1. Copyright 2009 John Wiley & Sons, Inc.12-1 Chapter 13: Inventory Management Lecture Outline   Elements of Inventory Management   Inventory Control Systems   Economic Order Quantity Models   Quantity Discounts   Reorder Point   Order Quantity for a Periodic Inventory System

2. Copyright 2009 John Wiley & Sons, Inc.12-2 What Is Inventory?   Stock of items kept to meet future demand   Purpose of inventory management how many units to order, Q when to order, T

3. Copyright 2009 John Wiley & Sons, Inc.12-3 Types of Inventory   Raw materials   Purchased parts and supplies   Work-in-process (partially completed) products (WIP)   Items being transported   Tools and equipment

4. Copyright 2009 John Wiley & Sons, Inc.12-4 Two Forms of Demand  Dependent  Demand for items used to produce final products   Tires stored at a Goodyear plant are an example of a dependent demand item  Independent  Demand for items used by external customers   Cars, appliances, computers, and houses are examples of independent demand inventory

5. Copyright 2009 John Wiley & Sons, Inc.12-5 Inventory Control Systems  Continuous system (fixed- order-quantity)  constant amount ordered when inventory declines to predetermined level  Periodic system (fixed-time- period)  order placed for variable amount after fixed passage of time

6. Copyright 2009 John Wiley & Sons, Inc.12-6 ABC Classification  Class A 5 – 15 % of units 5 – 15 % of units 70 – 80 % of value 70 – 80 % of value  Class B 30 % of units 30 % of units 15 % of value 15 % of value  Class C 50 – 60 % of units 50 – 60 % of units 5 – 10 % of value 5 – 10 % of value

7. Copyright 2009 John Wiley & Sons, Inc.12-7 ABC Classification: Example 1$ 6090 235040 330130 48060 530100 620180 710170 832050 951060 1020120 PARTUNIT COSTANNUAL USAGE

8. Copyright 2009 John Wiley & Sons, Inc.12-8 ABC Classification: Example (cont.) Example 10.1 1$ 6090 235040 330130 48060 530100 620180 710170 832050 951060 1020120 PARTUNIT COSTANNUAL USAGE TOTAL% OF TOTAL% OF TOTAL PARTVALUEVALUEQUANTITY% CUMMULATIVE 9$30,60035.96.06.0 816,00018.75.011.0 214,00016.44.015.0 15,4006.39.024.0 44,8005.66.030.0 33,9004.610.040.0 63,6004.218.058.0 53,0003.513.071.0 102,4002.812.083.0 71,7002.017.0100.0 $85,400 AB C

9. Copyright 2009 John Wiley & Sons, Inc.12-9 Economic Order Quantity (EOQ) Models   EOQ optimal order quantity that will minimize total inventory costs   Basic EOQ model   Production quantity model

10. Copyright 2009 John Wiley & Sons, Inc.12-10 Assumptions of Basic EOQ Model  Demand is known with certainty and is constant over time  No shortages are allowed  Lead time for the receipt of orders is constant  Order quantity is received all at once

11. Copyright 2009 John Wiley & Sons, Inc.12-11 Inventory Order Cycle Demand rate Time Lead time Order placed Order receipt Inventory Level Reorder point, R Order quantity, Q 0

12. Copyright 2009 John Wiley & Sons, Inc.12-12 Inventory Costs  Carrying cost  cost of holding an item in inventory  Ordering cost  cost of replenishing inventory  Shortage cost  temporary or permanent loss of sales when demand cannot be met

13. Copyright 2009 John Wiley & Sons, Inc.12-13 EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

14. Copyright 2009 John Wiley & Sons, Inc.12-14 EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

15. Copyright 2009 John Wiley & Sons, Inc.12-15 EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Total Cost Carrying Cost = CcQCcQ22CcQCcQ222 Slope = 0 Minimum total cost Optimal order Q opt Q opt Ordering Cost = CoDCoDQQCoDCoDQQQ

16. Copyright 2009 John Wiley & Sons, Inc.12-16 EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Orders per year = Order cycle time =

17. Copyright 2009 John Wiley & Sons, Inc.12-17 Production Quantity Model   An inventory system in which an order is received gradually, as inventory is simultaneously being depleted   AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed   p - daily rate at which an order is received over time, a.k.a. production rate   d - daily rate at which inventory is demanded

18. Copyright 2009 John Wiley & Sons, Inc.12-18 Production Quantity Model (cont.) Q(1-d/p) Inventorylevel (1-d/p) Q2 Time 0 Order receipt period BeginorderreceiptEndorderreceipt Maximum inventory level Average

19. Copyright 2009 John Wiley & Sons, Inc.12-19 Production Quantity Model (cont.) p = production rated = demand rate Maximum inventory level =Q - d =Q 1 - Qp dp Average inventory level = 1 - Q2 dp TC = + 1 - dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Q opt = 2C o D C c 1 - dp

20. Copyright 2009 John Wiley & Sons, Inc.12-20 Production Quantity Model: Example C c = $0.75 per yardC o = $150D = 10,000 yards d = 10,000/311 = 32.2 yards per dayp = 150 yards per day Q opt = = 2C o D C c 1 - dp TC = + 1 - = dp CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 Production run = = Qp

21. Copyright 2009 John Wiley & Sons, Inc.12-21 Production Quantity Model: Example (cont.) Number of production runs = = = DQDQ Maximum inventory level =Q 1 - = = dpdp

22. Copyright 2009 John Wiley & Sons, Inc.12-22 Quantity Discounts Price per unit decreases as order quantity increases TC = + + PD CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 where P = per unit price of the item D = annual demand

23. Copyright 2009 John Wiley & Sons, Inc.12-23 Quantity Discount Model (cont.) Q opt Carrying cost Ordering cost Inventory cost ($) Q( d 1 ) = 100 Q( d 2 ) = 200 TC ( d 2 = $6 ) TC ( d 1 = $8 ) TC = ($10 ) ORDER SIZE PRICE 0 - 99 $10 100 – 199 8 ( d 1 ) 200+ 6 ( d 2 )

24. Copyright 2009 John Wiley & Sons, Inc.12-24 Quantity Discount Model Rule  Begin with lowest price, calculate the EOQ for each price level until a feasible EOQ is found. It is feasible if it lies in the range corresponding to its price.  If the first feasible EOQ found is for the lowest price level, it is the best quantity. Otherwise, calculate the total cost for the first feasible EOQ and for the larger price break quantity at each lower price level. The optimal quantity is one with the lowest total cost.

25. Copyright 2009 John Wiley & Sons, Inc.12-25 Quantity Discount: Example QUANTITYPRICE 1 - 49$1,400 50 - 891,100 90+900 C o =$2,500 C c =$190 per computer D =200 Q opt = = = 72.5 PCs 2CoD2CoDCcCc2CoD2CoDCcCc2(2500)(200)190 TC = + + PD = C o D Q opt C c Q opt 2 For Q = 72.5 TC = + + PD = CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 For Q = 90

26. Copyright 2009 John Wiley & Sons, Inc.12-26 Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

27. Copyright 2009 John Wiley & Sons, Inc.12-27 Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL =

28. Copyright 2009 John Wiley & Sons, Inc.12-28 Safety Stocks  Safety stock  buffer added to on hand inventory during lead time  Stockout  an inventory shortage  Service level  probability that the inventory available during lead time will meet demand

29. Copyright 2009 John Wiley & Sons, Inc.12-29 Variable Demand with a Reorder Point Reorder point, R Q LT Time LT Inventory level 0

30. Copyright 2009 John Wiley & Sons, Inc.12-30 Reorder Point with a Safety Stock Reorder point, R Q LT Time LT Inventory level 0 Safety Stock

31. Copyright 2009 John Wiley & Sons, Inc.12-31 Reorder Point With Variable Demand R = dL + z  d L where d=average daily demand L=lead time  d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z  d L=safety stock

32. Copyright 2009 John Wiley & Sons, Inc.12-32 Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

33. Copyright 2009 John Wiley & Sons, Inc.12-33 Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d= 30 yards per day L= 10 days  d = 5 yards per day For a 95% service level, z = 1.65 R= dL + z  d L Safety stock= z  d L