1. 12-1 Operations Management Inventory Management Chapter 12 - Part I

2. 12-2 Outline  Functions of Inventory.  ABC Analysis.  Inventory Costs.  Inventory Models for Independent Demand.  Economic Order Quantity (EOQ) Model.  Production Order Quantity (POQ) Model.  Quantity Discount Model.  Probabilistic Models with Varying Demand.  Fixed Period Systems.

3. 12-3 Types of Inventory  Raw materials.  Work-in-progress.  Maintenance/repair/operating (MRO) supply.  Finished goods.

4. 12-4 The Functions of Inventory  To smooth production:  Decouple different parts of the production process.  Link varying supply and demand.  To provide goods for customers (quick response).  To take advantage of quantity discounts.  Buy more to get a reduced price.  To hedge against inflation and upward price changes (speculation).  Buy more now if you think price will rise.

5. 12-5 The Material Flow Cycle

6. 12-6  High cost - $$$$$  Money tied up in inventory could be better used elsewhere in the organization.  Difficult to control.  Inventories occur in many places.  Hides production problems.  Large inventories may overcome poor quality production or poor quality materials. Disadvantages of Inventory

7. 12-7  Divide inventory into 3 classes based on annual $ volume.  Annual $ volume = Annual demand x Unit cost. A class - Most important. Usually: 15-20% of products. 60-80% of value. B class -Less important. Usually: 20-40% of products. 15-30% of value. C class - Least important. Usually: 50-60% of products. 5-10% of value. ABC Analysis

8. 12-8  Sort products from largest to smallest annual $ volume.  Divide into A, B and C classes.  Focus on A products.  Develop class A suppliers more.  Give tighter physical control of A items.  Forecast A items more carefully.  Consider B products only after A products. ABC Analysis

9. 12-9 0 20 40 60 80 100 5 10 Product Annual $ Usage (x1000) Classifying Items as ABC 25 products sorted by Annual $ Volume (Sales) 15 20 25 ProductSales% 110014 2 9213 3 8812 4 60 8 5 58 8 6 53 7 7 49 7 8 41 6 9 32 4 10 26 4 11 21 3 12 18 2 13 16 2 14-25 66 9 Total720 1

10. 12-10 0 20 40 60 80 100 20 40 % of Products Classifying Items as ABC 60 80 100 A B C 0 Annual $ Usage (x1000) Class% $ Vol% Items A39% 12% (3/25) B52%40% (10/25) C9%48% (12/25)

11. 12-11  Inventory accuracy importance:  To determine when and how much to order.  To achieve high level of service.  Information system tracks inventory, but…  Not all items sold are entered (scanned) properly.  Some items disappear without being sold (theft, defective, damaged, etc.) Inventory Accuracy

12. 12-12  Count products periodically to verify inventory records.  Shut down facility and count everything at one time (once per year).  Cycle counting: count items continuously (count some each week).  Count A items most frequently (once a month).  Count B items less frequently (twice a year).  Count C items least frequently (once a year). Inventory Counting

13. 12-13 Inventory for Services  Can be large $.  “Shrinkage” (theft) is a problem.  Often over 3%!  Good personnel selection, training, and discipline is key.  Establish tight control of shipments entering and leaving the facility.  Enforce procedures for documenting product movement.  Information systems can monitor inventory levels and help ensure accuracy.

14. 12-14 Inventory Costs  Holding costs  Holding costs - Associated with holding or “carrying” inventory over time.  Ordering costs  Ordering costs - Associated with costs of placing order and receiving goods.  Setup costs  Setup costs - Cost to prepare a machine or process for manufacturing an order.  Stockout costs  Stockout costs - Cost of not making a sale and lost future sales.

15. 12-15 Holding Costs  Investment costs (borrowing, interest).  Insurance.  Taxes.  Storage and handling.  Extra staffing.  Pilferage, damage, spoilage, scrap.  Obsolescence.

16. 12-16 Inventory Holding Costs – Usually 20-30% of Total Category Investment costs Housing costs Material handling costs Labor cost from extra handling Pilferage, scrap, and obsolescence Cost as a % of Inventory Value 6 - 24% 3 - 10% 1 - 3.5% 3 - 5% 2 - 5%

17. 12-17 Ordering Costs To order and receive product:  Supplies.  Forms.  Order processing.  Clerical support.  etc.

18. 12-18 Setup Costs To change equipment and setup for new product:  Clean-up costs.  Re-tooling costs.  Adjustment costs.  etc.

19. 12-19 Stockout Costs For not making a sale and for lost future sales: - Customer may wait for a backorder, or - Cancel order (and acquire product elsewhere).  Backorder costs: expediting, special orders, rush shipments, etc.  Lost current sale cost.  Lost future sales (hard to estimate).

20. 12-20  How much to order (each time)?  100 units, 50 units, 23.624 units, etc.  When to order?  Every 3 days, every week, every month, etc.  When only 5 items are left, when only 10 items are left, when only 20 items are left, etc.  Many different models can be used, depending on nature of products and demand. Inventory Questions

21. 12-21 Independent vs. Dependent Demand  Independent demand  Independent demand - Demand for item is independent of demand for any other item.  Dependent demand  Dependent demand - Demand for item depends upon the demand for some other item.  Example: Demand for car engines depends on demand for new cars.  We will consider only independent demand.

22. 12-22  Fixed order-quantity models.  1. Economic order quantity (EOQ).  2. Production order quantity (POQ).  3. Quantity discount.  Probabilistic models.  Fixed order-period models. How much and when to order? Inventory Models

23. 12-23  Given a fixed annual demand for a product.  With many small orders:  Amount on hand is always small, so inventory is small.  Frequent orders means cost of ordering is large.  With few large orders:  Amount on hand may be large (when order arrives), so inventory may be large.  Infrequent orders mean cost of ordering is small. How Much and When to Order?

24. 12-24  How much to order (each time)?  Order size is a constant = Q  Q is selected to minimize total cost.  When to order?  Order when amount remaining = ROP  ROP is selected so chance of running out is small. EOQ – Economic Order Quanitity Models

25. 12-25  Known and constant demand.  Known and constant lead time.  Instantaneous receipt of material.  No quantity discounts.  Only order cost and holding cost.  No stockouts. EOQ Assumptions

26. 12-26 Order Quantity Annual Cost Holding Cost Curve Order Cost Curve EOQ Model - How Much to Order?

27. 12-27 Order Quantity Annual Cost Holding Cost Curve Total Cost Curve Order Cost Curve Optimal Order Quantity (EOQ=Q*) EOQ Model - How Much to Order?

28. 12-28  For fixed annual demand, larger order quantities means:  Larger inventory (larger amount ordered each time).  Larger inventory holding cost.  Example: Annual demand = 1200 units  Order 600 each time.  Maximum inventory = 600  Order 50 each time.  Maximum inventory = 50 Why Holding Costs Increase

29. 12-29  For fixed annual demand, larger order quantities means:  Fewer orders per year.  Smaller order cost per year.  Example: Annual demand = 1200 units  Order 600 each time.  1200/600 = 2 orders per year.  Order 50 each time.  1200/50 = 24 orders per year. Why Order Costs Decrease

30. 12-30 Deriving an EOQ  Develop an expression for total costs.  Total cost = order cost + holding cost  Find order quantity that gives minimum total cost (use calculus).  Minimum is when slope is flat.  Slope = Derivative.  Set derivative of total cost equal to 0 and solve for best order quantity.

31. 12-31 Expected Number of Orders per year == N D Q D = Annual demand (relatively constant) S = Order cost per order H = Holding (carrying) cost per unit per year d = Demand rate (units per day, units per week, etc.) L = Lead time (constant) (in days, weeks, hours, etc.) Determine: Q = Order size (number of items per order) EOQ Model Equations Order Cost per year = S D Q Holding Cost per year = (average inventory level)  H Given

32. 12-32 EOQ Model - Average Inventory Level Average Inventory (Q/2) Time Inventory Level Order Quantity (Q) 0 Maximum inventory = Q Minimum inventory = 0

33. 12-33 Expected Number of Orders per year == N D Q D = Annual demand (relatively constant) S = Order cost per order H = Holding (carrying) cost per unit per year d = Demand rate (units per day, units per week, etc.) L = Lead time (constant) (in days, weeks, hours, etc.) Determine: Q = Order size (number of items per order) EOQ Model Equations Order Cost per year = S D Q Holding Cost per year = (average inventory level)  H = Given H Q 2

34. 12-34 Order Quantity Annual Cost Holding Cost =(Q/2)H Total Cost Curve = (D/Q)S+(Q/2)H Order Cost Curve = (D/Q)S Optimal Order Quantity (EOQ=Q*) EOQ Model - How Much to Order?

35. 12-35 = ×× EOQ = Q* DS H 2 EOQ Total Cost Optimization Total Cost = D Q S + Q 2 H Take derivative of total cost with respect to Q and set equal to zero: Solve for Q to get optimal order size: D Q 2 S + 1 2 H = 0

36. 12-36 Optimal Order Quantity == ×× Q* DS H Expected Number of Orders == N D Q*Q* Expected Time Between Orders Working Days / Year == T N 2 D = Annual demand S = Order cost per order H = Holding (carrying) cost EOQ Model Equations

37. 12-37 Given Working Days / Year = =× d D ROPdL D = Annual demand (relatively constant) d = Demand per day L = Lead time in days Determine: ROP = reorder point (number of pieces or items remaining when order is to be placed) EOQ Model - When to order? Suppose demand is 10 per day and lead time is (always) 4 days. When should you order? When 40 are left!

38. 12-38 EOQ Model - When To Order Time Inventory Level Q* Reorder Point (ROP) 2nd order 3rd order 4th order 1st order placed 1st order received Lead Time = time between placing and receiving an order

39. 12-39 EOQ Example Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Suppose the firm currently orders every month. Order size = Q = 1200/12 = 100 Total Cost = 1200 100 50 + 100 2 5 = 600 + 250 = $850/year Can they do better?

40. 12-40 2 ×1200 ×50 EOQ Example Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year = Q* 5 = 154.92 units/order ; so order 155 each time Expected Number of Orders = N = 1200/year 155 = 7.74/year Total Cost = 1200 155 50 + 155 2 5 = 387.10 + 387.50 = $774.60/year Cost to order once a month ($850) is 9.7% higher!!

41. 12-41 EOQ is Robust Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Q = 155 units/order TC = $774.60/year Q* = 154.92 units/order TC = $774.60/year = 387.30 + 387.30 Suppose we must order in multiples of 20: Q = 140 units/order TC = $778.57/year (+0.5%) Q = 160 units/order TC = $775.00/year (+0.05%) Cost with Q=140 or Q=160 is nearly optimal! Total Cost = 1200 Q 50 + Q 2 5

42. 12-42 EOQ is Robust Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Q = 155 units/order TC = $774.60/year Q* = 154.92 units/order TC = $774.60/year = 387.30 + 387.30 Suppose we wish to order 6 times per year (every 2 months): Q = 1200/6 = 200 units/order (200/order is 29% above Q*) TC = $800.00/year = 300.00 + 500.00 (Cost is only 3.3% above optimal: $800 vs. $774.60 ) Total Cost = 1200 Q 50 + Q 2 5

43. 12-43 Order Quantity Annual Cost Total Cost Curve 154.92 EOQ Model is Robust Small variation in cost Large variation in order size

44. 12-44  EOQ amount can be adjusted to facilitate business practices.  If order size is reasonably near optimal (+ or - 20%), then cost will be very near optimal (within a few percent).  If parameters (order cost, holding cost, demand) are not known with certainty, then EOQ is still very useful. Robustness

45. 12-45 260 days/year = d 1200/year ROP = 4.615 units/day  5 days = 23.07 units -> Place an order whenever inventory falls to (or below) 23 units EOQ Model - When to order? Demand = 1200/year Order cost = $50/order Holding cost = $5 per year per item 260 working days per year Lead time = 5 days = 4.615/day