Inventory Management

1. Inventory Management Chapter 13

2. Learning Objectives • Define the term inventory • List the different types of inventory • Describe the main functions of inventory • Discuss the main requirements for effective inventory management • Describe the A-B-C approach and explain how it is useful • Describe the basic EOQ model and its assumptions and solve typical problems. • Describe the economic production quantity model and solve typical problems • Describe the quantity discount model and solve typical problems • Describe reorder point models and solve typical problems.

3. Inventory Management at Cox Hardware • From the video, what are the elements relevant to inventory management?

4. Inventory • Definition • A stock or store of goods • Dependent demand items • Items that are subassemblies or component parts to be used in the production of finished goods. • Independent demand items • Items that are ready to be sold or used • Inventories are a vital part of business: • necessary for operations • contribute to customer satisfaction

5. Types of Inventory • Raw materials and purchased parts • Work-in-process (WIP) • Finished goods inventories or merchandise • Tools and supplies • Maintenance and repairs (MRO) inventory • Goods-in-transit to warehouses or customers (pipeline inventory)

6. Discussion • Which of them are dependent demand items and independent demand items? • Raw materials and purchased parts • Work-in-process (WIP) • Finished goods inventories or merchandise • Tools and supplies • Maintenance and repairs (MRO) inventory • Goods-in-transit to warehouses or customers (pipeline inventory)

7. Inventory Functions • Inventories serve a number of functions such as: • To meet anticipated customer demand • To smooth production requirements • Firms that experience seasonal patterns in demand often build up inventories during preseason periods to meet overly high requirements during seasonal periods. • To decouple operations • Buffers between operations • To protect against stockouts • Delayed deliveries and unexpected increases in demand increase the risk of shortages.

8. Inventory Functions • Inventories serve a number of functions such as: • To take advantage of order cycles • It is usually economical to produce in large rather than small quantities. The excess output must be stored for later use. • To hedge against price increases • Occasionally a firm will suspect that a substantial price increase is about to occur and purchase larger-than-normal amounts to beat the increase • To permit operations • The fact that production operations take a certain amount of time (i.e., they are not instantaneous) means that there will generally be some work-in-process inventory. • To take advantage of quantity discounts • Suppliers may give discounts on large orders.

9. Objectives of Inventory Control • Inventory management has two main concerns: • Satisfactory Level of customer service • Having the right goods available in the right quantity in the right place at the right time • Costs of ordering and carrying inventories • The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds

10. Inventory Management • Management has two basic functions concerning inventory: • Establish a system for tracking items in inventory • Make decisions about • When to order • How much to order MIS 373: Basic Operations Management

11. Effective Inventory Management • Requires: • A system keep track of inventory • A reliable forecast of demand • Knowledge of lead time and lead time variability • Reasonable estimates of • holding costs • ordering costs • shortage costs • A classification system for inventory items MIS 373: Basic Operations Management

12. Measures of performance • Measures of performance: • Customer satisfaction • Number and quantity of backorders • Customer complaints • Inventory turnover = a ratio of during a period MIS 373: Basic Operations Management

13. Inventory Counting Systems • Periodic System • Physical count of items in inventory made at periodic intervals • Perpetual Inventory System • System that keeps track of removals from inventory continuously, thus monitoring current levels of each item • Point-of-sale (POS) systems • A system that electronically records actual sales • Radio Frequency Identification (RFID) MIS 373: Basic Operations Management

14. Inventory Costs • Purchase cost • The amount paid to buy the inventory • Holding (carrying) costs • Cost to carry an item in inventory for a length of time, usually a year • Interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security). • Ordering costs • Costs of ordering and receiving inventory • determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage. • Shortage costs • Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit MIS 373: Basic Operations Management

15. ABC Classification System • A-B-C approach • Classifying inventory according to some measure of importance, and allocating control efforts accordingly • A items (very important) • 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value • B items (moderately important) • C items (least important) • 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value MIS 373: Basic Operations Management

16. ABC Classification System • How to classify? • For each item, multiply annual volume by unit price to get the annual dollar value. • Arrange annual values in descending order. • A items: the few with the highest annual dollar value C items: the most with the lowest dollar value. B items: those in between MIS 373: Basic Operations Management

17. ABC Classification: Cycle Counting • Cycle counting • A physical count of items in inventory • Cycle counting management • How much accuracy is needed? • A items: ± 0.2 percent • B items: ± 1 percent • C items: ± 5 percent • When should cycle counting be performed? • Who should do it? MIS 373: Basic Operations Management

18. Inventory Models • Economic Order Quantity models: • identify the optimal order quantity • by minimizing total annual costs that vary with order size and frequency • The basic Economic Order Quantity model (EOQ) • The Quantity Discount model • The Economic Production Quantity model (EPQ) • Reorder Point Ordering (uncertainty, when to order) • Fixed-Order-Interval model • Single Period model (perishable items)

19. Basic EOQ Model • The basic EOQ model: • used to find a fixed order quantity that will minimize total annual inventory costs • continuous monitoring system • Assumptions: • Only one product is involved • Annual demand requirements are known • Demand is even throughout the year • Lead time does not vary • Each order is received in a single delivery • There are no quantity discounts MIS 373: Basic Operations Management

20. The Inventory Cycle Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Time Place order Receive order Receive order Receive order Place order Lead time MIS 373: Basic Operations Management

21. Discussion • What costs are associated with this model? • (Hint: Recall the 5 types of costs) • Purchase cost • Holding (carrying) cost • Ordering cost • Setup cost • Shortage cost (Backorder/Backlog cost) Instructor Slides

22. Total Annual Cost • Total Cost = Annual Holding Cost + Annual Ordering Cost (TC) where • Q = order quantity in units • H = holding (carrying) cost per unit, usually per year • D = demand, usually in units per year • S = ordering cost per order Number of orders Average number of units in inventory MIS 373: Basic Operations Management

23. Goal: Total Cost Minimization • The Total-Cost Curve is U-Shaped • There is a tradeoff between holding costs and ordering costs Annual Cost Holding Costs Ordering Costs Order Quantity (Q) (optimal order quantity) Q* MIS 373: Basic Operations Management

24. Deriving EOQ • Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. • The total cost curve reaches its minimum where the carrying and ordering costs are equal. MIS 373: Basic Operations Management

25. Example: Deriving EOQ • Tire distributer • D (Demand)=9,600 tires per year • H (Holding cost)=$16 per unit per year • S (Ordering cost) = $75 per order MIS 373: Basic Operations Management

26. Example: Deriving EOQ • D (Demand)=9,600 tires per year • H (Holding cost)=$16 per unit per year • S (Ordering cost) = $75 per order • Q*=300 tires • TCmin = 4,800 Let’s verify whether the Q* indeed gives the lowest cost. MIS 373: Basic Operations Management

27. Exercise • A local distributor for a national tire company expects to sell approximately 9,600 tires per year. Annual carrying cost is $16 per tire, and ordering cost is $75 per order. The distributor operates 288 working days a year. • a. What is the optimal order size? • b. How many times per year the store reorder? • c. What is the length of an order cycle? • d. What is the total annual cost if EOQ is placed? Instructor Slides

28. Solution • a • b • c • d Instructor Slides

29. Economic Production Quantity (EPQ) • The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate) • Assumptions • Only one item is involved • Annual demand requirements are known • Usage rate is constant (= even demand throughout the year) • Usage occurs continually, but production occurs periodically (batch production) • The production rate is constant • Production rate is greater than usage rater • Lead time does not vary • There are no quantity discounts 13-29 Instructor Slides

30. EPQ: Inventory Cycle Q Production and usage Usage only Production and usage Usage only Production and usage Qp Cumulative production Imax Amount on hand Time 13-30 Instructor Slides

31. Discussion • What costs are associated with this model? • (Hint: Recall the 5 types of costs) • Purchase cost • Holding (carrying) cost • Ordering cost • Setup cost • Shortage cost (Backorder/Backlog cost) • Our decision making in EPQ model is to determine the size of order (Q) each time. Why? Instructor Slides

32. EPQ Model Instructor Slides

33. EPQ – Total Cost 13-33 Instructor Slides

34. EPQ Optimal Batch size a.k.a Economic Produciton Quantity (EPQ) 13-34 Instructor Slides

35. Exercise • A toy manufacturer uses 48,000 wheels per year for toy trucks. The firm produces its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost is $45 per production run. The firm operates 240 days per year. • a. What is the optimal batch size? • b. What is the total annual cost if EPQ is produced each run? • c. What is cycle time (production stage + usage stage)? • d. What is the production cycle time? Instructor Slides

36. Solution • a • b Instructor Slides

37. Solution • c • d Instructor Slides

38. Quantity Discount Model • Quantity discount • Price reduction for larger orders offered to customers to induce them to buy in large quantities 13-38 Instructor Slides

39. When to Reorder • If delivery is not instantaneous, but there is a lead time:When to order? Order Quantity Q Inventory Lead Time Time Place order Receive order MIS 373: Basic Operations Management

40. When to Reorder • EOQ answers the “how much” question • The reorder-point (ROP) tells “when” to order • Reorder-Point • When the quantity on hand of an item drops to this amount (quantity-trigger), the item is reordered. • Determinants of the Reorder-Point • The rate of demand • The lead time • The extent of demand and/or lead time variability • The degree of stockout risk acceptable to management MIS 373: Basic Operations Management

41. Reorder-Point ROP = (Demand per day) * (Lead time for a new order in days) = d * L where d= (Demand per year) / (Number of working days in a year) Example: • Demand = 12,000 iPads per year • 300 working day year • Lead time for orders is 3 working days In other words, the manager should place the order when only 120 units left in the inventory. d = 12,000 / 300 = 40 units ROP = d * L = 40 units per day * 3 days of leading time = 120 units MIS 373: Basic Operations Management

42. The Inventory Cycle Q: When shall we order? A: When inventory = ROP Q: How much shall we order? A: Q = EOQ Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point ROP = LxD Time Place order Receive order Receive order Receive order Place order D: demand per period L: Lead time in periods Lead time MIS 373: Basic Operations Management

43. Exercise: EOQ & ROP • Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? (Assuming that the lead time to receive cars is 10 days and that there are 365 working days in a year) Recall: EOQ = ROP = (Demand per day) * (Lead time for a new order in days) = d * L where d = (Demand per year) / (Number of working days in a year)

44. Exercise: EOQ & ROP • Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year. How many times should the dealer order, and what should be the order size? Since d is given in years, first convert: 5000/365 =13.7 cars per working day So, ROP = 13.7 * 10 = 137 So, when the number of cars on the lot reaches 137, order 548 more cars.

45. But demand is rarely predictable! Inventory Level When Actual Demand < Expected Demand Order Quantity Lead Time Demand ROP Inventory at time of receipt Time Place order Receive order Lead Time MIS 373: Basic Operations Management

46. But demand is rarely predictable! Inventory Level When Actual Demand > Expected Demand Order Quantity Stockout Point ROP Time Unfilled demand Place order Lead Time Receive order MIS 373: Basic Operations Management

47. But demand is rarely predictable! Inventory Level If ROP = expected demand, inventory left 50% of the time, stock outs 50% of the time. Order Quantity ROP = Expected Demand Average Uncertain Demand Time MIS 373: Basic Operations Management

48. Expected LT Demand Safety Stock Safety Stock Inventory Level To reduce stockouts we add safety stock Order Quantity Order Quantity Q = EOQ ROP = Safety Stock + Expected LT Demand Expected Lead-time Demand Place order Time Lead Time Receive order MIS 373: Basic Operations Management

49. How Much Safety Stock? • The amount of safety stock that is appropriate for a given situation depends upon: • The average demand rate and average lead time • Demand and lead time variability • The desired service level • Service level = probability of NOT stocking out • Reorder point (ROP) = Expected demand during lead time + z*σdLT Where z = number of standard deviations σdLT = the standard deviation of lead time demand MIS 373: Basic Operations Management

50. Reorder Point • The ROP based on a normal distribution of lead time demand Risk of stockout Service level (probability of not stockout) Quantity Safety Stock Expected demand ROP Z scale MIS 373: Basic Operations Management Z 0