Page 26 - Azerbaijan State University of Economics

Salah Salimian, Kiumars Shahbazi, Mahdi M. Beknazar: Locating The Sale Agents In Spoke Model
Through Uniform Distribution Of Consumers

Each sale agent is inevitable to invest F > 0 to create sale agents. At the end, it is
assumed that transportation cost per unit of distance is t=1.
In this condition, the issue for monopolist is determination of optimal location for sale
agent (when he wants to have a sale agent or several sale agents) and the decision
making interval on the number of sale agents. In addition, assume that B indicates the
1
D
main value considered for product by each consumer and B > + + p is the
2
desirability function of each i consumer, i= 1, 2, …, N defined as follow:

D
B − − p ℎ

1
B − ( − ) − p ℎ
D

U i 2 (1)
1
B − ( + ) − p ℎ ℎ
D
2
{ 0 ℎ

Such that p , is the received price by sale agent from final consumer. Moreover, these
D
relations indicate that if the consumers purchase from the sale agent located at the
D
center or any other street, all will pay the same p price.

The above desirability function is extracted such that:
If the consumer is located in one of the streets and the sale agent at city center, in
order to purchase from sale agent at the center, he should pay the product price in
addition to transportation costs (in respect to distance from city center).

If the consumer is located in one of the streets and the sale agent is also on the same
street, in order to purchase from sale agent in its street, he should pay the product price
in addition to transportation costs (in respect to distance from sale agent on the same
street).

If the consumer is located in one of the streets and the sale agent on another street, in
order to purchase from sale agent in other street, he should pay the product price in
addition to transportation costs (first transportation cost to city center and then
transportation cost to sale agent).

In case of lack of purchase, he will achieve desirability equal to zero.
The monopolist confronts with the following states in deciding on the location and the
number of sale agents: 1. launching a sale agent at city center or margin areas; 2.
launching a sale agent at city center or several sale agents in suburb areas or margins;
3. launching an agent at city center or a sale agent at city center and several sale agents
in suburb areas.

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