1. Professor Goodchild Spring 08
Logistics Cost
Professor Goodchild
Spring 08

2. Follow the path of an item
Carried from production area to storage area
Held in temporary storage
Loaded into transport vehicle
Transported to the destination
Unloaded, handled, and held for consumption

3. What incurs cost? Overcoming distance (motion):
transportation cost (over the road/rail)
handling cost (through a terminal, in and out of vehicles)
Overcoming time (holding):
holding cost:
Rent (proportional to D’H)
Waiting (value*time*interest rate)
In transit
pipeline
How you calculate the value depends on the analysis you are doing (cost or price)
We will include all costs, regardless of who pays them (we are designing systems)

4. Cumulative Number of Items Diagram
Production (rate D’)
shipments
cumulative
number of
items
An item is a fixed quantity of infinitely divisible quantity (e.g. person, parcel, case of beer) H tm
Consumption (D’)
arrivals
time
Consider units on area

5. Queue Discipline FIFO: First In First Out LIFO: Last In First Out
Others
If LIFO inventory cost is usually underestimated

6. Holding cost: Rent proportional to max. accumulation
Independent of flow rate, D’
Proportional to max. time between dispatches

7. Holding cost: Waiting Cost associated with delay to items ciHi+citm
Stationary+pipeline inventory
Determining ci is difficult

8. Transportation Cost
Shipment cost has fixed and variable portions: cf+cvv (v is number of items)
Fixed cost: driver wage
Variable cost: increased fuel consumption
Cost for n shipments: cfn+cvV (V is total items across shipments, n is number of shipments)

9. Transportation cost Cost per item: cf/vavg+cv
Economies of scale from sharing fixed cost
Also cost per item is (cf/D’Havg)+cv
Transportation cost decreases with average headway
Holding cost increased with maximum headway
Therefore shipments should be spread so as to minimize the maximum (all the same)

10. Transportation cost and distance
cf is independent of v (items) but both cf and cv are typically functions of distance (d)
cf=cs+cdd
cv=c’s+c’dd
Cost for n shipments: cfn+cvV
csn+cddn+c’sV+c’ddV
Add cost of stopping: cs(1+ns)n+cddn+c’sV+c’ddV
So small we neglect it

11. Transportation cost Cost per item (divide by nvavg):
cs(1+ns)/vavg+cdd/vavg+c’s or
cs(1+ns)/D’Havg+cdd/D’Havg+c’s
If headways vary a lot so do shipment sizes, and therefore truck sizes, better to use consistent truck sizes (second reason to keep shipment sizes consistent)

12. Capacity Restrictions
Trans. Cost
Per
shipment cv cf
Slope is total cost per item, lowest
when truck full
vmax – number of items that will fit in vehicle
shipment size

13. Relationship to size
Magnitude of fixed and variable cost determine most economic choice as a function of shipment size.
Trans. Cost
Per
shipment
As shipment size increases, favor lower variable and higher fixed costs.
shipment size

14. Inventory Cost Captures time-value of holding product
Perishability, theft, opportunity cost of cash, insurance, shrinkage, obsolescence
Usually 10-15% for electronics
Value of good*interest rate*time

15. Exercise Fuel economy: 10 mpg Driver wages: $15/hour
Ignore depreciation of vehicle, insurance
Speed of vehicle: 25 mph
Price of fuel: $2.50 per gallon
Value of goods in a truck: $100,000
Interest rate: 6% per year
Time spent at DC: 3 days
Handling cost at DC: $50 per truck
Ignore rent, operating cost of DC
Calculate one way transportation
cost and one way inventory cost. 60
miles
100
miles
100
miles DC 40
miles
100
miles 50
miles 50
miles

16. Cost Comparison Transportation Inventory Handling Total Direct
3($60+$25)
=$255
3($2.74)
=$8.22 $0
$263.22
DC (3 days)
($36+$15)+
2($30+$12.50)
+($24+$10)
=$170
$4.93+
2($1.37)+
$1.10+
3*($49.32)
=$156.73
$150
$476.73
DC (1 days)
$49.32
=$58.09
$378.09

17. Hypothetical curves Minim cost shipment frequency total transportation
inventory
Shipment frequency
We will identify the optimal when we talk about distribution systems

18. Cumulative Number of Items Diagram
Production (rate D’)
shipments
cumulative
number of
items
An item is a fixed quantity of infinitely divisible quantity (e.g. person, parcel, case of beer) H tm
Consumption (D’)
arrivals
time
Consider units on area

19. Cumulative Number Diagram
Good for one origin/one destination problems
Identify production and consumption rates
Items waiting to be shipped
Shipment times
Shipment sizes
Items waiting to be consumed
Total wait time from production to consumption (if FIFO)
Headway (H)
Travel time
Units
Storage space proportional to max accumulation is D’H

20. Network Structures Trade-off inventory cost and transportation cost
Milk-run
Hub and spoke (distribution center)
Direct Shipping

21. Higher transportation expense
warehouse
crossdocks
No DC cost
Reduce lead times
Higher transportation expense
Good if fully loaded trucks or timely goods
Store goods to pool inventory risk
Trade-offs in size as more demand can be pooled, but then farther from destination
Not stored for a significant length of time
Sorted, consolidated, shipped out directly
Use different containers
Requires high volume

22. Exercise Inventory Pooling What is the inventory held
in the system without
the distribution center?
in the system with the
distribution center? 60
miles
100
miles
100
miles DC 40
miles
100
miles 50
miles 50
miles

23. Inventory Aggregation
Store 1
Store 2
Store 3
Average demand
10 units/day
20 units/day
30 units/day
Standard deviation of demand
2 units/day
4 units/day
6 units/day
Calculate number required on hand if held at 3 stores, central facility.
Online retailers as well as traditional retailers
Typically increases transportation cost (think outbound, but who pays?)

24. Inventory Management Improve service level Reduce logistics cost
Cope with randomness and seasonality
Speculate on price
Overcoming inefficiencies in managing the logistics system