Inventory Management: Optimal Ordering and Cost Minimization

1. BUAD306 Chapter 13 - Inventory Management

2. Everyday Inventory • Food • Gasoline • Clean clothes… What else?

3. Inventory • Stock or quantity of items kept to meet demand • Takes on different forms • Final goods • Raw materials • Purchased/component parts • Labor • In-process materials • Working capital

4. Inventory • Static – only one opportunity to buy and sell units • Dynamic – ongoing need for units; reordering must take place

5. Demand • Dependent Demand • Items are used internally to produce a final product • Independent Demand • Items are final products demanded by external customers

6. Reasons To Hold Inventory • To meet anticipated demand • To smooth production requirements • To decouple components of the production-distribution system • To protect against stock-outs • To take advantage of order cycles • To hedge against price increases or to take advantage of quantity discounts • To permit operations

7. Inventory Costs • Carrying Costs • Costs of holding an item in inventory • Ordering Costs • Costs of replenishing inventory • Shortage (stockout) Costs • Temporary or permanent loss of sales when demand cannot be met

8. Inventory Management • Objective: To keep enough inventory to meet customer demand and also be cost-effective • Purpose: To determine the amount of inventory to keep in stock - how much to order and when to order How much and when to order inventory?

9. Inventory Management Requirements • A system to keep track of the inventory on hand and on order • A reliable forecast of demand • Knowledge of lead times • Reasonable estimates of inventory costs • A classification system for inventory items (ABC)

10. Inventory Control Systems • Control the level of inventory by determining how much to order and when • Continuous (Perpetual) Inventory System - a continual record of the inventory level for every item is maintained • Periodic Inventory System - inventory on hand is counted at specific time intervals

11. 0 214800 232087768 Other Control Systems/Tools • Two-Bin System - two containers of inventory; reorder when the first is empty • Universal Product Code (UPC) - Bar code printed on a label that has information about the item to which it is attached • RFID Tags

12. Considerations • Lead Time • Time interval between ordering and receiving the order • Cycle Counting • Physical count of items in inventory • Usage Rate • Rate at which amount of inventory is depleted

13. Inventory Cycle Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Time Place order Place order Receive order Receive order Receive order Lead time

14. Economic Order Quantity • The EOQ Model determines the optimal order size that minimizes total inventory costs

15. Inventory Costs • Carrying Costs – cost associated with keeping an item in stock • Includes: storage, warehousing, insurance, security, taxes, opportunity cost, depreciation, etc. • Ordering Costs – cost associated with ordering and receiving inventory • Determining quantities needed, preparing documentation, shipping, inspection of goods, etc.

16. 2DS H Optimal Order Quantity 2 (Annual Demand) (Order Cost) Q = = o Annual Holding Cost per unit Qo D Length of order cycle = D Qo # Orders / Year =

17. Annual carrying cost Annual ordering cost Total cost = + Qo D S H TC = + 2 Qo Basic EOQ Model Where: Qo = Economic order quantity in units H = Holding (carrying) cost per unit D = Demand, usually in units per year S = Ordering cost

18. Cost Minimization Goal The Total-Cost Curve is U-Shaped Annual Cost Carrying Costs Ordering Costs Order Quantity (Q) QO (optimal order quantity)

19. EOQ Example 1 A local office supply store expects to sell 2400 printers next year. Annual carrying cost is $50 per printer, and ordering cost is $30. The company operates 300 days a year. A) What is the EOQ? B) How many times per year does the store reorder? C) What is the length of an order cycle? D) What is the total annual cost if the EOQ quantity is ordered?

20. EOQ Example 2 A local electronics store expects to sell 500 flat-screen TVs each month during next year. Annual carrying cost is $60 per TV, and ordering cost is $50. The company operates 364 days a year. A) What is the EOQ? B) How many times per year does the store reorder? C) What is the length of an order cycle? D) What is the total annual cost if the EOQ quantity is ordered?

21. Quantity Discounts • A price discount on an item if predetermined numbers of units are ordered TC = Carrying cost + Ordering cost + Purchasing cost = (Q / 2) H + (D / Q) S + PD where P = Unit Price

22. Quantity Discount Example Campus Computers 2Go Inc. wants to reduce a large stock of laptops it is discontinuing. It has offered the University Bookstore a quantity discount pricing schedule as shown below. Given the discount schedule and its known costs, the bookstore wants to determine if it should take advantage of this discount or order the basic EOQ order size.

23. HW #13 A mail-order house uses 18,000 boxes a year. Carrying costs are $.60 per box per year and ordering costs are $96. The following price schedule is offered. Determine the EOQ and the # of orders per year.

24. EOQ with Incremental Replenishment (EPQ) • Used when company makes its own product • Considers a variety of costs/terms: • Carrying Cost • Setup Cost (analogous to ordering costs) • Maximum and Average Inventory Levels • Economic Run Quantity • Cycle Time • Run Time

25. EOQ with Incremental Replenishment (EPQ) • Definitions • S = Setup Cost • H = Holding Cost • Imax = Maximum Inventory • Iavg = Average Inventory • D = Demand/Year • p = Production or Delivery Rate • u = Usage Rate

26. EOQ with Incremental Replenishment

27. Assumptions • Only one item is involved • Annual demand is known • Usage rate is constant • Usage occurs continually, production periodically • Production rate is constant • Lead time doesn’t vary • No quantity discounts

28. EOQ Replenishment Example A toy manufacturer uses 48,000 rubber wheels per year for its product. The firm makes 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 for a production run of wheels is $45. The firm operates 240 days per year. Determine the: • Optimal run size • Minimum total annual cost for carrying and setup • Cycle time for the optimal run size • Run time

29. 600 1200 1800 1600 1400 1200 1000 800 600 400 200 0 START ALL OVER

30. Other Considerations • Safety Stock • Reorder Point • Seasonality