1. CHAPTER THIRTEEN INVENTORY MANAGEMENT Chapter 13 Inventory Management

2. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-2 Independent Demand (Chapter 13) A B(4) C(2) D(2)E(1) D(3) F(2) Dependent Demand (Chapter 14) Independent demand is uncertain. Dependent demand is certain.

3. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-3 Types of Inventories (1 of 2) Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories –(manufacturing firms) or merchandise (retail stores)

4. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-4 Types of Inventories (2 of 2) Replacement parts, tools, & supplies Goods-in-transit (pipeline) to warehouses or customers

5. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-5 Supplier – Production – Distribution System Supplier Distribution Inventories Raw material in-transit Sub-assembly parts in- transit Maintenance, repair, and operating supplies in-transit Raw Material Inventory Work-in-process Inventory Factory Finished Goods Inventor y Component Inventory MRO Inventor y Purchasing Production and Inventory Control Shipping and Traffic Retailer Inventor y Orders Warehouse Inventory Production Inventories Customer Distribution Inventories Orders Supplier

6. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-6 Functions of Inventory Meet anticipated demand Smooth production requirements Decouple components (areas) of the production- distribution Protect against stock-outs Take advantage of order cycles Help hedge against price increases or to take advantage of quantity discounts Permit operations (operation lead time)

7. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-7 Concerns of Inventory Control Level of customer service –have the right goods, in sufficient quantities, in the right place, at the right time –in other words, the customer gets what ever he/she wants when he/she wants it Inventory-related costs –ordering costs –carrying costs

8. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-8 Objectives of Inventory Management (1 of 2) Achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Two fundamental decisions –how much to order –when to place the order

9. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-9 Possible performance measures –customer satisfaction number of backorders/lost sales number of customer complaints –inventory turnover ratio of annual cost of goods sold to average inventory investment –days of inventory expected number of days of sales that can be supplied from existing inventory Objectives of Inventory Management (2 of 2)

10. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-10 Requirements for Effective Inventory Management A system to keep track of the inventory on hand and on order A classification system for inventory items A reliable forecast of demand that includes an measure of forecast error Reasonable estimates of inventory holding costs, ordering costs, and shortage costs Knowledge of lead times and lead time variability

11. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-11 Inventory Counting Systems (1 of 2) Perpetual Inventory (Continual) System –Keeps track of removals from and receipts into inventory continuously Cycle counting - taking physical counts of items and reconciling with records on a continual rotating basis

12. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-12 0 214800 232087768 Inventory Counting Systems (2 of 2) Universal Product Code - Bar code printed on a label that has information about the item to which it is attached Periodic System –Physical count of items made at periodic intervals

13. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-13 ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly A A - very important B B - mod. important C C - least important Figure 13-1 Annual $ volume of items A B C High Low Few Many Number of Items

14. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-14 Demand Forecast and Lead Time Information Reliable estimates of the amount and timing of demand Lead time - time interval between ordering and receiving the order Extent of variability in demand and lead time

15. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-15 The Typical Procurement Cycle Internal Order Cycle Order Request/Requisition Authorization signatures obtained Verification by inventory control Purchasing researches vendors, obtains quotes, etc. Order transferred to vendor Internal Order Cycle Order Request/Requisition Authorization signatures obtained Verification by inventory control Purchasing researches vendors, obtains quotes, etc. Order transferred to vendor Vendor Cycle Receives and enters order Manufactures or “picks” order Ships order Vendor Cycle Receives and enters order Manufactures or “picks” order Ships order Internal Receiving Cycle Receiving Incoming inspection Inventory control receives order, updates records, and notifies department Internal Receiving Cycle Receiving Incoming inspection Inventory control receives order, updates records, and notifies department

16. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-16 Cost Information Holding or carrying costs Ordering costs

17. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-17 Holding or Carrying Costs Cost to carry a unit in inventory for a length of time Includes interest (opportunity cost), insurance, taxes, depreciation, obsolescence, deterioration May be expressed as a percentage of unit price or as a dollar amount per unit

18. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-18 Ordering Costs Cost of ordering and receiving inventory Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality Generally expressed as a fixed dollar amount, regardless of order size

19. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-19 Shortage Costs Result when demand exceeds the inventory on hand Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime Difficult to measure, thus may have be subjectively estimated

20. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-20 Basic Systems for Independent Demand Fixed-order-quantity systems –basic economic order quantity (EOQ) model [purchasing model] –basic economic order quantity model with incremental or noninstantaneous replenishment [production order quantity] –quantity discount model Fixed-order-interval systems

21. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-21 qOnly one product is involved qAnnual demand requirements are known qDemand is spread evenly throughout the year so that the demand rate is reasonable constant qLead time does not vary qEach order is received in a single delivery qThere are no quantity discounts, i.e., the price is constant Basic EOQ Model Assumptions

22. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-22 How the Basic Fixed- Order-Quantity Model Works Profile of Inventory Level Over Time Quantity on hand Time Figure 13-2

23. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-23 Total Annual Cost Annual carrying cost Annual ordering cost Total cost =+ Q 2 H D Q S TC = +

24. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-24 Cost Minimization Goal Order Quantity (Q) Annual Cost Figure 13-4

25. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-25 Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Alternatively we can use calculus by taking the first derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

26. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-26 Basic Fixed Order Quantity Model With Incremental Replenishment Used to determine the order size, production lot, if an item is produced at one stage of production and then sent to the next stage or the customer Differs from the basic model because orders are assumed to be supplied or produced at a uniform rate (p) rather than the order being received all at once

27. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-27 Basic Fixed Order Quantity Model With Incremental Replenishment Profile of Inventory Level Over Time Quantity on hand Q Start to receive order Place order Start to receive order Place order Receive order Lead time Reorder point Usage rate Time Finish receiving order Production rate - usage rate

28. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-28 Basic Fixed Order Quantity Model With Incremental Replenishment Profile of Inventory Level Over Time Quantity on hand Q Start to receive order Place order Start to receive order Place order Receive order Lead time Reorder point Usage rate Time Finish receiving order Production rate - usage rate

29. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-29 Basic Fixed Order Quantity Model With Incremental Replenishment It is also assumed that the supply rate, p, is greater than the usage rate, u Figure 13-6, page 573, shows the difference between the basic EOQ model and this model The change in maximum inventory level requires modification of the TC equation

30. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-30 Basic Fixed Order Quantity Model With Incremental Replenishment The optimization results in

31. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-31 Quantity Discount Model (1 of 4) This model differs from the basic model because the price per unit (P) may vary with the quantity ordered The supplier offers a lower unit price if larger quantities are ordered at one time This is presented as a price or discount schedule, i.e., a certain unit price covers a certain order quantity range

32. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-32 Quantity Discount (2 of 4) Under this condition, annual product cost becomes an incremental cost and must be considered in the determination of the EOQ The total annual costs (TC) = Annual holding cost + annual setup cost + annual product cost TC = (Q/2)H + (D/Q)S + DP

33. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-33 Costs Functions Under Quantity Discount Order Quantity $ cost

34. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-34 Quantity Discount (3 of 4) To find the EOQ, the following procedure is used ¬ Compute the basic EOQ using the lowest unit price and H=IP where I is an interest rate. If the resulting EOQ is feasible, i.e., that quantity can be purchased at the price used, it is optimal. Otherwise, go on to Step 2

35. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-35 Quantity Discount (4 of 4) ­ Using the EOQ from Step 1 and the discount schedule, find the price that should have been used and compute a new EOQ using this price. This new EOQ should be feasible. ® Compute the TC for the EOQ found in Step 2 ¯ Compute the TC for all quantities greater than Step 2’s EOQ where a discount begins. Select the quantity with the lowest TC as the EOQ

36. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-36 Basis for Setting the Reorder Point In the fixed quantity system, the ordering process is triggered when the inventory level drops to a critical point, the reorder point (ROP) This starts all activities associated with placing, filling and receiving the order, or the lead time for the item

37. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-37 Basis for Setting the Reorder Point During the lead time, customers continue to draw down the inventory level It is during this period that the inventory is vulnerable to stockout (run out of inventory) When the demand during the lead time is not known or not constant, a certain amount of inventory above the average or expected demand is carried; this is safety stock

38. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-38 LT Time Expected demand during lead time Maximum probable demand during lead time ROP Quantity Safety stock Reorder Point

39. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-39 Basis for Setting the Reorder Point Determinants of the reorder point –The rate and distribution of demand –The distribution of lead time –The degree of stockout risk acceptable to management, customer service level Reorder point (ROP) = Expected demand during lead time + safety stock

40. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-40 Basis for Setting the Reorder Point Customer service level –order cycle service level is the probability that demand will not exceed supply during the lead time –annual service level is the percentage of demand filled directly from inventory

41. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-41 LT Time Expected demand during lead time Maximum probable demand during lead time ROP Quantity Safety stock Reorder Point

42. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-42 Lead Time Demand ROP Place order safety stock Distribution of lead time demand Service level Risk of shortage Distributions of daily demand with mean of and a standard deviation of

43. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-43 ROP Risk of a stockout Service level Probability of no stockout Mean or expected demand = Safety stock 0z Quantity z-scale Figure 13-13 Distribution of Lead Time Demand Standard deviation =

44. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-44 ROP = + Risk of a stockout Service level Probability of no stockout Mean or expected demand = Safety stock Quantity Distribution of Lead Time Demand Standard deviation =

45. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-45 Administration of the System Using the perpetual counting system, a signal is given when the records indicate that the inventory reaches the ROP Using the periodic counting system, a two-bin system could be used –two bins of inventory –bin A holds an amount equal to the reorder point –bin B holds the remainder of the order –customers are supplied out of bin B –when bin B is empty, it is time to reorder –customers are then supplied out of bin A until the order arrives

46. CHAPTER THIRTEEN INVENTORY MANAGEMENT Fixed-Order-Interval Model

47. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-47 Basic Fixed-Order-Interval System Inventory Level Over Time Time Inventory Level Target Maximum Minimum Inventory Order Quantity OI Order Quantity Order Quantity Order Quantity OI When to order How much to order

48. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-48 Operation of Fixed-Order-Interval Systems As demand for the inventoried item occurs, the inventory level drops When a prescribed period of time has elapsed, the ordering process is triggered, i.e., the time between orders is fixed or constant At that time the order quantity is determined using order quantity = target maximum level - current inventory level

49. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-49 After the lead time elapses, the ordered quantity is received, and the inventory level increases The maximum inventory level is expected demand during protection interval + safety stock, or Operation of Fixed-Order-Interval Systems

50. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-50 Administration of the System Using the periodic counting system, the inventory is reviewed (counted) at the end of each order interval Using the perpetual counting system, an item’s inventory level is checked in the inventory at the end of each order internal

51. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-51 Reasons to Use Supplier’s policy might encourage use Some situations do not lend themselves to continuous monitoring Used where it is desirable to physically count inventory each time an order is placed

52. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-52 Benefits/Advantages Benefits –results in tight control needed for A items in a A-B-C classification –grouping ordering to one supplier may result in savings Disadvantages –larger amount of safety stock needed for the same service level –cost of periodic reviews

53. CHAPTER THIRTEEN INVENTORY MANAGEMENT Single-Period Model

54. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-54 Single-Period Model Used to handle ordering of perishables and items with a limited useful life Focuses on two costs –shortage cost - unrealized profit per unit = revenue per unit minus cost per unit –excess cost - purchase cost minus salvage value

55. CHAPTER THIRTEEN INVENTORY MANAGEMENT MTSU Management 36213-55 Optimal Stocking Level In the case where the distribution of demand is continuous, find the order quantity that provides the area under the distribution and to the left equal to the optimal service level In the case where the distribution of demand is discrete, choose the order quantity so that provides the optimal service level is equaled or exceeded