Topic-14

1. Topic-14 Inventory Management

2. Inventory Management • Inventory: A quantity of goods/materials in the control of a firm and hold for a time in a relatively idle state awaiting its intend use or sale • Inventory Management: To determine an optimal level of holding such idle resources through certain procedures/rules on the decisions of when/how much to order for procurement or production

3. How Much? When!

4. Conflicting Pressures on Inventory Levels

5. Inventory Management (II) • Major objectives of inventory management: 1. Minimizing total inventory management cost under given constraints 2. Satisfying desired customer service level

6. Functions of Inventory • 1. To prevent fluctuation in demand • 2. To meet seasonal demand change • 3. To protect variation in supply • 4. To obtain economy of scale in procurement/production • 5. To maintain independence of operations • 6. To smooth production process • 7. To provide flexibility for production planning and scheduling

7. Type of Inventory Inventory types: • 1. RM/purchased parts/subassemblies • 2. Work-in-process • 3. Finished goods

10. Inventory: Purpose and Types Purpose: Buffering against any uncertainty in the work flow process from material purchasing to finished goods shipping through providing a buffer between successive work flow stages. Types:

11. Costs Constraints and Customer Service Relevant costs in inventory management: • 1. Fixed costs: purchase ordering cost/production setup cost • 2. Variable costs: holding cost/shortage cost/purchase cost Major constraint in inventory management: • 1. Supply constraint • 2. Internal constraint • 3. Marketing constraint

12. Inventory Management Costs affected by inventory decisions

13. Inventory Costs • Interest or opportunity Cost • Storage and Handling Costs • Taxes, Insurance, and Shrinkage • Customer Service Cost • Ordering Cost/Setup Cost • Labor and Equipment Cost • Transportation Costs • Payments to Suppliers

14. Customer Service in Inventory Management • Customer Service: measured by the availability of items when needed a performance measure of inventory management • Customer may be: purchaser of FG/distribution/another plant or shop where next operation is performed • Customer Service Level: a target level for keeping initial delivery schedules and backorders

15. Service Level and Safety Stock • Service level: an inventory management performance criterion measured by ---the percentage of stock-out occurrence defined as service level=1-P(percentage of stock-out) • Safety stock: a quantity of inventory which have been set aside to reduce the probability of stock-out or to improve the service level.

16. Service Level and Safety Stock Safety Stock is: A Quantity of Inventory which have been set aside to reduce the Probability of Stock-Out, or to improve the Service Level. The General Relationship Between Safety Stock and Services Level is:

19. The ABC Classification Method • A small percentage of the items that would account for a large percent of the total values of annual usage- these are called “A” items • A large percentage of the item that would account for a small percentage of the total value of annual usage- these are called “C” items • Items in between “A” and “C” items- these are called “B” items A typical relationship among A, B and C items is:

20. 100 — 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 — Class C Class B Class A Percentage of dollar value 10 20 30 40 50 60 70 80 90 100 Percentage of items ABC Analysis Figure 15.2

21. See ABC Classification Example on your Supplement (p.15-8) Reading Article about 80/20 Rule on p. 15-11.

22. ABC Classification Examples A wholesaler has ten items in a product line. The item number, selling price, and estimated annual volume in units are:

23. The first step in categorizing the item is to estimate the dollar value of annual usage for each item (multiply the selling price by the estimated annual usage). Then, they should be arranged in descending order. The result of these two steps are:

24. Assume the wholesaler wants to construct the ABC classification with “A” items representing 75% of the sales, “B” using the table above the classification would be:

25. Classification of Inventory Control Models • Demand Characteristics: 1. Independent Demand Item (finished goods): demand of an item is independent to others usually with high uncertainty uncontrollable and external determined 2. Dependent Demand Item (RM/part/ subassembly): demand of an item is dependent on other items’ requirements usually with certainty controllable and internal determined

26. Types of Demand • Independent Demand • When item’s demand is influenced by market conditions and is not related to (i.e. “independent” of) production decisions for any other item • Only end items can qualify in manufacturing • Demand must be forecast (uncontrollable) • Dependent Demand • When item’s demand derives from (i.e. “depends” on) the production decisions for its parent • All intermediate and purchased items in manufacturing • Demand should be derived (can be controlled) Some items can be viewed as both “independent” and “dependent” demand items!

27. Classification of Inventory Control Models • Single item inventory vs. multiple-item inventory • Single stage inventory vs. multi-stage • Static demand vs. dynamic demand • Stochastic demand vs. determined demand

28. Five Types of Inventory Control System for Independent Demand Items • 1. Fixed Order Quantity (Q)- Reorder Point (R) System: (Q,R) • Continue review on inventory status (It), • 2. Fixed Order Interval (T)- Maximum Level (M) System: (T,M) • Periodical review at fixed time interval (T) • Place an order at end of each period with a quantity that build On- Hand Inventory up to M • 3. Hybrid System: Combination of Fixed Order Interval (T) and Reorder Point System (R) (Several Possible Combinations). • 4. Time-Phased Order Point System: (MRP Application on Independent Demand Items) • 5. Single-Period Model: for Perishable Items (Newspaper/ Flower)

29. Basic Fixed-Order Quantity Model

30. Receive order Inventory depletion (demand rate) Q On-hand inventory (units) Average cycle inventory Q — 2 1 cycle Time Economic Order Quantity Figure 15.3

31. Fixed-Interval Inventory System(T,M) System

32. Soup Soup Soup IP IP IP Order received Order received Order received Order received Q Q Q On-hand inventory OH OH OH R Order placed Order placed Order placed Time L L L TBO TBO TBO Continuous Review Figure 15.7

33. T IP IP IP Order received Order received Order received Q3 Q1 OH OH Q2 IP1 IP3 IP2 On-hand inventory Order placed Order placed Order placed L L L Time P P Protection interval Periodic Review Systems Figure 15.12

34. Fixed Order Quantity System A perceptual system (sometimes called a fixed quantity or Q/R system) is one that used a fixed reorder point (R) and a fixed order quantity (Q). The time between orders varies depending on when the inventory reaches the reorder point.

35. (d) Q Q R SS= 0 LT LT LT Fixed Order Quantity System • The inventory behavior is:

36. Fixed Order Quantity System Where: R= reorder point = (d*L) + SS Q= economic order quantity = EOQ = √ D= annual demand (expressed in units/ year) L= reorder lead time (expressed as a fraction of a year) S= ordering cost (expressed as $ per order) C= item cost (expressed in $ per unit) F= inventory holding cost fraction (expressed as a fraction of item cost per year) H= holding cost = (C*F) The total annual cost (TC) for a purchased item managed with a perpetual inventory system can be calculated as follows: TC= (cost of the item) + (ordering cost) + (inventory holding cost) D*C + ( Q/2)*H + (D/Q)*S 2* DS H

37. 3000 — 2000 — 1000 — 0 — Q 2 D Q Total cost = (H) + (S) Q 2 Annual cost (dollars) Holding cost = (H) D Q Ordering cost = (S) | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q) Example 15.2 Economic Order Quantity

38. Total cost = HC + OC Annual cost (dollars) Holding cost (HC) Ordering cost (OC) Lot Size (Q) Economic Order Quantity Figure 15.4

39. See Example on Your Supplement • P. 15-15.

40. Example of Determining Economic Order Quantity An importer/distributor or toys uses a standard, corrugated cardboard box for shipping orders to customers. These boxes are used at the rate of 120,000 per year. Each box costs $0.30, and the estimated annual holding cost is 60% of the purchase price. It requires 20 minutes (or 0.33 hours) to prepare an order for this item. The wage rate of the inventory and purchasing clerks is $5.00 per hour. D=120,000; C=0.30; F=0.60; H=0.3x0.6=0.18 Problem: Determine how many boxes should be ordered from the supplier each time. Solution: S= (1/3) x $5= $1.65 EOQ= √2.D.S/H = √2x120,000x1.65/0.18 = 1,483 ≈1,500

41. Problem: If lead time is one day and there are 250 working days during the year, what is the reorder point? Solution: d= 120,000/250= 480, L=1, SS=0 R= d.L + SS= (480X1) + 0 = 480 Problem: What is the total annual cost of this reordering system? Solution: TC = D.C + (D/Q).S + (Q/2).H = (120,000)(0.3) + (120,000/1,483)1.65+(1483/2)X0.18 = $36,267

42. Economic Order Quantity Assumptions Demand rate is constant No constraints on lot size Only relevant costs are holding and ordering/setup Decisions for items are independent from other items No uncertainty in lead time or supply One Time delivery.

43. Fixed Order Quantity System with Gradual Replenishment • The inventory behavior is:

44. P 2*D*S P-d H Fixed Order Quantity System with Gradual Replenishment EPQ= economic production quantity = √ Where D= annual demand (expressed in units/ year) S= ordering cost (expressed as $ per order) C= item cost (expressed in $ per unit) F= inventory holding cost fraction (expressed as a fraction of item cost per year) P= production rate (expressed in units per period) d= usage rate (expressed in units per period) TC = [D*C] + ( )*S + ( )*H*( ) Q P-d D P 2 Q

45. Production quantity Q Demand during production interval Imax On-hand inventory Maximum inventory Imax = (p – d) = Q( ) p – d p Q p p – d Time Production and demand Demand only TBO Figure E.1 Special Inventory Models

46. See Example on Your Supplement • P. 15-17.

47. Example of Determining Economic Production Quantity A manufacturer of steel products uses a large, special bolt as a fastener in all products in a particular product line. The usage rate of this item is 2000 per day. There are 250 working days in the year. It takes 30 minutes to prepare a manufacturing order for this bolt. The clerks make $5.00 per hour. It takes one hour to change the tooling to begin a production run for the bolt. The setup personnel make $9.00 per hour. The production run is 5000 units per day. C=1.30; F=25%; H=(1.3x25%)=0.325; d= 2,000; D=2,000x250=500,000 Problem: What is the economic production quantity for this item assuming a manufacturing cost of $1.30 and an annual holding cost of 25% of the manufacturing cost? S: (0.5x5) + (1x9)= $11.50, P=5,000 EPQ= √(2.D.S)x P/H.(P-d) = √(2x500,000x11.50)x5,000/0.325X(5,000-2,000) ≈7,680

48. Problem: If lead time is 1.5 days, what is the reorder point? Solution: L= 1.5; SS=0 R = d.L +SS = 2,000X1.5+0 = 3,000

49. Periodic Systems

50. Periodic Systems T= economic order interval = L= reorder lead time (expressed as a fraction of a year) S= ordering cost (expressed as a fraction of a year) D= annual demand (expressed in units/year) C= item cost (expressed in $ per unit) F= inventory holding cost fraction (expressed as a fraction of item cost per year) Order quantity = Q= d(L+T) + SS – It = M- It (M= (Base-Level) = d(L+T) + SS It = [On-Hand] + [On-Order] – [Back Order])