# Logistics

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```					                 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

60       Value of goods in a truck: \$100,000
miles    Interest rate: 6% per year

Time spent at DC: 3 days
Handling cost at DC: \$50 per truck
100             100                DC       Ignore rent, operating cost of DC
miles           miles
Calculate one way transportation
cost and one way inventory cost.

50      40         50
100
miles   miles      miles
miles
Cost Comparison
Transportation   Inventory    Handling   Total
Direct   3(\$60+\$25)       3(\$2.74)     \$0         \$263.22
=\$255            =\$8.22

DC (3    (\$36+\$15)+       \$4.93+       \$150       \$476.73
days)    2(\$30+\$12.50)    2(\$1.37)+
+(\$24+\$10)       \$1.10+
=\$170            3*(\$49.32)
=\$156.73
DC (1    (\$36+\$15)+       \$4.93+       \$150       \$378.09
days)    2(\$30+\$12.50)    2(\$1.37)+
+(\$24+\$10)       \$1.10+
=\$170            \$49.32
=\$58.09
Hypothetical curves
Minim cost shipment frequency

total

transportation

cost

inventory

Shipment frequency

We will identify the optimal when we talk about distribution systems
Cumulative Number of Items
Diagram     Production (rate D’)

shipments

cumulative
number of
items

An item is a
fixed quantity
of infinitely                 H
divisible
quantity (e.g.
person,
parcel, case                 tm
of beer)                                            Consumption (D’)
arrivals

time                Consider units on area
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)
   Travel time
   Units
   Storage space proportional to max accumulation is D’H
Network Structures
   Trade-off inventory cost and transportation cost
   Milk-run
   Hub and spoke (distribution center)
   Direct Shipping
warehouse                crossdocks

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

Inventory Pooling

What is the inventory held
in the system without
60              the distribution center?
miles
What is the inventory held
in the system with the
distribution center?
100             100                DC
miles           miles

50      40         50
100
miles   miles      miles
miles
Inventory Aggregation
Store 1              Store 2             Store 3
Average            10 units/day 20 units/day 30 units/day
demand
Standard           2 units/day          4 units/day         6 units/day
deviation of
demand

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
   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 2009
Distribution systems
   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)
   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)
   Why should these be equal?
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
   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:
   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:
   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

total
Cost per item delivered

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

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