Presensattion
Distribution and Network Models
Transportation Problem
• Network Representation
• General LP Formulation
Transshipment Problem
• Network Representation
• General LP Formulation
Shortest route method
• Network Representation
• General LP Formulation
© 2008 Thomson South-Western. All Rights Reserved
Slide 1
Transportation, Assignment, and
Transshipment Problems
A network model is one which can be represented by a set of nodes, a set of arcs, and functions (e.g. costs, supplies, demands, etc.) associated with the arcs and/or nodes.
Transportation, assignment, transshipment, shortest-route, and maximal flow problems of this chapter as well as the minimal spanning tree and
PERT/CPM problems (in others chapter) are all examples of network problems.
© 2008 Thomson South-Western. All Rights Reserved
Slide 2
Transportation, Assignment, and
Transshipment Problems
Each of the five models of this chapter can be formulated as linear programs and solved by general purpose linear programming codes.
For each of the five models, if the right-hand side of the linear programming formulations are all integers, the optimal solution will be in terms of integer values for the decision variables.
However, there are many computer packages
(including The Management Scientist) that contain separate computer codes for these models which take advantage of their network structure.
© 2008 Thomson South-Western. All Rights Reserved
Slide 3
Transportation Problem
The transportation problem seeks to minimize the total shipping costs of transporting goods from m origins (each with a supply si) to n destinations
(each with a demand dj), when the unit shipping cost from an origin, i, to a destination, j, is cij.
The network representation for a transportation problem with two sources and three destinations is given on the next slide.
© 2008 Thomson South-Western. All Rights
Transportation Problem
• Network Representation
• General LP Formulation
Transshipment Problem
• Network Representation
• General LP Formulation
Shortest route method
• Network Representation
• General LP Formulation
© 2008 Thomson South-Western. All Rights Reserved
Slide 1
Transportation, Assignment, and
Transshipment Problems
A network model is one which can be represented by a set of nodes, a set of arcs, and functions (e.g. costs, supplies, demands, etc.) associated with the arcs and/or nodes.
Transportation, assignment, transshipment, shortest-route, and maximal flow problems of this chapter as well as the minimal spanning tree and
PERT/CPM problems (in others chapter) are all examples of network problems.
© 2008 Thomson South-Western. All Rights Reserved
Slide 2
Transportation, Assignment, and
Transshipment Problems
Each of the five models of this chapter can be formulated as linear programs and solved by general purpose linear programming codes.
For each of the five models, if the right-hand side of the linear programming formulations are all integers, the optimal solution will be in terms of integer values for the decision variables.
However, there are many computer packages
(including The Management Scientist) that contain separate computer codes for these models which take advantage of their network structure.
© 2008 Thomson South-Western. All Rights Reserved
Slide 3
Transportation Problem
The transportation problem seeks to minimize the total shipping costs of transporting goods from m origins (each with a supply si) to n destinations
(each with a demand dj), when the unit shipping cost from an origin, i, to a destination, j, is cij.
The network representation for a transportation problem with two sources and three destinations is given on the next slide.
© 2008 Thomson South-Western. All Rights