1. A quick introduction

2.  What is it?

3.  Why maintain inventory?  Why minimize inventory?

4.  There are many inventory models.  You pick the one that most closely resembles your situation.  We’ll examine the easiest model. It assumes:  Demand is known and constant  Costs are known and constant  Lead time is known and constant  We are managing inventory for only one item  Continuous review

5.  An inventory policy answers two questions: 1.How much to order at a time? 2.When to place an order?

6.  Economic Order Quantity  Used when each order arrives all at once and when backorders/shortages aren’t allowed  Notation: (These items are typically inputs) D = annual demand or usage d = daily demand C = unit cost of items I = annual inventory holding rate C o = fixed cost of placing an order m = lead time (in days)

7.  Notation: (These items are typically calculated) C h = IC = holding cost per item per year Q = order quantity or “lot size” T = Q/D = cycle time (in years) r = md = reorder point (as long as m < T) TC = Total annual cost of managing inventory

8.  Consider graph of Inventory level over time

9. D = 3600 cases per year C o = $20 I = 25% C = $3.00 per case m = 5 days C h = $_____ per case per year d = _____ cases/day (Suppose there are 250 working days per year)

10.  TC (=Total annual costs) = Holding costs + Ordering costs + Cost of Items Holding costs = C h * (Q/2) Ordering costs = C o * (D/Q) Unit costs = C * D

11.  So, for any value of Q, we can calculate TC as TC = C h (Q/2) + C o (D/Q) + C D  We seek a value for Q which minimizes costs  How to find it?

12.  Trial and error? If Q = 300, then TC =.75(300/2) + 20(3600/300) + 3(3600) = 112.50 + 240 + 10800 = $11,152.50 If Q = 400, then TC =.75(400/2) + 20(3600/400) + 3(3600) = 150 + 180 + 10800 = $11,130.00

13.  Consider graph of costs

14.  Is there an easier way to find Q*?

16.  What is TC if Q = 438? TC = C h (Q/2) + C o (D/Q) + C D =.75(438/2) + 20(3600/438) + 3(3600) = 164.25 + 164.38 + 10,800 = $11,128.63

17.  How often to order? T = Q/D = 438/3600 =.121666 years.121666 * 250 = 30.4 days

18.  When to order? r = md = 5(14.4) = 72 cases i.e. Optimal inventory policy is this: Order 438 cases whenever inventory level drops to 72 cases. (This will happen about every 30 working days, and this policy will cost about $11,128 per year.)

19.  Would you ever consider ordering some quantity other than 438 cases at a time?

20.  It turns out the EOQ model is not very sensitive to small changes in the costs or demand  This is good!

21.  I have posted an inventory problem (and solutios) on Blackboard.