost) expected sales (cost salvage value) expected left over = $ $ = $ expected sales expected fill rate= % expected demand 3192 Order quantity=3456 in stock probability = F(Q) = 29 In-Stock Probability and Fill Rate for Hammer 3/2 In Stock probability 只 考 慮 是 否 發 生 缺 貨, 可 能 明 顯 低 於 fill rate 100% 90% 80% Expected fill 70% 60% 50% In-stock probability 40% 30% 20% 10% 0% Order quantity 30 15

16 6. Retail Discounting Model S = current selling price D = discount price P = profit margin on cost (% markup as decimal) Y = average number of years to sell entire stock of dogs at current price (total years to clear stock divided by 2) N = inventory turns (in 1 year) Loss per item = Gain from revenue S D = D(PNY) D S ( 1 PNY) 31 流 行 性 商 品 必 須 在 銷 售 季 節 前 決 定 採 購 量 單 一 機 會 的 採 購 經 常 因 庫 存 過 剩 而 必 須 賠 售 出 清 預 測 與 銷 售 之 間 的 誤 差 可 來 自 於 需 求 的 不 確 定 性 利 用 前 幾 季 的 預 測 誤 差 來 估 算 未 來 需 求 的 變 化 兩 個 預 測 需 求 相 當 的 品 項 可 能 有 明 顯 不 同 的 需 求 變 異 性, 導 致 採 購 量 的 差 異 最 佳 採 購 量 取 決 於 缺 貨 成 本 與 降 價 出 清 的 損 失 32 16