1. John H. Vande Vate Spring 2006
Practice Final
John H. Vande Vate
Spring 2006 1

2. Question 1
In class we described how a model that holds inventory of incoming supplies to buffer the supply chain from variations in customer demand. 2

3. Question 1
Under the model, the supplier normally ships the same quantity every day. When inventory rises to S, the model recommends curtailing shipments until it falls to Q and when inventory falls to 0, the model recommends expediting shipments or sending an unusually large shipment to bring inventory levels back up to q. 3

4. Question 1 Consider the special case in which:
a. there is no inventory holding cost (h = 0)
b. because of space limitations, the maximum inventory level S for the part cannot exceed a given level M
c. the fixed costs of expediting and curtailing shipments are equal (K = L > 0)
d. There are no variable costs for expediting and curtailing shipments (k = l = 0) 4

5. Question 1 What is the optimal strategy in this special case? S = Q =
What is the optimal strategy in this special case?
S =
Q =
q = 5

6. Answer
S = M
Q = q = M/2
Reasoning: Inventory is free, so we are only concerned with running into the bounds 0 and M, which we want to do as infrequently as possible. Since there are no variable costs to expedite and curtail, when we do expedite, we should expedite as much as we can to prevent having to expedite or curtail again. Symmetry leads us to Q = q = M/2 6

7. Question 2
We argued in class that, under a periodic review regime, increasing the frequency of shipments generally reduces total inventory and expediting costs. We made this argument assuming that the costs of increasing frequency were negligible. 7

8. Question 2
Suppose
inventory carrying costs are h = $100 per item per year
ordering costs are c = $1,000 per shipment
Demand over time is relatively constant at D = 200,000 per year
The average lead time is 4 weeks with a standard deviation of 2 days.
If we intend to hold safety stock constant regardless of the frequency of orders, how frequently should we order? 8

9. Solution
The lead time information is a red herring. It’s irrelevant as we have decided to hold safety stock constant.
This becomes a simple EOQ type problem with n, the number of times to order as the variable. The total cost formula is
hD/2n + cn
The solution is n = SQRT(hD/2c) = 100 9

10. Question 3
We receive a shipment from our supplier once each week. The lead time for those shipments is 4 weeks with a standard deviation of 2 days. Demand each day is normally distributed with mean 100 and standard deviation 10. How much safety stock should we hold to ensure that the chances of stocking out before a shipment (not the annual chances of stocking out) are only 2%? 10

11. Solution
Calculate the variance in demand during the lead time plus the order period. This is
(T+E[L]) sD2 +D2 sL2
Careful with the units. Let’s work in days
T = 7 days
E[L] = 28 days
D = 100 units/day
sD2 = 100 units2/day
sL2 = 4 days2 11

12. Solution So the variance is (T+E[L]) sD2 +D2 sL2
35*100+40,000 = 43,500
And the standard deviation is about units
We want to carry just over 2 standard deviations or about 417 items 12

13. Question 4
We ship products from Asia to Europe for sale to customers and are interested in strategies that reduce the “avoidable” costs of supply.
Under a periodic review regime, which of the following strategies will help reduce pipeline (in-transit) inventories?
Increasing frequency
Improving forecast accuracy
Reducing the safety lead-time
Moving our source for the products closer to Europe
Changing to a faster mode of transportation 13

14. Question 4
B. Under a periodic review regime, which of the following strategies will help reduce cycle inventories (on-hand inventory excluding safety stock)?
Increasing frequency
Improving forecast accuracy
Reducing the safety lead-time
Moving our source for the products closer to Europe
Changing to a faster mode of transportation 14

15. Question 4
C. Under a periodic review regime, which of the following strategies will allow us to reduce safety stock without compromising product availability?
Increasing frequency
Improving forecast accuracy
Reducing the safety lead-time
Moving our source for the products closer to Europe
Changing to a faster mode of transportation 15

16. Solution
Under a periodic review regime, which of the following strategies will help reduce pipeline (in-transit) inventories?
Increasing frequency
Improving forecast accuracy
Reducing the safety lead-time
Moving our source for the products closer to Europe
Changing to a faster mode of transportation 16

17. Question 4
B. Under a periodic review regime, which of the following strategies will help reduce cycle inventories (on-hand inventory excluding safety stock)?
Increasing frequency
Improving forecast accuracy
Reducing the safety lead-time
Moving our source for the products closer to Europe
Changing to a faster mode of transportation
Only the first of these is direct. The rest are secondary effects achieved through improved forecast accuracy. We might argue that these only affected safety stock 17

18. Question 4
C. Under a periodic review regime, which of the following strategies will allow us to reduce safety stock without compromising product availability?
Increasing frequency
Improving forecast accuracy
Reducing the safety lead-time
Moving our source for the products closer to Europe
Changing to a faster mode of transportation
We strongly suspect increasing frequency will reduce safety stock, but it is not always evident because we face the reduced risks more often. 18

19. Issues Raised in Projects
DaimlerChrysler Project
Which makes the most sense?
Front Suspension => Power Train => Assembly
Power Train => Front Suspension => Assembly
Power Train => Front Suspension =>
The issues are:
Operating and Fixed Cost
Risk of shutting down assembly
Inventory …
Assembly 19

20. Lost capacity at one process does NOT mean lost capacity at another
Risk of Shutting Down
What is the issue?
Where do we want the bottleneck?
Important to note the relationships
Front
Suspension
Power
Train
Power
train
Front
Suspension
Front
Suspension
Power
Train
Assembly
Assembly
Assembly
Lost capacity at one process does NOT mean lost capacity at another 20

21. Joint Replenishment Several parts from a single supplier
How often to ship and how much?
Assume every part on every truck
ci = unit cost of part I
Di = Annual demand for part I
N = number of joint shipments per year
T = cost of transportation per shipment
h = holding cost percentage
Total Cost = Ordering Costs + Inventory Costs 21

22. Joint Replenishment Ordering Costs: T*N Inventory Costs: Total Cost
N shipments at $T per shipment
Inventory Costs:
Di/N items per shipment
ciDi/N value of a shipment
hciDi/2N (one-sided inventory cost)
Total Cost
TN+sum (hciDi/2N)
N = sqrt(sum(hciDi/2)/T)
Qi = Di/N 22

23. Supply Consolidation
The replenishment is scheduled to share the transportation cost among products from the same supplier.
- Find the right demand
Daily production x % Usage x Usage by BOM
Compute EOQ and T respectively for different parts
[step 1]:Round T to nearest power of two, minimal T*
Re-compute order quantity (Q=DT) and thus holding cost with reduced transportation cost (A)
- [step 2]: Decrease T for all parts towards T*
Re-compute order quantity (Q=DT) and thus holding cost with A unchanged 23

24. Team’s Approach Don’t have every part on every truck
Compute EOQ quantities for each part to get Ti, the ideal time between shipments for each part
Take the smallest of these as T*
Trucks run that frequently
Other parts don’t get on every truck. Make them regular
Round Ti to one of 2T*, 4T*, 8T*…
I.e, gets on every other truck, every 4th truck, …
Step 2? 24

25. Newgistics Case Economics Pulling from RDU has three effects
Cost of pulling from RDU
Savings in postal costs to BMC
Reduced volume picked up from BMC and so (perhaps) truck costs
Hard part:
Estimate cost of pulling from RDU 25

26. Cost of Avg weight bag is not Avg cost of a bag
Estimating RDU Costs
Carrier bags packages charges by bag based on weight
This charge is not $A/bag + $B/lb so…
This charge does include a fixed component per bag so….
Cost of Avg weight bag is not Avg cost of a bag
The cost per package (inferred) rises as the volume at the RDU drops 26

27. The Optimization
What happens at 1 BMC has no impact on what happens at another – the problem separates
Variables:
How many trucks to the BMC
Whether of not to pull from each RDU
The objective is:
RDU pickup cost +
Postal cost to BMC +
Truck cost from BMW
Constraints are:
Enough trucks to meet frequency requirements at BMC
Enough trucks to meet volume requirements at BMC 27

28. Question For you to think about:
How could you solve this problem if you did not have access to an optimization application? 28

29. BMW Projects Frequency Project Interesting question:
Current Approach: Assumed transport costs across Atlantic are similar (turned out not true)
Optimize on the basis of lead-time
Simulate to determine
Total cost
Best split of shipments across routes
Interesting question:
Good model of total cost where variables are routes used and the quantities shipped on each 29

30. Ship-to-Average Ship-to-Forecast Places orders with regular frequency
But the order quantities change
Goal: Maintain regular inventory 30

31. Inventory On-hand inventory* with ship-to-forecast: constant level?
*) Data of engine # , high runner 31

32. Ship-to-Average Increasing frequency
reduces relevant level of forecast accuracy
Increases shipment volatility 32

33. Use forecast accuracy over longer period of time!
Forecast error
Why try to chase the daily forecast? %
Use forecast accuracy over longer period of time! 33

34. Demand Variability* Standard Deviation: 42/day Mean Demand: 78/day
*) Data of engine # , high runner 34

35. Ship-to-Average Reduces the variability in the order quantities
Does not raise the total avoidable cost
Simplifies the process 35

36. Shipment Comparison ship-to-forecast ship-to-average Goal #2 achieved!
(shipment adjustment: 66%)
= shipment quantity changes more than 10% compared to previous one
ship-to-average
(shipment adjustment: 14%)
Shipment adjustments happen in 14% of all shipments
Goal #2 achieved! 36

37. Summary Table 55.83% -5.36% -0.45% 29.60% +15.22% -3.87% 48.84% 14.00%
HIGH
29.60%
+15.22%
-3.87%
LOW
48.84%
14.00%
-1.67%
21.79%
60.45%
-0.94%
56.04%
0.00%
-3.85%
51.46%
-16.32%
32.22%
47.11%
Shipment
changes
57.71% %
77.14%
+25.25%
Air cost
-0.56%
-5.70%
-6.47%
-0.36%
Total
avoidable
cost
Part # 37

38. I will think of some clever questions38

39. Shelter First Design a shelter and a logistics network to deliver it
Immediate (2-3 days)
Temporary
Change in thinking
Old thinking: Framework agreements with suppliers
Source from low cost countries
Often poorly served by international carriers 39

40. Beneficiaries (Disaster Zone)
Current Thinking
Before Disaster
Supplier to Pre-positioned stock
$’s are driver.
Use ocean and ground
After Disaster
Warehouses to Staging Area
Time is the driver
Use Commercial Air freight
Staging Area to Beneficiaries
If feasible, airdrop
If not, boats, helicopters, small trucks, animal carts…
Warehouse
Staging Area
Beneficiaries (Disaster Zone)
500 to 2000 miles
~ 100 miles
Supplier 40

41. Mobilization and Procurement Delivery to Beneficiaries
Response Time
Current Timeline
Mobilization and Procurement
(21 days)
Delivery to Beneficiaries
(7 days)
Proposed Timeline
Long Haul Transit
(1-2 day)
Last “100-Mile”
(1-2 day)
Mobilization
(3 days) 41

42. Challenges
Limited space available on commercial aircraft on short-notice basis
Charters appear to offer potential solution
Design requirements of the shelter must be more focused on the goal
Immediate (smaller and lighter)
Temporary (so smaller and lighter may be ok)
Questions: Models to balance pre-positioned stocks vs expensive air freight in an environment of tight budgets and volatile demand. 42

43. Milliken Domestic and XYZ
Freight Consolidation
Where are the opportunities?
Volume
Sensitivity to distance
What are the economics?
Very hard to estimate LTL rates on lanes we don’t use
What Supply/Demand?
Model each customer/supplier or aggregate?
Volatility and Service
Model uses average volumes through consolidation, actual volumes fluctuate
Both a frequency and a volume component to truck costs
Optimization limitation (other)
Fooling the fixed costs 43

44. Milliken Asia Model of total costs based on number and location of DCs
How is this different than BMW Frequency project? (Claim: It’s harder)
Data issues
Too much required, too little available
Demand! What other approaches?
Safety Stock: How to calculate from historical order information 44

45. Projects
I hope you have gotten meaningful feedback from me and your sponsor on your projects. If not. See me.
Pleased with level of work. Always possible to do more, better, …
Get me your files! Organized
Assessment of contributions (any form)
If you want to participate in Summer Special Topics Course get a Request for Approval of Special Projects form from Pam or Valarie for me to sign 45

46. Exam Scheduled for 11:30 – 2:20 Friday May 5 Flexible about dates
Can’t hurt your grade 46