1. Copyright 2011 John Wiley & Sons, Inc. Chapter 9 Inventory Management 9-1

2. Lecture Outline 9-2 Basics of Inventory Management Inventory Systems Fixed-Order Quantity System Fixed-Time Period Systems Independent vs. Dependent Demand Managing Supply Chain Inventory Copyright 2011 John Wiley & Sons, Inc.

3. What is Inventory? 9-3 Copyright 2011 John Wiley & Sons, Inc. Inventory is quantities of goods in stock Manufacturing Inventory –raw materials –component parts –work-in-process (WIP) –finished goods Service Inventory –involves all activities carried out in advance of the customer’s arrival

4. Inventory Policy Inventory policy addresses two questions concerning replenishment of inventory: When to order? How much to Order? 9-4 Copyright 2011 John Wiley & Sons, Inc.

5. Reasons for Carrying Inventory Protect Against Lead Time Demand Maintain Independence of Operations Balance Supply and Demand Buffer Uncertainty Economic Purchase Orders 9-5 Copyright 2011 John Wiley & Sons, Inc.

6. Types of Inventory Cycle Stock –inventory for immediate use –typically produced in batches (production cycle) Safety Stock –extra inventory carried for uncertainties in supply and demand –also called buffer stock Anticipation Inventory –inventory carried in anticipation of events –smooth out the flow of products in supply chain –also called seasonal or hedge inventory 9-6 Copyright 2011 John Wiley & Sons, Inc.

7. Types of Inventory Continued Pipeline Inventory –inventory in transit –exists because points of supply and demand are not the same –also called transportation inventory Maintenance, Repair and Operating Items (MRO) –inventories not directly related to product creation 9-7 Copyright 2011 John Wiley & Sons, Inc.

8. Inventory Costs Holding Cost –costs that vary with the amount of inventory held –typically described as a % of inventory value –also called carrying cost Ordering Cost –costs involved in placing an order –sometimes called setup cost –inversely related to holding cost Shortage Cost –occur when we run out of stock 9-8 Copyright 2011 John Wiley & Sons, Inc.

9. Inventory Systems Inventory systems answer the questions: when to order and how much to order There are two categories: Fixed-Order Quantity System –an order of fixed quantity, Q, is placed when inventory drops to a reorder point, ROP Fixed-Time Period System –inventory is checked in fixed time periods, T, and the quantity ordered varies 9-9 Copyright 2011 John Wiley & Sons, Inc.

10. Fixed-Order Quantity System –assumes a constant demand rate of d –the inventory position, IP, is reduced by a rate of d –order placed when the reorder point, ROP is reached –when inventory is received, the IP is increased by the order quantity, Q 9-10 Copyright 2011 John Wiley & Sons, Inc.

11. Fixed-Order Quantity System Continued –there is a lead time, L, during which we have to wait for the order –inventory is checked on a continual basis –Q is computed as the economic order quantity, EOQ 9-11 Copyright 2011 John Wiley & Sons, Inc.

12. Fixed-Order Quantity System 9-12 Copyright 2011 John Wiley & Sons, Inc.

13. Fixed-Time Period System –inventory levels checked in fixed time periods, T –a target inventory level, R, is restored when order received –sometimes called Periodic Review System –quantity ordered varies: Q = R – IP where: Q = order quantity R = target inventory level IP = inventory position 9-13 Copyright 2011 John Wiley & Sons, Inc.

14. Fixed-Time Period System 9-14 Copyright 2011 John Wiley & Sons, Inc.

15. Compare Inventory Systems 9-15 Copyright 2011 John Wiley & Sons, Inc.

16. Fixed-Order Quantity System There are two main variables to calculate in the Fixed-Order Quantity System: Order Quantity (Q) –EOQ is the most Economic Order Quantity Reorder Point (ROP) Assume: –demand (d), lead time (L), holding cost (H), stock-out cost (S), and unit price (C) are constant 9-16 Copyright 2011 John Wiley & Sons, Inc.

17. Economic Order Quantity (EOQ) The EOQ minimizes the total annual inventory cost Total Cost = Purchase + Ordering + Holding TC = DC + (D/Q)S + (Q/2)H where: TC = Total costD = Annual demand C = Unit costQ = Order quantity S = Ordering costH = Holding cost 9-17 Copyright 2011 John Wiley & Sons, Inc. costcostcost

18. EOQ Continued TC = DC + (D/Q)S + (Q/2)H Notice: DC = Annual purchase cost D/Q = # orders placed per year  Annual ordering cost = # orders/yr x cost/order Q/2 = average inventory level  Annual holding cost = avg. inventory x cost/unit 9-18 Copyright 2011 John Wiley & Sons, Inc.

19. EOQ Continued 9-19 Copyright 2011 John Wiley & Sons, Inc.

20. Solving for EOQ The EOQ can be found by taking the derivative of TC with respect to Q and set = 0 Total Cost Equation: TC = DC + (D/Q)S + (Q/2)H 1 st Derivative: Solve for Q optimal: 9-20 Copyright 2011 John Wiley & Sons, Inc.

21. EOQ Example Given: Demand = 1000 items per month Holding Cost = 15% of product cost Ordering Cost = $300 per order Product Cost = $60 per unit EOQ Orders per year Annual Holding Cost 9-21 Copyright 2011 John Wiley & Sons, Inc.

22. Reorder Point (ROP) The ROP provides enough inventory to ensure that demand is covered during the lead time (L) ROP = Demand during Lead Time = dL Given: Lead time = 1 week d = 250 items/week ROP = dL = (1) x (250) = 250 items  order is placed when inventory level = 250 items 9-22 Copyright 2011 John Wiley & Sons, Inc.

23. Safety Stock Safety stock is inventory carried in addition to the demand during lead time It is common to carry safety stock when demand (d) or lead time (L) are not constant ROP = demand during lead time + safety stock ROP = dL + Z k σ L –value of Z for a particular service level (k) –service level = probability of being in stock – σ L = standard deviation of demand over the lead time 9-23 Copyright 2011 John Wiley & Sons, Inc.

24. Safety Stock Example Given: Desired service level = 95% Demand = 1000 items per month Lead time = 1 week σ L 2 = 64 Determine the Reorder Point ROP = dL + Z k σ L ROP = 9-24 Copyright 2011 John Wiley & Sons, Inc.

25. Economic Production Quantity (EPQ) Recall that EOQ assumes the entire order, Q, arrives at once at the end of the lead time When produced items are delivered to the operation during completion of the order, it is called economic production quantity (EPQ) –sometimes called the production rate model –maximum inventory position (and therefore average inventory) are less than with EOQ –Q and ROP calculated differently 9-25 Copyright 2011 John Wiley & Sons, Inc.

26. EPQ 9-26 Copyright 2011 John Wiley & Sons, Inc.

27. Calculating EPQ Annual Total Cost: where: I max = maximum inventory p = daily production rate d = average daily demand rate 9-27 Copyright 2011 John Wiley & Sons, Inc.

28. Calculating EPQ Continued Substitute I max into Annual Total Cost: Use calculus to solve for EPQ: 9-28 Copyright 2011 John Wiley & Sons, Inc.

29. EPQ Example A manufacturer uses 50,000 wheels per year. The manufacturer produces its own wheels at a rate of 600 per day. Carrying cost per wheel is $1/year and setup cost for a production run is $45. The plant operates 250 days per year. What is EPQ and I max ? 9-29 Copyright 2011 John Wiley & Sons, Inc.

30. EPQ Example Continued 9-30 Copyright 2011 John Wiley & Sons, Inc.

31. Fixed-Time Period Systems An order is placed after a set time interval, T, to bring inventory up to the target inventory level Q = R - IP where: Q = order quantity R = target inventory level IP = inventory position at time T T can be set for a particular Q: 9-31 Copyright 2011 John Wiley & Sons, Inc.

32. Computing Target Inventory Target inventory should cover: –demand during lead time, L –demand during review period, T –safety stock R = demand during L + demand during T + safety stock where t = interval over which standard deviation is given 9-32 Copyright 2011 John Wiley & Sons, Inc.

33. Fixed-Time Period Example Given: T = 14 days d = 30 units per day L = 7 days σ day = 10 units no more than 2 stockouts/year calculate k = 9-33 Copyright 2011 John Wiley & Sons, Inc.

34. Independent vs. Dependent Demand Inventory policy is based on the type of demand Independent Demand –demand for a finished product Dependent Demand –demand for components parts or subassemblies –order quantities computed with Material Requirements Planning (MRP) –relationship between independent and dependent demand is shown in a bill of materials (BOM) 9-34 Copyright 2011 John Wiley & Sons, Inc.

35. Bill of Materials 9-35 Copyright 2011 John Wiley & Sons, Inc.

36. Managing Supply Chain Inventory In addition to the quantitative models, there are a number of practical implications to consider: ABC Inventory Classification Practical Considerations of EOQ Measuring Inventory Performance Vendor Managed Inventory 9-36 Copyright 2011 John Wiley & Sons, Inc.

37. ABC Inventory Classification ABC system classifies inventory based on its degree of importance Steps: 1.Determine annual usage or sales for each item 2.Determine % of total usage or sales for each item 3.Rank items from highest to lowest % 4.Classify items into groups: A: highest value, B: moderate value, C: least valuable 9-37 Copyright 2011 John Wiley & Sons, Inc.

38. ABC Inventory Classification 9-38 Copyright 2011 John Wiley & Sons, Inc.

39. Practical Considerations of EOQ Lumpy Demand –can use Periodic Order Quantity (POQ) when demand is not uniform EOQ Adjustments –total cost changes little on either side of the EOQ  managers can adjust to accommodate needs Capacity Constraints –storage capacity and costs should be considered when ordering large quantities 9-39 Copyright 2011 John Wiley & Sons, Inc.

40. Measuring Inventory Performance Common metrics for inventory: Units –# units available Dollars –dollars tied up in inventory Weeks of Supply –(avg. on-hand inventory) / (avg. weekly usage) Inventory Turns –(cost of good sold) / (avg. inventory value) 9-40 Copyright 2011 John Wiley & Sons, Inc.

41. Average Inventory Example Given a fixed-order quantity model with: Annual Demand (D) = 1,000 units Order Quantity (Q) = 250 units Safety Stock (SS) = 50 units Average Inventory = Q/2 + SS = 250/2 + 50 = 175 units Inventory Turn = D/(Q/2 + SS) = 1,000/175 = 5.71 turns per year 9-41 Copyright 2011 John Wiley & Sons, Inc.

42. Vendor Managed Inventory (VMI) VMI arrangements have the vendor responsible for managing the inventory located at a customer’s facility The vendor: –stocks inventory –places replenishment orders –arranges the display –typically owns inventory until purchased –is required to work closely with customer 9-42 Copyright 2011 John Wiley & Sons, Inc.

43. Review 1.Reasons to carry inventory include protecting against lead time demand, maintaining independence, buffering against uncertainty. 2.Inventory types include: cycle stock, safety stock, anticipation, pipeline, and MRO. 3.3 inventory costs: holding, ordering, & shortage. 4.a. Inventory systems answer: when to order and how much to order. 9-43 Copyright 2011 John Wiley & Sons, Inc.

44. Review Continued 4.b. Two most common systems are: fixed-order quantity and fixed-time period. 5.Fixed-order quantity systems have a reorder point (ROP). The basic system utilizes the economic order quantity (EOQ), and when production feeds demand, it utilizes the economic production quantity (EPQ). 6.In fixed-time period systems the time between orders, T, is constant, and the order quantity varies. Orders bring the IP to a target level, R. 9-44 Copyright 2011 John Wiley & Sons, Inc.

45. Review Continued 7.Independent demand is for a finished product and dependent demand is for components. 8.ABC classification defines the degree of importance for inventory. 9.The most common ways to measure inventory are in units, dollars, weeks of supply, and inventory returns. 10.Vendor managed inventory (VMI) is where the vendor is responsible for the inventory located at a customer’s facility. 9-45 Copyright 2011 John Wiley & Sons, Inc.

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