1. Announcements Quiz 3 Tomorrow
If you can’t do what you’re supposed to do;
DO SOMETHING
CHECK you submission!

2. Using EOQ for the Distribution Game: Multi-Echelon Systems
MGTSC 352
Lecture 21:
Inventory Management
A&E Noise example Methods for finding good inventory policies: 1) simulation 2) EOQ + LTD models
Using EOQ for the Distribution Game: Multi-Echelon Systems

3. Coordination
Suppose each retailer uses QLower = 20. If all retailers order at once, the total is 60.
Active learning: you are the warehouse manager. Knowing the retailer order sizes, how would you pick the warehouse order size?

4. Using EOQ for a 2-echelon system: the details
Upper echelon:
DUpper = 3  DRetailer
SUpper = SWarehouse
HUpper = HWarehouse
LTUpper = LTSupplier  Warehouse + LTWarehouse  Retailer
ROPUpper = DUpper  LTUpper
Lower echelon
DLower = DRetailer
SLower = SRetailer
HLower = HRetailer - HWarehouse
LTLower = LTWarehouse  Retailer
ROPLower = DLower  LTLower
Coordination: QUpper = n  SUM(QLower)
Choose n (an integer) and QLower to minimize total cost for the whole system

5. Data Supplier to warehouse transit time: 15 days
Assume open 250 days / year
Supplier to warehouse transit time: 15 days
Warehouse to retailer transit time: 5 days
Demand per retailer: 730 per year
Selling price: $100/unit
Purchase price: $70/unit
Supplier to warehouse order cost: $200
Warehouse to retailer order cost: $2.75
Warehouse holding cost: $14.70/unit/year
Retailer holding cost: $17.50/unit/year
… To Excel

6. BigBluePills, Inc. Expensive drug treatments
Pg. 161
BigBluePills, Inc.
Expensive drug treatments
Perishable – last only 3 months
Order once every 3 months
Regular cost: $400 per treatment
If demand > order size, place rush order
Rush cost: $1,000 per treatment
Price to patient: $650
How much should they order?

7. Single period models Perishable product Past demand data
Must decide how much to order before knowing actual demand for the period
Must live with the consequences
Q > D wasted product
Q < D lost profit
We’ve seen this before: it’s called the “newsvendor problem”

8. Five Years of Demand Data

9. Solution 1 Average demand = 18, so … Q < D  lose ? / unit
… let’s order 18 each quarter
Profit = 18  (650 – 400) = $4,500
Right?
Q < D  lose ? / unit
Q > D  lose ? / unit
Do these cancel out on average?

10. Solution 2: simulation
Solution 1 predicted this profit with Q = 18

11. The Flaw of Averages When input is uncertain...
output given average input
may not equal
the average output

12. Huh? Average BigBluePill demand = 18
Profit for Q = 18, given D = 18: $4,500
Average profit with Q = 18: $1,740
Less than half
Optimal Q = 20, with avg. profit: $1,786
Using avg. demand (ignoring variability)
Seriously overestimates profit
Results in a suboptimal decision

13. How bad can it get? What if rush cost is $1,800 (instead of $1,000)
The “averaging analyst” will still recommend
Q = 18 and estimate P = $4,500.
The actual profit with Q = 18 will be -$565.
Using Q = 20 generates P = $1,217
Using average inputs is a bad idea. “How bad” will depend on data.

14. In general  Profit(AVERAGE(Demand1, Demand2, …, Demandn))
AVERAGE(Profit(Demand1), Profit(Demand2), …, Profit(Demandn))

15. Simple example of the flaw of averages:
A drunk on a highway
Random walk

16. Consider the drunk’s condition
The AVERAGE location of the drunk
Middle of the road
The outcome at the middle of the road
ALIVE
What do you think the average outcome for the drunk is?
DEAD
Average inputs do not result in average outputs.