Ch 6: Transportation

1
Ch 6 Transportation

• I. Formulation
• II. Northwest Corner
• III. Production Smoothing

2
Formulation

• Application Decision about how many units to
  ship from factory to warehouse, given several
  factories and several warehouses
• If planning new factory or new warehouse, can be
  used to decide location (ex Pennsylvania Rite
  Aid built warehouse at Palmdale)

3
Linear Programming

• Objective MINIMIZE transportation cost
• Constraints Supply, demand
• Supply Factory capacity
• Demand Warehouse requirement

4
Example

• Three warehouses Albuq, Boston, Cleve
• Three factories Des Moines,Evansville,
• Ft Lauderdale
• Next slide Data given

5
Transportation matrix
To From A B C Supply
D 100
E 300
F 300
Demand 300 200 200 700
6
Northwest Corner

• Start at northwest corner
• Number of units MIN (supply,demand)
• Ex Row D,Col A MIN(100,300)100
• After allocation, subtract units

7
Transportation matrix
To From A B C Supply
D 100 100
E 300
F 300
Demand 300 200 200 700
8
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 300
F 300
Demand 300-100 200 200 200 700
9
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 300
F 300
Demand 300-100 200 200 200 700
10
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 300-200 100
F 0 300
Demand 300-100 200 200 200 700
11
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 100 300-200 100
F 0 300
Demand 300-100 200 200 200 700
12
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 100 0 300-200 100
F 0 300
Demand 300-100 200 200-100 100 200 700
13
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 100 0 300-200 100
F 0 100 300
Demand 300-100 200 200-100 100 200 700
14
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 100 0 300-200 100
F 0 100 300-100 200
Demand 300-100 200 200-100 100 200 700
15
Transportation matrix
To From A B C Supply
D 100 0 0 100
E 200 100 0 300-200 100
F 0 100 200 300-100 200
Demand 300-100 200 200-100 100 200 700
16
MIN Cost

• Would need unit cost between factory and
  warehouse
• Use Excel to minimize cost
• Northwest Corner is initial allocation

17
Production Smoothing

• Factory replaced by production period
• Warehouse repl by demand period

18
Two month example
Month Feb Mar Supply
Feb 15 5inventory end of Feb 20
Mar 0 20 20
Demand 15 25 40