3/7: Inventory Planning & Control

1. 3/7: Inventory Planning & Control • Roll call / collect homework / hand back hmwk • Go over homework (?) • Understanding inventory issues • The basic numbers involved • Holding cost, ordering cost, demand • Basic EOQ model • EOQ model with allowed shortages • Assign homework • Have a good Spring Break

2. Holding Cost • Made of many things: • Cost of capital (money tied up in inventory) • Expressed as a % of amount invested (% of purch. price) • Insurance • Breakage • Pilferage (Theft) • Overhead, etc. • Also expressed as a % of amount invested

3. Holding Cost • Made of many things: • Cost of capital (money tied up in inventory) • Expressed as a % of amount invested (% of purch. price) • Other holding costs • Also expressed as a % of amount invested • EX: I have $10,000 worth of 100 comic books. I estimate my cost of capital to be 11% and other holding costs to be 4%. What is my total holding cost in dollars? What is my holding cost per unit?

4. Ordering Cost • A fixed cost • Doesn’t change with quantity ordered • Is charged each time a order is placed • Made of many things: • Salaries of purchasing department • Cost of preparation of the order documents • Cost of processing the order, etc.

5. Demand • How much is required of the product • In the Economic Order Quantity (EOQ) model, we assume that demand is CONSTANT. • EX: Each month, I sell 200 comic books.

6. EOQ: The Dilemma • We seek a balance while satisfying demand: • Ordering costs must be kept as low as possible (over time), and • Holding costs must be kept as low as possible. • So how much do we order each time to minimize overall inventory costs?

7. EOQ: The Dilemma • So how much do we order each time to minimize overall inventory costs? Daily demand(slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

8. The Basic EOQ Model • EOQ: Economic Order Quantity • Assumptions of EOQ models: • Demand is constant (unvarying ), expressed as annual demand (units per year (or other time unit) ). • 2 variable costs: setup cost and holding cost. • Lead time is constant & known. • Models use continuous review, not periodic review. • Quantity discounts are not possible.

9. EOQ: Symbols & Assumptions • Q: Maximum in inventory, as well as order quantity. What is the average inventory? Daily demand(slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

10. EOQ: Symbols & Assumptions • Lead time (L or l ) is constant & known, so we can order replenishment to be received when inventory hits zero. Measured in time units. Daily demand(slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

11. EOQ: Symbols & Assumptions • Reorder point (r) is the level of inventory at which a replenishment order will be triggered. Measured in units of inventory (portion of Q). Daily demand(slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

12. EOQ: Symbols & Assumptions • Cycle time (T) is the length of time it takes to use up the inventory (Q). Daily demand(slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

13. EOQ: Calculating it • EOQ = Annual holding cost of average inventory + Annual ordering cost • EOQ = AHC + AOC

14. EOQ: Annual Holding Cost • I = annual holding cost rate (note: RATE, %) • C = unit cost of the inventory item • Ch = annual cost of holding one unit in inventoryCh = I * C • Annual holding cost of the average inventory is:avg. inventory level * ann. holding cost per unit

15. EOQ: Annual Ordering Cost • D = annual demand for item (measured in units of item) • D / Q = number of orders per year • Co = Cost per order

16. EOQ: Total Annual Cost

17. Example: Magazine Distributor • Annual demand: 150,000 copies of Vogue • Cost of ordering (Co) is $10 • Cost per magazine is $1.50 • Annual holding cost rate is 10%

18. Ex: Magazine Distributor • Annual demand: 150,000 copies of Vogue • Cost of ordering (Co) is $10 • Cost per magazine is $1.50 • Annual holding cost rate is 10% • We still need to know what the order quantity is.

19. Total Cost vs. Order Quantity Combined curve: holding & setup. Annual Cost Minimum annual cost Holding cost curve We’ll find an equation for this amount Setup cost curve Optimal order quantity Order Quantity

20. So How Much Should We Order? • The best order quantity will be found where AOC = AHC. Annual Cost Combined curve: holding + setup. Minimum annual cost Holding cost curve Setup cost curve Optimal order quantity Order Quantity

21. Where AOC = AHC • We replace AOC & AHC with their respective equations and then solve for Q. • This value of Q is the Economic Order Quantity. We use Q* as its symbol.

22. Back to EX: Magazine Distributor • Annual demand: 150,000 copies of Vogue • Co is $10, cost per magazine is $1.50 • Annual holding cost rate is 10% • EOQ = 4472 magazines per order

23. But When Should We Order It? • The reorder point (r) is expressed in units of inventory. • Related to the lead time (m) (time it takes for an order to be fulfilled) by looking at the demand per day (d). • Days per year is not necessarily 365 – it’s working days per year.

24. And How Long Will the Order Last? • Since we know how many orders will be placed per year ( D / Q* ), we can calculate the cycle time in days. Go to Excel setup

25. New Situation: Planned Shortages • Allows for backordering • Q: amount of order, S: greatest shortage • ThereforeQ – S isamountof greatestinventory Q - S Daily demand(slope) (d) Inventory r S time Lead time ( L, l ) Cycle time (T)

26. Shortages: Cycle Time Sections • T is divided into two distinct phases: t1 & t2 • t1 is timewithpositiveinventory. • t2 is timewith ashortage. Q - S Daily demand(slope) (d) Inventory t1 t2 r S time Lead time ( L, l ) Cycle time (T)

27. Shortages: Average Inventory Cost • Calculating the average inventory: • Q – S is greatest inventory, and S is greatest shortage, but you can’t go lower than zero. • We need a weighted average of: • The average inventory in t1 and 0 in t2.

28. Shortages: Average Inventory Cost • Calculating the average inventory: • Since we know that t1 = (Q–S) / d , & T = Q/d,

29. Shortages: Average Backorder Level • And since and

30. Shortages: Average Backorder Level • We can calculate the average backorder level as:

31. Total Inventory Cost for Shortages • The total cost of the inventory system that allows for backorders is= AHC + AOC + annual cost of backordering • Where Ch = cost to inventory 1 unit for 1 year Cb = cost to backorder 1 unit for 1 year Co = cost per order

32. So the EOQ for Shortages is… • (Trust me…)

33. Homework due 3/21 • Ch. 11 #1 a-d (note: “Total Annual Cost” of the Inventory System) (do by hand) • Ch. 11 #4 a-d (do with Excel) • Ch. 11 #6 a-d (do with Excel) • Ch. 11 #15 a-e (do by hand) • Ch. 11 #17 (do with Excel)