1. Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Manufacturing Planning and Control MPC 6 th Edition Chapter 11

2. 11-2 Order Point Inventory Control Methods Order point methods are used to determine appropriate order quantities and timing for individual independent-demand product items that are characterized by random customer demand. Performed well, these inventory management functions can provide appropriate levels of customer service without excess levels of inventory and/or cost.

3. 11-3 Agenda–Order Point Inventory Control Methods DefinitionBasic ConceptsManagement IssuesInventory CostsEconomic Order Quantity (EOQ)Order TimingMulti-Item ManagementPrinciples

4. 11-4 Basic Concepts Inventory supports both independent- and dependent-demand items Independent-demand inventories–primarily influenced by factors outside of company decisions (e.g. random variation) Demand forecasts estimate the average usage rate and pattern of variation Dependent-demand inventories–influenced mainly by internal factors within the firm’s control

5. 11-5 Transit stock-goods moving from one location to another Cycle stock-inventory created when order quantities exceed immediate requirements Safety stock-inventory that provides protection from uncertainty in demand or supply Anticipation stock- goods held to satisfy peak demand or unusual order patterns (e.g. promotions) Inventory Functions

6. 11-6 Inventory Management Issues Routine inventory decisions–how much to order and when to order Inventory control decision rules can simplify these decisions

7. 11-7 Parameters: Q Order a fixed quantity Q. S : Order up to a fiexed expected opening inventory quantity S R : Place an order when the inventrory drops to R level. T : Place order every (T) period

8. 11-8 Inventory Management Issues Determining Inventory System Performance Inventory turnover (annual sales divided by average inventory investment) Fill rate (percentage of units available when requested by customers) Allows comparison of different systems and evaluation of system changes

9. 11-9 Inventory Management Issues Implementing Changes in Managing Inventory–making the appropriate changes at the right time is critical More formalized change management system is required as the scope of the business increases

10. 11-10 Inventory-Related Costs Inventory Cost Sources Order preparation- costs incurred each time an order is placed (clerical, receiving, shipping, etc.) Inventory carrying costs-cost of holding items in stock (cost of capital, loss, damage, taxes, etc.) Shortage and customer service costs-costs incurred when demand exceeds supply (expediting, customer dissatisfaction, lost sales) Incremental costs–does the cost represent an actual expenditure or lost profit? Does the cost actually vary with the decision being made?

11. 11-11 Economic Order Quantity (EOQ) Model Describes the relationship between cost of ordering, cost of carrying inventory, and the order quantity Total Costs Ordering Costs Inventory Holding Costs

12. 11-12 Determining the EOQ– Graphical Method A = 1,250 C p = 6.25 C H = 25 TAC=(1,250/Q)6.25+(Q/2)25 TAC curve shows clear minimum value at Q=25

13. 11-13 Determining the EOQ– Deriving the EOQ Formula Derivative of TAC with respect to Q Set derivative equal to zero and solve for Q Economic time between orders (TBO)

14. 11-14 TV Retailer example: _________ EOQ = √2*C p *A/C H If A = 1250 units/year C p = 6.25 $/order (or setting up) C H = 25 $/unit/year ______________ EOQ = √2*6.25*1250/25 = 25 When we buy tv’s we should buy them in lots of 25.

15. 11-15 Number of Orders NO = Demand/EOQ = 1250/25 = 50 orders/year (once a week) Time between orders TBO (weeks) TBO = EOQ/Acerage weekly demand Decision Rule: Q,T. Buy 25 every weak Total Annual Cost TAC = (A/Q)* C p + (Q/2)*C H =1250/25*6.25+25/2*25=625

16. 11-16 Example A major equipment producer sells 4000 units of its $90/unit product per year. Ordering costs are $30 and holding costs are 8% of the product unit value per year. Each items requires 5 square meters for storage (product cannot be piled on top of each other) and there is currently space in the warehouse. The space available is of size 20 by 40 meters to store the items. a) What lot size should he use? b) What is the total annual cost? c) Does he need additional space? How much, if any?

17. 11-17 Example (Cont.) ________________ a) Q * = √2*4000*30/(.08*90) = 182.6 b) TSC = 4000/182.6*30 + 182.6/2*(.08*90) = 652.6 + 652.6 c) Area = 182.6*5 = 912.9 Area = 20*40 = 800 Additional area needed = 112.9 m2

18. 11-18 Example For a manufacturing operation, parts are needed at a rate of 180 parts per day. Set up costs is $150 and the carrying cost is $0.25 per unit per year. The firm operates 250 days per year. a) What is the economic lot size? b) What is the total stocking cost?

19. 11-19 Example (cont.) __________________ a) Q * = √2*150/0.25 = 7348.5 b) TAC = 7348.5/2*.25 + 250*180/7348.5*150 = 918.6 + 918.6 = 1837.1

20. 11-20 Order Timing Decisions Q,R rule When stock reaches predetermined inventory level (R), a fixed quantity (Q) is ordered Order point is influenced by demand rate, replenishment lead time, uncertainty of demand rate and replenishment lead time, and acceptable level of customer service Safety stock is the difference between average demand during lead time and the reorder point

21. 11-21 Safety Stock in a Q,R system S R Inventory level Time Lead time Order quantity (Q) Reorder point Safety stock

22. 11-22 Determining the Safety Stock in a Q,R system Stockout probability–specify an acceptable risk of stocking out during any given replenishment cycle Carry stock sufficient to satisfy expected demand with this probability Customer service level–define an acceptable level of customer service (percent of demand met from inventory)

23. 11-23 Stockout Probability With a lead time of one day, 95% of cycles will experience demand for 7 or fewer units Sum of demand probability is 0.05 (5%) Safety stock of 7 units will provide 5% chance of stockout during a one day lead time

24. 11-24 Customer Service Level Sum = 0.35 A reorder point of 5 units has a 35% chance of stockout, with an average of 0.56 units short each cycle

25. 11-25 Discrete Distribution ex: Problem : Demand during lead time discrete distribution: Probability0.050.150.20.30.10.150.05 Deman 20 21 22 23 24 25 26 What is the probability of demand to be less than 22? What is the probability of demand to exceed 22? What is the expected demand during lead time?.2 = % 20.3 +.1 +.15 +.05 =.6 =% 60 (.05)20 + (.15)21 + (.2)22 + (.3)23 + (.1)24 + (.15)25 + (.05)26 = 22.9 units

26. 11-26 Olasılık0.050.150.20.30.10.150.05 Talep 20 21 22 23 24 25 26 If we take our reorder point as 22, what is our expected units short (the demand that cant be filled)? If demand is 20, 21, or 22, we don’t have any units short We have shortage, only if demand is 23, 24 or 25 Expected units short= (.3)23 +.1(24) +.15(25) +.05(26) = 1.15 If the order quantity is 23, what would be our customer service level ? 1 – 1.15/23 =.95 = 95 %

27. 11-27 Safety Stock with Continuous Distributions Reorder pointProbability of at least one stockout during cycle Expected number of stockouts per cycle

28. 11-28 Probability of Stocking Out R = d avg + S (average deman during lead time d avg + Safety Stock S) S = Z σ d R = d avg + Zσ d Z, standart deviation multiple corresponding to relevant stockout probablility according to normal distribution (Example% 5 Stockout = 95% SL  Z=1,645). σ d... Standard deviation in demand, during lead time

29. 11-29 Probability of Stocking Out Safety stock = Zσ d Reorder point = mean demand during replenishment lead time + Zσ d Z = appropriate value from standard normal table σ d = standard deviation of demand during replenishment lead time Probability of demand between 3.5 and 6.5 units is 0.6827. Probability of stockout when safety stock is 1 unit is 0.3173 (1 – 0.6827)

30. 11-30 Example Q = 5; σ d = 1.5; Stockout Probability = % 5 -> SL = 95% R = d + Z σ d = 5 + 1.645*1.5 = 5 + 2.5 = 7.5 Result: Reorder Point =8 ; Order Quantity Q=5 Safety Stock= 3

31. 11-31 Customer Service Criterion Find the calculated E(Z) in the chart to determine the Z value Calculate E(Z) using the desired service level (SL) and reorder quantity (Q) Safety stock = Zσ d

32. 11-32 Customer Service Criterion Annual stockout quantity= Stockout probability* annual demand (1 – SL) * D This value is equal to stockout quantity per order (σ d E(Z)) * number of orders per year (1 – SL) * D = σ d E(Z) [D/Q] (1-SL) = σ d E(Z)/Q E(Z) = Q(1- SL)/σ d

33. 11-33 Example Q = 5; σ d = 1.5SL = 95% E(Z) = Q(1 -.05)/σ d = 5*.05/1.5 =.167 From the normal distribution table  Z = 0.6 R = d + Zσ d = 5 + 0.6*1.5 = 5 + 0.9 = 5.9 Order Q=5, once inventory drops to 5.9 (6)

34. 11-34 Example: D = Annual demand 1000 LT=15 days Q = 200 Service Level = 95 % (.95) Annual number of days= 250 σ d =50 units Average daily demand=1000/250 = 4 /day R = d + Z σ d = 4*15 + Z(50) E(Z)=(1-.95)200/50 = 0.2 from tables Z = 0.49 R = 4(15) + 0.49*50 = 84.5

35. 11-35 Example (Cont.) Policy: When inventory level gets to 85 or less then order 200. What is the expected number of units short per order? E(Z) σ d = 0.2 * 50 = 10 How many orders per year? (1000/200)= 5 Total number of units short? 10*5 = 50 (Service level is 95%; 950/1000)

36. 11-36 Time Period Correction Factor Variations in demand and lead time complicate the calculations When standard deviation of demand is measured over a different time period than the lead time, correction is required When both demand and lead time vary, additional adjustments are required

37. 11-37 Forecast Error Distribution Safety stock can be based on forecast error rather than historical demand variation Standard deviation = 1.25 MAD MAD – mean absolution deviation

38. 11-38 Multi-Item Management Management attention should be focused on the most important items ABC analysis segments the inventoried items according to annual cost volume usage (unit cost x annual usage) A items are the most important This small percentage of items usually makes up a majority of annual cost volume usage B and C items are progressively less critical

39. 11-39 3 classes A class, B class, C class Basic classification parameter is annual cost $ volume = Annual demand x Unit cost Result of ABC analysis A class material is important Accurate Ccunting of A class material is more important Forecasts regarding class A materials are of more signaficance ABC Analysis

40. 11-40 ABC Analizi Dollar Usage Category # of items % of items % of $ use A151184% B251515 C8874 1 Total128100100

41. 11-41 ABC Analysis - Criticality Criticality Category # of items % of items % of $ use I 5 440% II 483956 III7557 4 Total128100100

42. 11-42 ABC Analysis – Two sided view Criticality Dollar Usage I II III Total A2 12 1 15 B1 19 5 25 C2 17 69 88 Total5 48 75 128

43. 11-43 ABC Analysis – Combined Combined #% Category of items of items of $ use AA 141178% BB 161312 CC 987610 Total 128100 100

44. 11-44 Inventory management policies according to multi-criteria ABC analysis AABBCC Counting Frequency monthlyEvery six months yearly Order quantityLow quatity EOQLarge quantity Safety stockHigh for critical items Low or none ReclassificationEvery 6 months yearly

45. 11-45 Principles The difference between dependent and independent demand must serve as the first basis for determining appropriate inventory management procedures. Organizational criteria must be clearly established before we set safety stock levels and measure performance. A sound basic independent demand system must be in place before attempting to implement advanced techniques.

46. 11-46 Savings in inventory-related costs can be achieved by a joint determination of the order point and order quantity parameters. All criteria should be taken into account in classifying inventory items for management priorities. The functions of inventory are useful principles to apply in determining whether or not inventory reductions can be made. Principles

47. 11-47 Quiz – Chapter 11 Order point methods are generally used for _____________ demand items. Cycle stock is are a result of manufacturing lot sizes? (True/False) Stock produced for upcoming promotional events would be considered _______________ stock. The two main decisions when managing independent demand items are _______________ and ______________. A measurement that relates inventory levels to product sales volume is ___________ _____________. The three types of costs associated with holding inventory are ____________, ______________, and ____________.