OPSM 301 Operations Management

1. Koç University OPSM 301 Operations Management Class 21: Inventory Management: the newsvendor Zeynep Aksin zaksin@ku.edu.tr

2. Announcements • Quiz 5 on Thursday • Study: Location and transportation • Use questions at the end of the chapter to practice • Midterm 2 next Tuesday on 20/12 at 17:00 CAS-Z08 • Exam does not include MT1 topics • Will have a review the same day in class

3. Single Period Inventory Control • Examples: • Style goods • Perishable goods (flowers, foods) • Goods that become obsolete (newspapers) • Services that are perishable (airline seats)

4. Example • Mean demand=3.85How much would you order? Demand Probability 1 0.10 2 0.15 3 0.20 4 0.20 5 0.15 6 0.10 7 0.10 Total 1.00

5. Single Period Inventory Control • Economics of the Situation Known: 1. Demand > Stock --> Underage (under stocking) CostCu= Cost of foregone profit, loss of goodwill 2. Demand < Stock --> Overage (over stocking) CostCo= Cost of excess inventory • Co = 10 and Cu = 20 How much would you order? More than 3.85 or less than 3.85?

6. Incremental Analysis Probability Probability Incremental Incremental that incremental that incremental Expected Demand Decision unit is not needed unit is needed Contribution 1 First 0.00 1.00 -10(0.00)+20(1.00) =20 2 Second 0.10 0.90 -10(0.10)+20(0.90) =17 3 Third 0.25 0.75 12.5 4 Fourth 0.45 0.55 6.5 5 Fifth 0.65 0.35 0.5 6 Sixth 0.80 0.20 -4 7 Seventh 0.90 0.10 -7 Co = 10 and Cu = 20

7. nth unit needed Pr{Demand  n} Stock n Decision Point nth unit not needed Pr{Demand  n-1} Base Case Stock n-1 Generalization of the Incremental Analysis Cash Flow Cu -Co 0 Chance Point

8. Stock n Chance Point Decision Point Base Case Stock n-1 Generalization of the Incremental Analysis Expected Cash Flow Cu Pr{Demand  n} -Co Pr{Demand  n-1}

9. Generalization of the Incremental Analysis • Order the nth unit if Cu Pr{Demand  n} -Co Pr{Demand  n-1} >= 0 or Cu (1-Pr{Demand  n-1}) -Co Pr{Demand  n-1} >= 0 or Cu -Cu Pr{Demand  n-1} -Co Pr{Demand  n-1} >= 0 or Pr{Demand  n-1} =< Cu /(Co +Cu) • Then order n units, where n is the greatest number that satisfies the above inequality.

10. Incremental Analysis Incremental Demand Decision Pr{Demand  n-1}Order the unit? 1 First 0.00 YES 2 Second 0.10 YES 3 Third 0.25 YES 4 Fourth 0.45 YES 5 Fifth 0.65 YES 6 Sixth 0.80 NO - 7 Seventh 0.90 NO Cu /(Co +Cu)=20/(10+20)=0.66 • Order quantity n should satisfy: P(Demand  n-1) Cu /(Co +Cu)< P(Demand  n)

11. Order Quantity for Single Period, Normal Demand • Find the z*: z value such that F(z)= Cu /(Co +Cu) • Optimal order quantity is: • Do we order more or less than the mean if: • Cu > Co ? • Cu < Co ?

12. Example 1: Single Period Model • Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game? • Cu = $10 and Co= $5; P≤ $10 / ($10 + $5) = .667 Z.667 = .4 (from standard normal table or using NORMSINV() in Excel) therefore we need 2,400 + .4(350) = 2,540 shirts

13. Example 2: Finding Cu and Co A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290. The demand for winter has a normal distribution with mean 32,500 and std dev 6750. • How much should they order from China??