Ch 12 存貨管理.

Presentation on theme: "Ch 12 存貨管理."— Presentation transcript:

1 Ch 12 存貨管理

2 Outline Global Company Profile: Amazon.com The Importance of Inventory
Functions of Inventory Types of Inventory © 2011 Pearson Education

3 Outline – Continued Managing Inventory Inventory Models ABC Analysis
Record Accuracy Cycle Counting Control of Service Inventories Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs © 2011 Pearson Education

4 Outline – Continued Inventory Models for Independent Demand
The Basic Economic Order Quantity (EOQ) Model Minimizing Costs Reorder Points Production Order Quantity Model Quantity Discount Models © 2011 Pearson Education

5 Outline – Continued Probabilistic Models and Safety Stock
Other Probabilistic Models Fixed-Period (P) Systems © 2011 Pearson Education

6 Amazon.com Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others Growth has forced Amazon.com to become a world leader in warehousing and inventory management © 2011 Pearson Education

7 Amazon.com Each order is assigned by computer to the closest distribution center that has the product(s) A “flow meister” at each distribution center assigns work crews Lights indicate products that are to be picked and the light is reset Items are placed in crates on a conveyor, bar code scanners scan each item 15 times to virtually eliminate errors © 2011 Pearson Education

8 Amazon.com Crates arrive at central point where items are boxed and labeled with new bar code Gift wrapping is done by hand at 30 packages per hour Completed boxes are packed, taped, weighed and labeled before leaving warehouse in a truck Order arrives at customer within days © 2011 Pearson Education

9 存貨的功能 存貨管理的目標即是在存貨投資與顧客服務之間達到平衡。 存貨的重要性
One of the most expensive assets of many companies representing as much as 50% of total invested capital Operations managers must balance inventory investment and customer service

10 存貨的功能 存貨能達到提升公司營運彈性的功能。存貨的四大功能為： 「 降低」或分散各部分生產過程的波動。
降低公司的需求波動，並提供商品的存貨供顧客選擇。 獲得批量折扣的好處，因為大量購買能減低商品的成本或所需的運輸費用。 對抗通貨膨脹以及上游價格調整。

11 存貨的種類 存貨的種類 原料存貨 在製品存貨 維護／修理／營運（MRO）供應存貨 完成品存貨 已購買但尚未處理的存貨。
經過一些處理但尚未變成成品的原料或元件。 維護／修理／營運（MRO）供應存貨 MRO存貨為維護／修理／營運供應所需要的存貨，用來讓機器與流程能持續生產。 完成品存貨 等待運送的完成商品。

12 The Material Flow Cycle

13 存貨管理 建立管理存貨系統的兩個要素： 如何分類存貨項目（稱為 ABC分析） 如何進行精確的存貨記錄

14 ABC分析法 ABC分析法（ABC analysis）將現有存貨依照年度用量價值(annual dollar volume)分為三個範疇。
Used to establish policies that focus on the few critical parts and not the many trivial ones

15 ABC分析法

16 範例 1 晶片製造商的ABC分析 Silicon Chips集團專門生產超快速 DRAM 晶片，希望透過ABC分析來分類出十種主要存貨。

17 Percent of Number of Items Stocked Percent of Annual Dollar Volume
ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units) x Unit Cost = Annual Dollar Volume Percent of Annual Dollar Volume Class #10286 20% 1,000 $ 90.00 $ 90,000 38.8% A #11526 500 154.00 77,000 33.2% #12760 1,550 17.00 26,350 11.3% B #10867 30% 350 42.86 15,001 6.4% #10500 12.50 12,500 5.4% 72% 23% © 2011 Pearson Education

18 Percent of Number of Items Stocked Percent of Annual Dollar Volume
ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units) x Unit Cost = Annual Dollar Volume Percent of Annual Dollar Volume Class #12572 600 $ 14.17 $ 8,502 3.7% C #14075 2,000 .60 1,200 .5% #01036 50% 100 8.50 850 .4% #01307 .42 504 .2% #10572 250 150 .1% 8,550 $232,057 100.0% 5% © 2011 Pearson Education

19 ABC Analysis Other criteria than annual dollar volume may be used
Anticipated engineering changes Delivery problems Quality problems High unit cost © 2011 Pearson Education

20 ABC分析法 ABC分析所制訂的策略方針如下： A類項目花在供應商開發的購買資源應該 要比C類項目高。

21 精確的存貨記錄 記錄正確性 Accurate records are a critical ingredient in production and inventory systems Allows organization to focus on what is needed Necessary to make precise decisions about ordering, scheduling, and shipping Incoming and outgoing record keeping must be accurate Stockrooms should be secure

22 精確的存貨記錄 週期盤點 記錄必須要透過持續的稽核來驗證，這樣的稽核方法稱為週期盤點（cycle counting）
A類項目會經常被盤點也許一個月一次。 B 類項目會比A 類項目稍微少一點盤點次數，也許是一季一次。 C類項目可能每六個月盤點一次。

23 精確的存貨記錄 週期盤點有下列好處： 消除年度實體存貨盤點時必做的設施關閉與中斷。 消除年度存貨調整。
經過訓練的工作人員能提升稽核存貨的正確性。 可以找出錯誤的原因，以及採取補救措施。 維持正確的存貨記錄。

24 範例 2 貨車製造商的週期盤點 Cole’s Trucks 集團是一個高品質的垃圾車製造商，它有大約5,000個品項存貨；它想知道每一天有多少個品項需要週期盤點。

25 Cycle Counting Example
5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) Item Class Quantity Cycle Counting Policy Number of Items Counted per Day A 500 Each month 500/20 = 25/day B 1,750 Each quarter 1,750/60 = 29/day C 2,750 Every 6 months 2,750/120 = 23/day 77/day © 2011 Pearson Education

26 存貨控制 存貨的控制 存貨在收到及賣出的過程中不見的話稱為耗損（shrinkage）。 存貨遭竊可稱為小竊（pilferage）。
正確的存貨與存貨控制很重要，可應用技術如下： 好的工作人員選擇、訓練與紀律 嚴格控制輸入 有效的控制從廠房設施輸出的貨品

27 存貨模型 獨立與相依需求 獨立需求 the demand for item is independent of the demand for any other item in inventory 相依需求 the demand for item is dependent upon the demand for some other item in the inventory

28 存貨模型 持有、訂貨與整備成本 持有成本（holding costs）是與持有或維持一段子存貨相關的成本。
訂貨成本（ordering costs）包含供應、表單、訂單處理、採買、書記等成本。 整備成本（setup costs）是為了製造商品前準備機器或流程所需的成本。 整備成本與整備時間（setup time）有高度關聯。

29 存貨模型

30 獨立需求的存貨模型 三個存貨模型： 基本經濟訂購量（EOQ）模型 生產訂貨數量模型 數量折扣模型

31 獨立需求的存貨模型 基本經濟訂購量模型 經濟訂購量模型（economic order quality, EOQ）是其中一個最早且最常用來做存貨控制的技術。 需符合下列假設： 需求是已知、恆定且獨立的。 前置時間（Lead time）—也就是在訂單與取貨之間的時間—是已知且恆定的。 存貨收取的時間是即時、快速且完整的。 沒有數量折扣的情形。. 唯一的變動成本為整備或訂貨的成本以及持有或保存存貨的成本。 忽略存貨不足（缺貨）。

32 獨立需求的存貨模型

33 獨立需求的存貨模型 極小化成本

34 獨立需求的存貨模型 在經濟訂購量模型中，最佳訂貨量會發生在總整備成本等於總持有成本的時候。 利用此特性，發展公式來直接求Q* 的解， 如下：
發展一個表示整備或訂貨成本的運算式。 發展一個表示持有成本的運算式。 讓整備成本等於訂貨成本。 求等式的解以找出最佳訂貨量。

35 獨立需求的存貨模型 利用下列的變數，我們可以決定整備與持有成本，並找出Q*： Q = 每次訂單所訂貨的數量
Q* = 每次訂貨的最佳訂貨量（EOQ） D = 此存貨項目的年度需求單位 S = 每次訂貨的整備或訂貨成本 H = 每年度單位持有或維持成本

36 Number of units in each order Setup or order cost per order
The EOQ Model Annual setup cost = S D Q Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order Setup or order cost per order = = (S) D Q © 2011 Pearson Education

37 The EOQ Model Q = Number of pieces per order
Annual setup cost = S D Q Annual holding cost = H Q 2 Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Annual holding cost = (Average inventory level) x (Holding cost per unit per year) Order quantity 2 = (Holding cost per unit per year) = (H) Q 2 © 2011 Pearson Education

38 The EOQ Model 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H
Annual setup cost = S D Q Annual holding cost = H Q 2 Q = Number of pieces per order Q* = Optimal number of pieces per order (EOQ) D = Annual demand in units for the inventory item S = Setup or ordering cost for each order H = Holding or carrying cost per unit per year Optimal order quantity is found when annual setup cost equals annual holding cost D Q S = H 2 Solving for Q* 2DS = Q2H Q2 = 2DS/H Q* = 2DS/H © 2011 Pearson Education

39 獨立需求的存貨模型 年度整備成本 年度持有成本 年度整備成本等於年度持有成本時，可得到最佳訂 貨量：
為了求出Q*，只要將公式交叉相乘後，將Q移至等 號左邊：

40 範例 3 Sharp 集團的最適訂單量 Sharp 集團，販賣無痛皮下注射器給醫院，希望透過決定每筆訂單的最適訂購量來降低成本。

41 An EOQ Example Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units
Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units © 2011 Pearson Education

42 範例 4 計算Sharp集團需要的訂單次數及訂貨間隔時間
Sharp 集團（如範例3）一年有250 個工作天，它想要知道訂貨次數（N）以及預期訂貨間隔時間（T）。

43 Expected number of orders
An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order H = $.50 per unit per year = N = = Expected number of orders Demand Order quantity D Q* N = = 5 orders per year 1,000 200 © 2011 Pearson Education

44 Expected time between orders Number of working days per year
An EOQ Example Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year = T = Expected time between orders Number of working days per year N T = = 50 days between orders 250 5 © 2011 Pearson Education

45 範例 5 計算訂貨成本與持有成本的總數 Sharp 集團（如範例3 與範例4）想要計算年度訂貨成本與持有成本的總數。

46 An EOQ Example Determine optimal number of needles to order
D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total annual cost = Setup cost + Holding cost TC = S H D Q 2 TC = ($10) ($.50) 1,000 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100 © 2011 Pearson Education

47 獨立需求的存貨模型 穩健模型 EOQ模型的好處就是它很穩健。 穩健（robust）即表示，即使參數有很大的變異，仍然可以得到令人滿意的結果。

48 範例 6 EOQ是一個穩健模型 Sharp 集團夏普的管理階層在用同樣的Q 值時，低估了50％的年度需求量（也就是實際需求為1,500 支針，而不是1,000 支針）。試問年度存貨會受到怎麼樣的影響？

49 An EOQ Example Management underestimated demand by 50%
D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days 1,500 units TC = S H D Q 2 TC = ($10) ($.50) = $75 + $50 = $125 1,500 200 2 Total annual cost increases by only 25% © 2011 Pearson Education

50 An EOQ Example Actual EOQ for new demand is 244.9 units
D = 1,000 units Q* = units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days 1,500 units TC = S H D Q 2 Only 2% less than the total cost of $125 when the order quantity was 200 TC = ($10) ($.50) 1,500 244.9 2 TC = $ $61.24 = $122.48 © 2011 Pearson Education

51 獨立需求的存貨模型 EOQ answers the “how much” question
The reorder point (ROP) tells “when” to order 再訂購點 一個訂單的下單時間與收到訂貨的時間間隔， 稱為前置時間（lead time）。

52 獨立需求的存貨模型 再訂購點 ROP = ( 每日需求) × ( 新訂單的前置時間) = d × L
安全庫存：為了防範不穩定的需求所保有的 額外存量；一種緩衝機制。 每日的需求d 為年度需求D 除以一年內的工 作天數：

53

54 範例 7 計算iPod的再訂購點（ROP） 一家蘋果（Apple）電腦的批發商，其每年iPod 需求為8,000 個單位，此公司每年有250 個工作天，平均來說履行一次訂單需要三個工作天。公司想要計算再訂購點。

55 Number of working days in a year
Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days d = D Number of working days in a year = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units © 2011 Pearson Education

56 獨立需求的存貨模型 生產訂貨量模型 應用於兩種情況： 當下訂單後，存貨在一段時間內持續地流入或製造。
產品同時生產並賣出。在這些情況下，我們考量了每日生產速率以及每日需求速率。

57 獨立需求的存貨模型 利用下列符號來表示生產訂貨量模型的年度存貨持有成本： Q = 每次訂單所訂貨的數量 H = 每年度單位持有成本
p = 每日生產速率 d = 每日需求速率或使用率 t = 生產時間長度（以天為單位）

58 Production Order Quantity Model
Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days = (Average inventory level) x Annual inventory holding cost Holding cost per unit per year = (Maximum inventory level)/2 Annual inventory level = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt © 2011 Pearson Education

59 Production Order Quantity Model
Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Maximum inventory level = p – d = Q 1 – Q p d Holding cost = (H) = – H d p Q 2 Maximum inventory level © 2011 Pearson Education

60 Production Order Quantity Model
Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate D = Annual demand Setup cost = (D/Q)S Holding cost = HQ[1 - (d/p)] 1 2 (D/Q)S = HQ[1 - (d/p)] 1 2 Q2 = 2DS H[1 - (d/p)] Q* = 2DS H[1 - (d/p)] p © 2011 Pearson Education

61 獨立需求的存貨模型 年度存貨持有成本 = 平均存貨水準 × 每年度單位持有成本 平均存貨水準 = 最大存貨水準/2
最大存貨水準 = 在生產進行中的總生產量 – 在生產進行中 的總存貨使用量 = pt – dt 然而Q = 總生產量 = pt，所以t = Q/p，因此： 最大存貨水準 = 年度存貨持有成本（或持有成本） =

62 獨立需求的存貨模型 將整備成本與持有成本設成相等，可得QP：

63 範例 8 最佳生產量模型 Nathan Manufacturing 公司生產特殊的轂蓋，供應汽車維修零組件市場。Nathan 明年的車輪轂蓋市場的需求預測是1,000 單位，平均每天的需求是4 單位，其生產過程最有效率的狀態一天可以生產8 單位。因此，公司可以生產 8 單位，但實際使用量只有4 單位。公司希望能求出每筆訂單的最適訂購量。（注意，公司生產轂蓋的排程是依據市場需求，每年營運250 天）

64 Production Order Quantity Example
D = 1,000 units p = 8 units per day S = $10 d = 4 units per day H = $0.50 per unit per year Q* = 2DS H[1 - (d/p)] = or 283 hubcaps Q* = = ,000 2(1,000)(10) 0.50[1 - (4/8)] © 2011 Pearson Education

65 獨立需求的存貨模型 數量折扣 簡單來說就是一個商品在大批購買時會有個折扣價格。整體目標是極小化成本。 總成本=整備成本+持有成本+產品成本
或 Q = 訂購數量 D = 年度需求單位 S = 每次訂單或每次整備的訂貨或整備成本 P = 每單位價格 H = 每年度單位持有成本

66 Quantity Discount Models
A typical quantity discount schedule Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 no discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75 Table 12.2 © 2011 Pearson Education

67 獨立需求的存貨模型 決定能最小化總年度存貨成本的訂貨量，此程序包含了四個步驟：
步驟一： 針對每一種折扣方式，利用下列算式各計算出最佳訂貨量Q*： 步驟二： 對於所有折扣而言，如果訂貨量太低而 無法達到折扣數量時，要向上調整訂購量至最低 折扣量。 H = IP I: 持有成本佔單價的比例

68 獨立需求的存貨模型 步驟三： 利用先前介紹的總成本等式，計算在步 驟一、二所算得的每一個Q*的總成本

69 範例 9 數量折扣模型 Wohl’s 商店進貨許多玩具賽車。最近，供貨商對這些玩具賽車提出數量折扣方案，表12-2 是折扣計畫的詳細內容。玩具賽車平常的價格是每輛5 美元，如果訂購1,000~1,999 輛的話，價格是4.80 美元；而如果訂購超過2,000 輛，單位售價只需4.75 美元。至於訂單成本是每筆訂單49.00 美元，每年的需求是5,000 輛賽車，存貨的持有成本是單價的 2 成，試問訂購多少輛將才能夠將存貨成本最小化？

70 Quantity Discount Example
2DS IP Calculate Q* for every discount Q1* = = 700 cars/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 cars/order 2(5,000)(49) (.2)(4.80) Q3* = = 718 cars/order 2(5,000)(49) (.2)(4.75) © 2011 Pearson Education

71 Quantity Discount Example
2DS IP Calculate Q* for every discount Q1* = = 700 cars/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 cars/order 2(5,000)(49) (.2)(4.80) 1,000 — adjusted Q3* = = 718 cars/order 2(5,000)(49) (.2)(4.75) 2,000 — adjusted © 2011 Pearson Education

72 Quantity Discount Example
Discount Number Unit Price Order Quantity Annual Product Cost Annual Ordering Cost Annual Holding Cost Total 1 $5.00 700 $25,000 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50 Table 12.3 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit 49 * 5000/1000 = 245 © 2011 Pearson Education

73 獨立需求的存貨模型

74 機率模型與安全存貨 機率模型 再訂購點 = ROP = d × L 一個可應用於產品需求或其他任何變數是未知。
Use safety stock to achieve a desired service level and avoid stockouts 再訂購點 = ROP = d × L d = 每日需求 L = 訂單前置時間

75 機率模型與安全存貨 安全存貨 (ss) 的運算式改寫為： ROP = d × L + ss
年度缺貨成本 = 每一個需求水準的缺貨單位×每一個需求水準 的發生機率×缺貨單位成本×每年度的訂單數量 缺貨（stockout）

76 範例 10 計算當需求為機率分配且前置時間為常數時的安全存量
David Rivera Optical 已經決定其鏡框的再訂購點為50（d×L）單位。它每年每單位的持有成本為5 美元，而每鏡框的缺貨（或銷售流失）成本為40 美元。此商店在再訂購期間內的需求呈現一個機率分配。每年最佳的訂貨次數為6。

77 Safety Stock Example Number of Units Probability 30 .2 40 ROP  50 .3
ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Number of Units Probability 30 .2 40 ROP  50 .3 60 70 .1 1.0 © 2011 Pearson Education

78 Safety Stock Example ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost Stockout Cost Total Cost 20 (20)($5) = $100 $0 $100 10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960 A safety stock of 20 frames gives the lowest total cost ROP = = 70 frames © 2011 Pearson Education

79

80 機率模型與安全存貨 Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = 前置期間內的期望需求 + Z σLT Z = 標準差個數 σLT = 前置期間內的需求標準差

81 Probabilistic Demand Probability of no stockout 95% of the time
Mean demand 350 Risk of a stockout (5% of area of normal curve) ROP = ? kits Quantity Safety stock Number of standard deviations z © 2011 Pearson Education

82 範例 11 需求為一個機率分配的安全存量 Memphis 地區醫院儲存一種緊急急救復甦工具，此工具在再訂購點期間的需求為常態分配。再訂購點期間內的平均需求為350 單位，而標準差為10 單位。醫院管理人想要執行一個新政策，讓缺貨只佔總時間的5％。(a) Z 值應為多少才合適？ (b) 此醫院應該具備多少安全存量？ (c) 再訂購點為何？

83 Probabilistic Example
Average demand = m = 350 kits Standard deviation of demand during lead time = sdLT = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZsdLT = 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock = 350 kits kits of safety stock = or 367 kits © 2011 Pearson Education

84 機率模型與安全存貨 When data on demand during lead time is not available, there are other models available 需求是變動的，但前置時間固定。 前置時間是變動的，但需求固定。 需求與前置時間都是變動的。 需求是變動的，但前置時間固定 ROP = 每日平均需求×前置時間(以天為單位) + ZσdLT σdLT = 前置時間內的需求標準差 = σd = 每日的需求標準差

85 範例12 計算需求變動且前置時間固定時的ROP
在電路城（Circuit Town）商店中，蘋果電腦的iPod 每日平均需求為15 單位、標準差為5 單位，且前置時間固定為2 天。如果管理階層需要90％的服務水準（缺貨風險只佔總時間的10％），試問其安全存貨為何？

86 Probabilistic Example
Average daily demand (normally distributed) = 15 Standard deviation = 5 Lead time is constant at 2 days 90% service level desired Z for 90% = 1.28 From Appendix I ROP = (15 units x 2 days) + ZsdLT = (5)( 2) = = ≈ 39 Safety stock is about 9 iPods © 2011 Pearson Education

87 Other Probabilistic Models
Lead time is variable and demand is constant ROP = (daily demand x average lead time in days) + Z x (daily demand) x sLT where sLT = standard deviation of lead time in days © 2011 Pearson Education

88 範例 13 計算需求固定但前置時間為變動時的ROP
在範例12 中的電路城每日賣出約10 台數位相機（幾乎是固定的數量）。相機送貨的前置時間為常態分配，其平均時間為6 天，且標準差為3 天。如果管理階層需要98％的服務水準，試問其再訂購點為何。

89 Probabilistic Example
Z for 98% = 2.055 From Appendix I Daily demand (constant) = 10 Average lead time = 6 days Standard deviation of lead time = sLT = 3 98% service level desired ROP = (10 units x 6 days) (10 units)(3) = = Reorder point is about 122 cameras © 2011 Pearson Education

90 機率模型與安全存貨 需求與前置時間都是變動的 ROP = (每日平均需求× 平均前置時間)+ ZσdLT σd = 每日的需求標準差

91 範例 14 計算需求變動且前置時間也為變動時的ROP
電路城商店最受歡迎的商品是1 包6 個裝的9 福特電池。每天售出的電池約為150 包，其需求呈常態分配，且標準差為16 包。電池是訂購別州的批發商；前置時間亦呈常態分配，其平均為5 天，標準差為1 天。如果為了維持95％的服務水準，試問適當的再訂購點為何？

92 Probabilistic Example
Average daily demand (normally distributed) = 150 Standard deviation = sd = 16 Average lead time 5 days (normally distributed) Standard deviation = sLT = 1 day 95% service level desired Z for 95% = 1.65 From Appendix I ROP = (150 packs x 5 days) sdLT = (150 x 5) (5 days x 162) + (1502 x 12) = (154) = 1,004 packs © 2011 Pearson Education

93 固定期間（P）系統 定量（Q）系統 永續盤存制 固定期間系統（fixed-period）或稱P 系統 一個每次訂購相同量的EOQ訂購系統。
為了應用定量模型，必須持續地監測存貨量。 固定期間系統（fixed-period）或稱P 系統 在某一個特定期間結束時才下存貨訂單。

94 固定期間（P）系統 固定期間系統有許多與基本EOQ 定量系統同樣的假設： 相關的成本只有訂貨與持有成本。 前置時間為已知且恆定的。
各商品項目彼此是獨立的。

95

96 範例 15 P系統訂貨 硬石餐廳倫敦店的零售店中有三件皮衣外套的逾期訂單，目前存貨中沒有外套，也沒有未送達的訂單，而且到了該訂貨的時間。預計的外套數量為50 件，試問該訂多少件皮衣外套？ 解答： 訂貨數量（Q）= 預期數量（T）− 手邊的存貨數 − 尚未收到的前期訂單 + 逾期訂單 = 50 − 0 − = 53件外套。

97 固定期間（P）系統 P 系統的特性 Inventory is only counted at each review period
May be scheduled at convenient times Appropriate in routine situations 因為在檢視期間內沒有保存紀錄，因此在此期間內可能會有缺貨的情形。 May require increased safety stock