1 / 54

Inventory Management: Safety Inventory ( I )

Inventory Management: Safety Inventory ( I ). 第六單元： Inventory Management: Safety Inventory ( I ). 郭瑞祥教授. 【 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 】. 1. Safety Inventory.

lenore
Download Presentation

Inventory Management: Safety Inventory ( I )

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inventory Management: Safety Inventory ( I ) 第六單元：Inventory Management: Safety Inventory ( I ) 郭瑞祥教授 【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】 1

  2. Safety Inventory • Safety Inventory is inventory carried for the purpose of satisfying demand that exceeds the amount forecasted for a given period. • Purposes of holding safety inventory • Demand uncertainty • Supply uncertainty Inventory Cycle Inventory Average Inventory Safety Inventory Time 2

  3. Planning Safety Inventory • Appropriate level of safety inventory is determined by • Uncertainty of both demand and supply – Uncertainty increases, then safety inventory increases. • Desired level of product availability Desired level of product availability • – increases, then safety inventory increases. • Actions to improve product availability while reducing safety inventory 3

  4. k W= k k åsi2 +2 åCov(i,j) å P= Di = åsi2 +2årsisj i=1 i>j i=1 i=1 i>j W = s k D s k +2årsisj D i>j Measuring Demand Uncertainty • Uncertainty within lead time • Assume that demand for each period i, i=1,….,k is normally distributed with a mean Di and standard deviationsi . • The total demand during k period is normally distributed with a mean of P and a standard deviation of W : • If demand in each period is independent and normally distributed with a mean of D and a standard deviation of sD , then k åsi2 P=KD i=1 • Coefficient of variation CV= s/m 4

  5. Measuring Product Availability • Product fill rate ( fr ) • The fraction of product demand that is satisfied from product in inventory • It is equivalent to the probability that product demand is supplied from available inventory CoolCLIPS網站 • Order fill rate • The fraction of orders that are filled from available inventory • Order fill rates tend to be lower than product fill rates because all products must be in stock for an order to be filled • Cycle service level (CSL) • The fraction of replenishment cycles that end with all the customer demand being met • The CSL is equal to the probability of not having a stockout in a replenishment cycle • A CSL of 60 percent will typically result in a fill rate higher than 60% 5

  6. Cycle Measuring Product Availability -- Page 5 • Product fill rate ( fr ) • Order fill rate • Cycle service level (CSL) • An order for a total of 100 palms and has 90 in inventory → fill rate of 90% • Customer may order a palm along with a calculator. The order is filled only if both products are available. Order received • Don't run out of inventory in 6 out of 10 replenishment cycles → CSL = 60% On-hand inventory • In the 40% of the cycles where a stockout • does occur, most of the customer demand • is satisfied from inventory Filled demand Unfilled demand 0 → fill rate > 60% 6 Microsoft。 Microsoft。

  7. Q P Replenishment Policies • A replenishment policy consists of decisions regarding • When to reorder • How much to reorder. • Continuous review • Inventory is continuously tracked and an order for a lot size Q is placed when the inventory declines to the reorder point (ROP). • Periodic review • Inventory status is checked at regular periodic intervals and an order is placed to raise the inventory level to a specified threshold, i.e. order up to level (OUL) . 7

  8. Q P Replenishment Policies • A replenishment policy consists of decisions regarding • When to reorder • How much to reorder. • Continuous review • Inventory is continuously tracked and an order for a lot size Q is placed when the inventory declines to the reorder point (ROP). • Periodic review • Inventory status is checked at regular periodic intervals and an order is placed to raise the inventory level to a specified threshold. 8

  9. Continuous Review System • The remaining quantity of an item is reviewed each time a withdrawal is • made from inventory, to determine whether it is time to reorder. • Other names are: Reorder point system, fixed order quantity system • Inventory position IP = OH+SR-BO • IP = inventory position • OH = on-hand inventory • SR = scheduled receipts (open orders) • BO = units backordered or allocated • Decision rule • Whenever a withdrawal brings IP down to the reorder point (ROP), place • an order for Q (fixed) units. 9

  10. Continuous ReviewSystem ROP = average demand during lead time + safety stock IP IP Order received On-hand inventory Order received Q OH OH ROP ROP Order placed Order placed Time L3 L1 L2 TBO2 TBO3 TBO1 10

  11. FIX Continuous ReviewSystem ROP = average demand during lead time + safety stock IP IP Order received On-hand inventory Order received Q OH OH ROP Order placed Order placed Time L3 L1 L2 TBO2 TBO3 TBO1 11

  12. Continuous ReviewSystem ROP = average demand during lead time + safety stock IP IP Order received On-hand inventory Order received Q OH OH ROP Order placed Order placed Time L3 L1 L2 TBO2 TBO3 TBO1 12

  13. Example Given the following data • Average demand per week, D = 2,500 • Standard deviation of weekly demand, sD =500 • Average lead time for replacement, L = 2 weeks • Reorder point, ROP = 6,000 • Average lot size, Q = 10,000 • Safety inventory,ss • Cycle inventory • Average inventory • Average flow time =ROP-DL=6,000-5,000=1,000 =Q/2=10,000/2=5,000 =5,000+1,000=6,000 = Average inventory / Throughput=6,000/2,500 =2.4weeks 13

  14. ss=z LsD CSL Evaluating Cycle Service Level and Safety Inventory CSL= Prob (Demand during lead time of L weeks £ ROP) Demand during lead time is normally distributed with a mean of DL and a standard deviation of sL • CSL=Function ( ROP,DL,sL ) ROP=DL+Z LsD z=Fs-1(CSL) 14

  15. CSL = 85% Probability of stockout (1.0 - 0.85= 0.15) Finding Safety Stock with a Normal Probability Distribution for an 85 Percent CSL ? 1 Average demand during lead time 4:->ROP ROP 3 2 zsL Safety stock = zsL 15

  16. ss=z LsD Evaluating Cycle Service Level and Safety Inventory CSL= Prob (Demand during lead time of L weeks £ ROP) Demand during lead time is normally distributed with a mean of DL and a standard deviation of sL • CSL=Function ( ROP,DL,sL ) ROP=DL+Z LsD z=Fs-1(CSL) 16

  17. sL= L sD = 2 x500=707 Example Given the following data • Q = 10,000 • ROP = 6,000 • L = 2 weeks • D=2,500/week, σD=500 • DL=DL= 2x2,500=5,000 • CSL=Proability of not stocking out in a cycle =F(ROP, DL, sL )=F(6000,5000,707) =NORMDIST(6000,5000,707,1)=0.92 17

  18. Normal Distribution in Excel Commands (Page 12) 18

  19. Normal Distribution in Excel (Demo) 19 臺灣大學 郭瑞祥老師 臺灣大學 郭瑞祥老師

  20. sL= L sD = 2 x500=707 Example Given the following data • Q = 10,000 • ROP = 6,000 • L = 2 weeks • D=2,500/week, sD=500 • CSL=0.9 • DL=DL= 2x2,500=5,000 • ss=Fs-1(CSL) =F(ROP, DL, sL )=F(6000,5000,707) =NORMDIST(6000,5000,707,1)=0.92 20

  21. sL= L sD = 2 x500=707 Example Given the following data • D=2,500/week • sD=500 • L = 2 weeks • Q = 10,000, • CSL=0.9 • DL=DL= 2x2,500=5,000 • ss=Fs-1(CSL)xsL=NORMDIST(CSL)xsL =1.282x707=906 • ROP= 2x2,500+906=5,906 21

  22. sL= L sD = 2 x500=707 Example Given the following data • D=2,500/week • sD=500 • L = 2 weeks • Q = 10,000, • CSL=0.9 • DL=DL= 2x2,500=5,000 • ss=Fs-1(CSL)xsL=NORMDIST(CSL)xsL =1.282x707=906 • ROP= 2x2,500+906=5,906 22 臺灣大學 郭瑞祥老師 臺灣大學 郭瑞祥老師

  23. Periodic Review System • Other names are: fixed interval reorder system or periodic reorder system. • Decision Rule Review the item’s inventory position IP every T time periods. Place an order equal to (OUL-IP) where OUL is the target inventory, that is, the desired IP just after placing a new order. • The periodic review system has two parameters: T and OUL. • Here Q varies, and time between orders (TBO) is fixed. 23

  24. IP1 IP3 IP2 Periodic Review System OUL OUL IP IP Order received On-hand inventory Order placed Q1 Order placed Q3 Q2 OH OH Order placed L L L Time T T Protection interval 24

  25. Finding OUL • The new order must be large enough to make the inventory position, IP, last not only beyond the next review, which is T periods from now, but also for one lead time (L) after the next review. IP must be enough to cover demand over a protection interval of T + L. • OUL = Average demand during protection interval Safety stock for protection interval + 25

  26. Selecting the Reorder Interval (T ) • Administratively convenient (such as each Friday) • Approximation of EOQ • Example: Suppose D = 1200 /year and EOQ = 100 26

  27. DT+L= T+L sD= (4+2) x500=1,225 Example Given the following data • D=2,500/week • sD=500 • L = 2 weeks • T= 4weeks • CSL=0.9 • DT+L=(T+L)D= (4+2)x2,500=15,000 • ss=Fs-1(CSL)xsT+L=Fs-1(0.9)xsT+L =1,570 • OUL=DT+L+ss = 1,5000+1,570=16,570 27

  28. Periodic System versus Continuous System 28

  29. ¥ = (X-ROP) f(x)dx ESC ò X=ROP Q-ESC Q Evaluating Fill Rate Given a Replenishment Policy • For a continuous review policy Expected shortage per replenishment cycle (ESC) is the average units of demand that are not satisfied from inventory in stock per cycle f (x) is density function of demand distribution during the lead time ESC fr=1- = Q • In the case of normal distribution, we have 29

  30. ¥ = (X-ROP) f(x)dx ESC ò X=ROP Q-ESC Q Evaluating Fill Rate Given a Replenishment Policy • For a continuous review policy Expected shortage per replenishment cycle (ESC) is the average units of demand that are not satisfied from inventory in stock per cycle f (x) is the density function of demand distribution during the lead time ESC fr=1- = Q • In the case of normal distribution, we have 30

  31. ¥ = (X-ROP) f(x)dx ESC ò X=ROP Q-ESC Q Evaluating Fill Rate Given a Replenishment Policy • For a continuous review policy Expected shortage per replenishment cycle (ESC) is the average units of demand that are not satisfied from inventory in stock per cycle f (x) is density function of demand distribution during the lead time ESC fr=1- = Q • In the case of normal distribution, we have 31

  32. ¥ = (X-ROP) f(x)dx ESC ò X=ROP Q-ESC Q Evaluating Fill Rate Given a Replenishment Policy • For a continuous review policy Expected shortage per replenishment cycle (ESC) is the average units of demand that are not satisfied from inventory in stock per cycle f (x) is density function of demand distribution during the lead time ESC fr=1- = Q • In the case of normal distribution, we have 32

  33. Proof WIKIPEDIA WIKIPEDIA 33

  34. Proof sLdz Substituting Z=(X-DL)/sL and dx=sLdz , we have 34

  35. Substituting Z=(X-DL)/sL and dx=sLdz , we have Proof 35

  36. Proof 36

  37. Proof 37

  38. Proof dw=2zdz/2 dw=zdz 38

  39. 0 Proof ESC derivation 39

  40. Proof 40

  41. ¥ = (X-ROP) f(x)dx ESC ò X=ROP Q-ESC Q Evaluating Fill Rate Given a Replenishment Policy • For a continuous review policy Expected shortage per replenishment cycle (ESC) is the average units of demand that are not satisfied from inventory in stock per cycle f (x) is density function of demand distribution during the lead time ESC fr=1- = Q • In the case of normal distribution, we have 41

  42. 10,000-25 fr= =0.9975 10,000 Example For a continuous review system with the following data • Lot size ,Q=10,000 • DL=5,000 • sL = 707 • ss=ROP-DL=6,000-5,000=1,000 • ESC= -1,000[1-NORMDIST(1000/707,0,1,1)] +707xNORMDIST(1000/707,0,1,1) =25 42

  43. For a continuous review system with the following data • Lot size ,Q=10,000 • DL=5,000 • sL = 707 • ss=ROP-DL=6,000-5,000=1,000 • ESC= -1,000[1-NORMDIST(1000/707,0,1,1)] +707xNORMDIST(1000/707,0,1,1) =25 10,000-25 fr= =0.9975 10,000 Excel-Demo 43 臺灣大學 郭瑞祥老師

  44. Factors Affecting Fill Rate • Safety inventory Fill rate increases if safety inventory is increased. This also increases the cycle service level. • Lot size Fill rate increases with the increase of the lot size even though cycle service level does not change. 44

  45. Factors Affecting Fill Rate -- Page 42 • Safety inventory Fill rate increases if safety inventory is increased. This also increases the cycle service level. fr = 1- ESC/Q • Lot size Fill rate increases on increasing the lot size even though cycle service level does not change. fr = 1- ESC/Q CSL = F(ROP, DL, sL) is independent of Q 45

  46. Evaluating Safety Inventory Given Desired Fill Rate • If desired fill rate is fr = 0.975, how much safety inventory should be held? • ESC = (1 - fr)Q = 250 • Solve 46

  47. Excel-Demo 47 臺灣大學 郭瑞祥老師 臺灣大學 郭瑞祥老師

  48. Evaluating Safety Inventory Given Desired Fill Rate • If desired fill rate is fr = 0.975, how much safety inventory should be held? • ESC = (1 - fr)Q = 250 • Solve 48

  49. Evaluating Safety Inventory Given Fill Rate The required safety inventory grows rapidly with an increase in the desired product availability (fill rate). 49

  50. Two Managerial Levers to Reduce Safety Inventory Safety inventory increases with an increase in the lead time and the standard deviation of periodic demand. • Reduce the supplier lead time (L) • If lead time decreases by a factor of k, safety inventory in the retailer decreases by a factor of . • It is important for the retailer to share some of the resulting benefits to the supplier. • Reduce the underlying uncertainty of demand (sD ) • If sD is reduced by a factor of k, safety inventory decreases by a factor of k. • The reduction in sD can be achieved by reducing forecast uncertainty, such as by sharing demand information through the supply chain. 50

More Related