Logistics Cost Part II
Professor Goodchild
Spring 11
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
Cumulative Number Diagram
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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
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
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
100
miles
100
miles
60
miles
Value of goods in a truck: $100,000
Interest rate: 6% per year
DC
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.
100
miles
50
miles
40
miles
50
miles
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)
($36+$15)+
2($30+$12.50)
+($24+$10)
=$170
$4.93+
2($1.37)+
$1.10+
$49.32
=$58.09
$150
$378.09
Hypothetical curves
Minim cost shipment frequency
total
transportation
cost
inventory
Shipment frequency
We will identify the optimal when we talk about distribution systems
Network Structures
• Trade-off inventory cost and transportation
cost
• Best choice depends on qualities of product,
customer demand, and network
• Milk-run
• Hub and spoke (distribution center)
• Direct Shipping
warehouse
•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
crossdocks
•Not stored for a
significant length of time
•Sorted, consolidated,
shipped out directly
•Use different containers
•Requires high volume
Exercise
Inventory Pooling
What is the inventory held
in the system without
the distribution center?
60
miles
100
miles
What is the inventory held
in the system with the
distribution center?
100
miles
100
miles
DC
50
miles
40
miles
50
miles
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?)
Inventory Management
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Improve service level
Reduce logistics cost
Cope with randomness and seasonality
Speculate on price
Overcoming inefficiencies in managing the
logistics system
Distribution Systems
Prof. Anne Goodchild
Spring 2010
Distribution systems
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One to one
One to many
Many to one
Many to many
1-1 Distribution Examples
• Port to rail head drayage
• Small in scale and/or scope
• Decisions:
– Shipment frequency
– Route (this is typically a function of the network
and travel times)
– Shipment times
1-1 Distribution
• Constant demand
• Trade-off inventory and transportation cost:
z=minv{(ch/D’)v+cf/v}, s.t. v<vmax
• cf: fixed transportation cost
• ch: holding cost
• v*=sqrt{cfD’/ch}
EOQ (economic order quantity)
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z=minv{Av+B/v+C}
v*=sqrt{B/A}
z*=2sqrt{AB}
If v*>vmax use v=vmax
• v* makes both of the terms in the objective
function equal (motion cost = holding cost)
Lot Size problem with Variable Demand
• D(t) gives cumulative number of items demanded
between 0 and t
• D’(t) is variable demand rate
• Seek the set of times when shipments are to be
received and the shipment sizes that will minimize
sum of motion plus holding costs over some time
period
• With an infinite time horizon and constant demand
this is the EOQ problem just discussed
When holding cost close to rent
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Variable demand
Inventory cost negligible (big, cheap items)
Increases with maximum inventory accumulation
Recall motion cost independent of shipment sizes
and times (only dependent on total amount moved
or average)
• Thus we want to choose times and sizes to minimize
holding cost
• V*= D(tmax)/n, all equal minimizes cost
• cost/time=crD(tmax)/n+cfn/tmax, find n by minimizing
When rent is negligible
• Small, expensive items
• Simple expression cannot be obtained unless
D(t) varies slowly with t (CA method)
• Use numerical solution (e.g. dynamic
programming)
One to Many Distribution
• Movement of containers from the port to landside
destinations
• Delivery systems
• Decisions:
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Network structure
Fleet size (VRP and TSP)
Shipment frequency
Use of an intermediate facility (minimizing logistics cost)
Many to one distribution
• Export containers being delivered to a marine port
• Collection systems
• The same analytical methods can be used as with
one to many distribution
• Decisions:
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Network structure
Fleet size
Shipment frequency
Use of an intermediate facility
Many to Many Distribution
• Global distribution of marine containers
• Collection and distribution systems
• Decisions:
– Network structure
– Coordination of inbound
and outbound shipments
Many to many distribution
• The problem can often, and should often, be
broken down into pieces
– Inbound logistics (many to one)
– Outbound logistics (one to many)
– Be mindful of who is responsible for cost within
the supply chain
– Most supply chains are not operated by the same
entity
– Use terminals to consolidate some of the flow
Transshipment
Transshipment
1
Reduce line-haul cost through consolidation
Transshipment
Influence area
2
1
2
Introduce levels of transshipment terminals
These can be used on the collection side or the distribution side
Consider the use of tiered airports in a hub and spoke system
Influence Areas
Cost per item delivered
total
outbound
inbound
terminal
Size of influence area
Themes
• Scale
– What part of the logistics system will you
consider?
– Typically determined by ownership and operating
units but it depends on your goals
• Consistency
– Logistics systems are more manageable