1. Frequency
John H. Vande Vate
Fall, 2002 1

2. Review Our initial case study Direct deliveries Consolidation
Transportation Costs: $ ,800
Inventory Costs at DCs: $ 4,891,300
Inventory Costs at Plants: $ ,900
Total: $ ,757,000
Consolidation
Transportation Costs: $ ,000
Inventory Costs at DCs: $ 23,250,000
Inventory Costs at Plants: $ ,500
Total: $ 23,942,500! 2

3. The Trade Off Consolidation Increased Inventory at the Warehouse
Increased Transportation
Decreased Inventory at the DCs 3

4. Frequency Ship in less-than-full truck load quantities Why?
Increase Transportation … 4

5. Selecting Frequency Trade off Recognize this? Transportation cost
Truck costs the same regardless of load
Inventory cost
More the truck carries the greater the inventory at both ends
Recognize this? 5

6. A Model Start with the direct model Consider CPU’s from Green Bay
Q = quantity to send in each truck
Constraint: Q  6,000
Annual transportation cost to 1 destination
$/mile * Miles/trip * Trips/year
$1* 1000 * ?
Trips/year = Annual Demand/Q = 2,500/Q 6

7. More Model Annual transport cost to 1 destination Inventory cost
$1*1,000*2,500/Q = 2,500,000/Q $/year
Inventory cost
Start with 1 destination
Expand to many destinations
Inventory with 1 destination
Holding % * $/item * Average Inventory level
Average Inventory level = ? 7

8. EOQ Model Total Cost With 1 destination
$1*1,000*2,500/Q *$300*Q (or Q/2)
General Form with 1 destination
A = fixed cost per trip = $1,000
D = Annual Demand = 2,500
h = Holding percentage = 0.15
C = Cost per item = $300
Total Cost = AD/Q + hC*Q 8

9. Optimal Frequency Do the math Discrete Thinking
dTotalCost/dQ = 0
Discrete Thinking
One more item on the truck
Inventory cost of that item is hC
Transport impact is to save
AD/Q – AD/(Q+1) = AD/[Q(Q+1)] ~ AD/Q2
Stop adding when costs = savings
hC = AD/Q2
Intuition: Balance Inventory and Transport Cost
hCQ = AD/Q
Best Answer: Q = AD/hC 9

10. Optimal Frequency With One destination What if it had been 23,500?
A = fixed cost per trip = $1,000
D = Annual Demand = 2,500
h = Holding percentage = 0.15
C = Cost per item = $300
Total Cost = AD/Q + hC*Q
Q* = AD/hC = 2,500,000/45 ~ 235
What if it had been 23,500?
Remember, Q  6,000 10

11. Total Cost 11

12. With Several Destinations
item-days inventory at the plant accumulated for each shipment to DC #1, say, if the shipment size is Q?
Q2/(2*Production Rate) Q 12
Q/Production Rate

13. Total Item-Days How many such shipments will there be?
Annual Demand at DC #1/Q
So, the total item-days per year from shipments to DC #1 will be…
Q2/(2*Production Rate)*Demand at DC/Q
Q*Demand at DC/(2*Production Rate)
So, making shipments of size Q to DC #1 adds what to the average inventory at the plant? 13

14. Effect on Average Inventory
Q*Demand at DC/(2*Production Rate)
Example: Q*2500/(2*100*2500) = Q/200
Correct EOQ for Direct Shipments:
Total Cost:
hC*Q*D/(2*Production Rate)
+ hC*Q/2
+A*D/Q
Q* = 2*A*D/hC P/(D+P) 14

15. In Our Case Since Demands at the n DCs are equal
P/(D+P) = nD/(nD+D) = n/(n+1)
Q* = 2*A*D/hC P/(D+P)
Q* = 2*A*D/hC n/(n+1)
Q* = 2*1000*2500/(0.15*30) 100/101
Q* = 332
The main point is the 2 – that’s 40% larger!
Why? 15

16. Total Cost of Direct Strategy
CPU’s Q* = 332
Consoles Q* = 574
Monitors/TV’s Q* = 406
Transport Costs
CPU’s = 100*2500*1000/332 = $753,000
Monitors = 100*5000*1000/406 = $1,232,000
Consoles = 100*2500*1000/574 = $436,000
Total $2,421,000 16

17. Inventory Costs Inventory Costs CPU’s Consoles Monitors
At Plant Q/2 Why?
At DC Q/2
Total 101*Q/2
CPU’s
15%*$300*101*332/2 = $754,000
Consoles
15%*$100*101*574/2 = $435,000
Monitors
15%*$400*101*406/2 = $1,230,000
Total: $2,419,000 17

18. Strategies
Direct Full Trucks: $ 23,942,500 Consolidate Full Trucks: $ ,757,000
Direct EOQ: $ ,842,000
Other strategies? 18

19. Consolidate & EOQ EOQ from Plant to Indianapolis
This is like serving one destination
Q* = AD/hC
CPU’s from Green Bay
Q* = 400*250000/0.15*300 = 1490
Consoles from Denver
Q* = 1100*250000/0.15*100 = 4281!
Monitors/TV’s from Indianapolis
Q* = 0*500000/0.15*100 = 0 19

20. From the Plants Green Bay to Indianapolis Denver to Indianapolis
Transport: 400*250,000/1490 = $67,114
Inventory: The same = $67,114
Total = $134,228
Denver to Indianapolis
Transport: 1100*250,000/1,000 = $275,000
Inventory: 0.15*100* = $ 15,000
Total = $290,000 20

21. From the Warehouse This is a case of serving many D = 2,500
Q* = 2*A*D/hC P/(D+P) What’s P?
Q* = 2*A*D/hC n/(n+1)
D = 2,500
C = $1,200 Why?
A = $1,000
Q* = 2*1,000*2,500/180 100/101 = 165 21

22. Costs from Warehouse Transportation: Inventory:
1000*2,500/165 = $15,152 per DC
Total $1,515,200
Inventory:
0.15*1,200*101*Q/2 = $1,500,000
Total Cost of Strategy ~$3,439,000 22

23. Review of Options Direct Full Trucks: $ 23,942,500
Consolidate Full Trucks: $ ,757,000
Direct EOQ: $ ,842,000
Consolidate EOQ: $ 3,439,000
Other strategies? 23

24. Costs We Omitted? 24

25. Pipeline Inventory
Ford Finished Vehicle Case Study 25