Planning and Managing Inventories in a Supply Chain

1. Planning and Managing Inventories in a Supply Chain Cycle Inventory

2. In class discussion • The class should read prior to next week’s discussion the following: Chapter 10, pages 246-259 and 273-278

3. Role of Inventory in the Supply Chain • Overstocking: Amount available exceeds demand • Liquidation, Obsolescence, Holding • Understocking: Demand exceeds amount available • Stockout- backorders, lost sales Goal: Matching supply and demand

4. Why hold cycle inventory? • Economies of scale • Fixed costs associated with lots • Quantity discounts

5. EOQ Model • Assumptions • Demand is fixed and known at a rate of D per unit time (year) • Orders arrive instantaneously • We order Q units • Order placement incurs fixed cost of $ S, no matter how many units are ordered • Units cost $C each • Holding costs are $ H per unit per unit time (year), which is equivalent to $ H = $ hC • h is cost of holding $1 in inventory for one year. Decision Variable

6. Inventory Profile Inventory Slope = D Q Average Inventory Q/D Time Cycle

7. The EOQ Formula • How to find value of Q*? • How often do you order?

8. Total Cost • Total Annual Cost TC = CD + (D/Q)S + (Q/2)hC • Total Controllable Cost TCC =(D/Q)S + (Q/2)hC Holding Costs Order costs Material Costs

9. From Inventory Profile • What is average amount of inventory? Q/2 • So, what is the average annual holding cost? Q/2*H=Q/2*hC • How many orders do you make in a year? D/Q • So, what is annual ordering cost? S*D/Q • How many units do you buy in a year? D • So, what is annual material cost? C*D

10. Graphical Analysis Q*

11. Example 10.1 Demand for the Deskpro computer at Best Buy is 1,000 units per month. Best Buy incurs a fixed order placement cost of $4000 each time an order is placed. Each computer costs Best Buy $500, and the retailer has a holding cost of 20%. How many computers should Best Buy order in a lot? Demand, D = 1,000/month*12months/year = 12,000 computers per year Unit cost, C = $500 Holding cost, h = 0.2, hC = 0.2*$500=$100 Fixed cost, S = $4,000/order

12. Example 10.1 continued • How many orders does Best Buy place in a year? • What is annual cost of ordering 980 computers in a lot? TC = CD + (D/Q)S + (Q/2)hC

13. EOQ Model with Lead Time • What if it takes Wunits of time to get your product once you order it? Q W Order Arrives Order Placed

14. EOQ with Lead Time Example • Say demand for your product is 500 per year and the lead time to get the product once you place an order is 6 weeks. You have found that the optimal lot size is 250 units. When should you place an order?

15. How Realistic? • Do you think the assumptions used in the EOQ formula hold for real businesses? • Then why use? Ordering costs and holding costs are very stable around EOQ value. Just need to get close. • Say you order 1,100 in previous example TCCbefore=(D/Q)S +(Q/2)hC =(12000/980)(4000) + (980/2)(.2)(500) =97,979 TCCnow=(12000/1100)(4000) + (1100/2)(.2)(500) =98,636 Increased order by 120/980 = 12.2%, TCC increases by only 0.6%!

16. Other EOQ Insights • If demand increases by a factor of k, your order quantity should increase by a factor of √k • If demand increases by a factor of k, the number of orders you place in a year will also increase by √k • In other words, if demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and order twice as often. • In order to reduce the optimal lot size by a factor of k, the fixed order cost, $S, must be reduced by a factor of k2. • In other words, to reduce lot size by a factor of 2 order cost has to be reduced by a factor of 4.

17. Another Option … Minimize TC = (12000/Q)(4000) + (Q/2)(500)(0.2) Subject To: Q > 1 Note the non-linear objective function

18. Example 10-3 Lot Sizing with Multiple Products • Demand per year • DL = 12,000; DM = 1,200; DH = 120 • Common transportation cost, S = $4,000 • Product specific order cost • sL = $1,000; sM = $1,000; sH = $1,000 • Holding cost, h = 0.2 • Unit cost • CL = $500; CM = $500; CH = $500

19. Example 10-3 …

20. Delivery Options • No Aggregation: Each product ordered separately • Complete Aggregation: All products delivered on each truck

21. Another Option …

22. No Aggregation: Order each product independently Total cost = $155,140

23. Complete Aggregation: Order all products jointly Annual order cost = 9.75×$7,000 = $68,250 Annual total cost = $136,528

24. Impact of product specific order cost

25. Lessons From Aggregation • Aggregation allows firm to lower lot size without increasing cost • Complete aggregation is effective if product specific fixed cost is a small fraction of joint fixed cost

26. EPQ Order Quantity

27. Example Demand, D = 12,000 computers per year Unit cost, C = $500 Holding cost, h = 0.2 Fixed cost, S = $4,000/run Production rate = 60 computers/day # of working days/year = 250

28. Quantity Discounts • Lot size based • All units • How should buyer react?

29. 10,000 5,000 Order Quantity All-Unit Quantity Discounts Cost/Unit Total Material Cost $3 $2.96 $2.92 10,000 5,000 Order Quantity

30. All-Unit Quantity Discounts • Step I: Evaluate EOQ for the lowest unit cost. If EOQ is valid then find total cost which is the optimum (STOP) • Step II: If EOQ in step I is invalid find total cost at all break points. • Step III: Find EOQs at all other unit costs • Step IV: Find total cost at all valid EOQs in step III • Step V: Compare costs in steps II and IV and select the optimum