Backwaters Essay

1267 words - 6 pages

Transportation Model


Transportation Problems
• Transportation Problem
– A distribution-type problem in which supplies of goods that are
held at various locations are to be distributed to other receiving

– The solution of a transportation problem will indicate to a
manager the quantities and costs of various routes and the
resulting minimum cost.
– Used to compare location alternatives in deciding where to
locate factories and warehouses to achieve the minimum cost
distribution configuration.
– Some of the examples are: Shipment from factories to
warehouses, Shipment between departments within a
company, Shipment from warehouses to retailers

Formulating the Model
• A ...view middle of the document...

• The supply and demand values along the outside rim of a
tableau are called rim values.

Rim Values

Equal Supply and

Rim Values

Transportation Table for Harley’s Sand and Gravel
(Topsoil Shipment)


Transportation network: LP formulation
Xij = the tons of top soil shipment from a source Farm i to a demand Project j.
(i = 1,2,3 & j = 1,2,3)

Objective function:

Total Cost = ∑i ∑j cijXij

Transportation network: LP formulation
A. Supply constraints…
From Farm A (i=1) X11+X12+X13

= 100


From Farm B (i=2)

= 200
X31+X32+X33 = 200

From Farm C (i=3)

B. Demand constraints…
To Project 1 (j=1) X11
To Project 2 (j=2)
To Project 3 (j=3)


+ X31



C. Non-negativity constraints?
D. Any other constraints? Integer?

= 50



Xij >= 0


= 150
= 300

Total supply equals total
demand and hence all
constraints are written as

Input and Output Worksheet for the Transportation
(topsoil) Problem


Parameter Specification Screen for the Topsoil
Transportation Problem


Solver Options Screen


Solver Results


Answer Report for the Topsoil Transportation


Sensitivity Report for the Topsoil Transportation


Input and Output Sheet for the Revised Transportation (topsoil) Problem
When the Shipping Route between Farm B and Project 1 is Prohibited


Special Cases of Transportation Problems
• Maximization
– Transportation-type problems that concern profits or revenues rather
than costs with the objective to maximize profits rather than to
minimize costs.

• Unacceptable Routes
– Certain origin-destination combinations may be unacceptable due to
weather factors, equipment breakdowns, labor problems, or skill
requirements that either prohibit, or make undesirable, certain
combinations (routes).


Special Cases of Transportation Problems
• Unequal Supply and Demand
– Situations in which supply and demand are not equal such that it is
necessary to modify the original problem so that supply and demand
are equalized.
– Quantities in dummy routes in the optimal solution are not shipped
and serve to indicate which supplier will hold the excess supply, and
how much, or which destination will not receive its total demand,
and how much it will be short.

– The dummy is assigned unit cost of zero for each cells.

The Unbalanced Transportation Model
(1 of 2)
- When demand exceeds supply a dummy row is added to the tableau.

An Unbalanced Model
(Demand > Supply)

The unit
transportation cost
is zero

The Unbalanced Transportation Model
(2 of 2)
- When supply exceeds demand, a dummy column is added to the tableau.

An Unbalanced Model (Supply > Demand)

The unit
transportation cost
is zero

Transshipment Model


A Network Diagram of a Transshipment Problem



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