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 material.  Work-in-progress.  Maintenance/repair/operating (MRO) supply.  Finished goods.

4. 12-4 The Functions of Inventory  To ”decouple” or separate various parts of the production process.  To smooth production (link supply and demand).  To provide goods for customers (quick response).  To take advantage of quantity discounts.  To hedge against inflation and upward price changes (speculation).

5. 12-5 The Material Flow Cycle

6. 12-6  High cost - $$$$$  Item cost (if purchased).  Ordering (or setup) cost.  Costs of forms, clerks’ wages etc.  Holding (or carrying) cost.  Building lease, insurance, taxes etc.  Difficult to control.  Hides production problems. Disadvantages of Inventory

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

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 66 9 5 58 8 6 50 7 7 46 6 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  Count products to verify inventory records.  Count A items most frequently (for example, once a month).  Count B items less frequently (twice a year).  Count C items least frequently (once a year).  Do not shut down facility to count everything at one time (once per year). Cycle Counting

12. 12-12 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.

13. 12-13 Holding Costs  Investment costs (borrowing, interest).  Insurance.  Taxes.  Storage and handling.  Extra staffing.  Pilferage, damage, spoilage, scrap.  Obsolescence.

14. 12-14 Inventory Holding Costs 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%

15. 12-15 Ordering Costs To order and receive product:  Supplies.  Forms.  Order processing.  Clerical support.  etc.

16. 12-16 Setup Costs To change equipment and setup for new product:  Clean-up costs.  Re-tooling costs.  Adjustment costs.  etc.

17. 12-17 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).

18. 12-18  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.  How much to order (each time)?  100 units, 50 units, 23.624 units, etc.  Many different models can be used, depending on nature of products and demand. Inventory Questions

19. 12-19 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. (See Chapter 14 for dependent demand.)

20. 12-20  Fixed order-quantity models.  1. Economic order quantity (EOQ).  2. Production order quantity (POQ or ERS).  3. Quantity discount.  Probabilistic models.  Fixed order-period models. How much and when to order? Inventory Models

21. 12-21  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?

22. 12-22  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

23. 12-23 Order Quantity Annual Cost Holding Cost Curve Order Cost Curve EOQ Model - How Much to Order?

24. 12-24 Order Quantity Annual Cost Holding Cost Curve Total Cost Curve Order Cost Curve Optimal Order Quantity (EOQ=Q*) EOQ Model - How Much to Order?

25. 12-25  More units must be stored if more are ordered. Purchase Order DescriptionQty. Microwave1000 Order quantity Why Holding Costs Increase DescriptionQty. Microwave2 Order quantity

26. 12-26  Cost is spread over more units. Example: You need 1000 microwave ovens. Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 Purchase Order DescriptionQty. Microwave1 Purchase Order Description Qty. Microwave 2 1 Order (Postage $ 0.34) 500 Orders (Postage $170) Order quantity Purchase Order Description Qty. Microwave1000 Why Order Costs Decrease

27. 12-27 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.

28. 12-28 Expected Number of Orders per year == N D Q D = Demand per year (known and relatively constant) S = Order cost per order H = Holding (carrying) cost per unit per year d = Demand per day L = Lead time in days (known and relatively constant) Q = order size (number of pieces or items per order) EOQ Model Equations Order Cost per year = S D Q Holding Cost per year = (average inventory level)  H

29. 12-29 EOQ Model - average inventory level Average Inventory (Q/2) Time Inventory Level Order Quantity (Q) 0 Maximum inventory = Q Minimum inventory = 0

30. 12-30 Expected Number of Orders per year == N D Q D = Demand per year (known and relatively constant) S = Order cost per order H = Holding (carrying) cost per unit per year d = Demand per day (known and relatively constant) L = Lead time in days (known and relatively constant) Q = order size (number of pieces or items per order) EOQ Model Equations Order Cost per year = S D Q Holding Cost per year = (average inventory level)  H = H Q 2

31. 12-31 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?

32. 12-32 = ×× 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

33. 12-33 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 = Demand per year S = Order cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days EOQ Model Equations

34. 12-34 Working Days / Year = =× d D ROPdL D = Demand per year (known and relatively constant) d = Demand per day (known and relatively constant) L = Lead time in days (known and relatively constant) 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!

35. 12-35 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

36. 12-36 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 Expected Time Between Orders = T = 260 days/year 7.74 = 33.6 days Total Cost = 1200 155 50 + 155 2 5 = 387.10 + 387.50 = $774.60/year

37. 12-37 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%) Suppose we wish to order 6 times per year (every 2 months): Q = 1200/6 = 200 units/order TC = $800.00/year = 300.00 + 500.00 ( 200 units/order is 29% above Q* - but cost is only 3.3% above optimal )

38. 12-38 Order Quantity Annual Cost Total Cost Curve 154.92 EOQ Model is Robust Small variation in cost Large variation in order size

39. 12-39  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

40. 12-40 260 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