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OPSM 301 Operations Management
Class 21:
Logistic Drivers: Facilities and Transportation
Koç University
Zeynep [email protected]
Drivers of Supply Chain Performance
Efficiency Responsiveness
Inventory Transportation Facilities Information
Supply chain structure
Drivers
The Logistics Network
The Logistics Network consists of:
Facilities:Vendors, Manufacturing Centers, Warehouse/ Distribution Centers, and Customers
Raw materials and finished products that flow between the facilities.
4
Example: Efes Distribution Network
5
Costs
$0$2$4$6$8
$10$12$14$16$18$20
0 5 10 15
Number of DC's
Co
st (
$ m
illio
n)
Total Cost
Inventory
Transportation
Fixed Cost
Total cost
Inventory
transportation
Fixed costs
Number of distribution centers
cost
s ($
m
ilio
n)
6
Comparison between industries
Sources: CLM 1999, Herbert W. Davis & Co; LogicTools
Avg.NumberOf Depots 3 14 25
Pharmaceutical Grocery Chemicals
- Service is not important(or shipping is easy)- Inventory is more expensive than transportation
- Service is very important-Outbound transportation is -expensive
Transportation in the Supply Chain
Throughout the supply chain
SUPPLIERS
CUSTOMERS
WAREHOUSE
PRODUCTION
WAREHOUSE
Transport.
Transport.
Transport.
Transport.
Transportation Problem
DesMoines(100 unit capacity)
Fort Lauderdale(300 units capacity)
Cleveland(200 units required)
Evansville(300 units capacity)
Albuquerque(300 units required)
Boston(200 units required)
How much should be shipped from several sources to several destinations – Sources: Factories, warehouses, etc.– Destinations: Warehouses, stores, etc.
Transportation models– Find lowest cost shipping arrangement– Used primarily for existing distribution
systems
Transportation Problem
The Transportation Problem
D(demand)
D(demand)
D(demand)
D(demand)
S(supply)
S(supply)
S(supply)
Requirements for Transportation Model
List of origins and each one’s capacity
List of destinations and each one’s demand
Unit cost of shipping
The transportation problem
The setting– n factory (supply) locations– supplying m markets (demand points)– Cost of shipping one unit from factory i to
market j is cij
– Ki is the capacity of factory i– Dj is the demand in market j
Formulate as an LP
Transportation Model
Which market is served by which plant?
Which supply sources are used by a plant?
xij = Quantity shipped from plant site i to customer j 0
..
1
1
1 1
x
Kx
Dx
ts
xcMin
ij
i
m
jij
j
n
iij
n
i
m
jijij
5-13
A Transportation Problem:Tropicsun
Distances (in miles)CapacitySupply
275,000
400,000
300,000 225,000
600,000
200,000Mt. Dora
1
Eustis
2
Clermont
3
Groves
Ocala
4
Orlando
5
Leesburg
6
Processing Plants
21
50
40
3530
22
55
25
20
Defining the Decision Variables
Xij = # of bushels shipped from node i to node j
Specifically, the nine decision variables are:
X14 = # of bushels shipped from Mt. Dora (node 1) to Ocala (node 4)
X15 = # of bushels shipped from Mt. Dora (node 1) to Orlando (node 5)
X16 = # of bushels shipped from Mt. Dora (node 1) to Leesburg (node 6)
X24 = # of bushels shipped from Eustis (node 2) to Ocala (node 4)
X25 = # of bushels shipped from Eustis (node 2) to Orlando (node 5)
X26 = # of bushels shipped from Eustis (node 2) to Leesburg (node 6)
X34 = # of bushels shipped from Clermont (node 3) to Ocala (node 4)
X35 = # of bushels shipped from Clermont (node 3) to Orlando (node 5)
X36 = # of bushels shipped from Clermont (node 3) to Leesburg (node 6)
Defining the Objective Function
Minimize the total number of bushel-miles.
MIN: 21X14 + 50X15 + 40X16 +
35X24 + 30X25 + 22X26 +
55X34 + 20X35 + 25X36
Defining the Constraints
Capacity constraintsX14 + X24 + X34 <= 200,000 } Ocala
X15 + X25 + X35 <= 600,000 } Orlando
X16 + X26 + X36 <= 225,000 } Leesburg
Supply constraintsX14 + X15 + X16 = 275,000 } Mt. Dora
X24 + X25 + X26 = 400,000 } Eustis
X34 + X35 + X36 = 300,000 } Clermont
Nonnegativity conditionsXij >= 0 for all i and j
Implementing the Model