Backwaters Essay

1267 words - 6 pages

Transportation Model

1

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
locations.

– 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
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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
Demand

Rim Values

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

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Transportation network: LP formulation
Decisions:
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:
Minimize

Total Cost = ∑i ∑j cijXij

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

= 100

X21+X22+X23

From Farm B (i=2)

= 200
X31+X32+X33 = 200

From Farm C (i=3)

B. Demand constraints…
To Project 1 (j=1) X11
X12
To Project 2 (j=2)
To Project 3 (j=3)

+X21

+ X31

+X22

X13

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

= 50

+X32

+X23

Xij >= 0

+X33

= 150
= 300

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

Input and Output Worksheet for the Transportation
(topsoil) Problem

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Parameter Specification Screen for the Topsoil
Transportation Problem

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Solver Options Screen

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Solver Results

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Answer Report for the Topsoil Transportation
Problem

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Sensitivity Report for the Topsoil Transportation
Problem

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

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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).

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Special Cases of Transportation Problems
(cont’d)
• 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.
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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

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A Network Diagram of a Transshipment Problem

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