Some homogeneous goods are stocked in
storage centers in quantities
. The goods are required in
corresponding consumption centers
. Knowing the unit transportation costs
from each storage center to each consumption center, a plan that uses all the goods (offers) and satisfies all the consumers (requests) is needed.
denotes the quantity of goods transported from storage center
to consumption center
. The following is a mathematical model of the problem, where we try to minimize the total transportation cost
is the total offer,
is the total request.
The transportation problem can be solved if
, we introduce a fictional consumption center with the offer
and transportation cost 0. if
, we introduce a fictional storage center with the request
and transportation cost 0.
The problem is shown for
. The result shows a matrix whose row and column sums are the
. This matrix shows the quantity that each storage center should ship to each consumption center. If
, we can obtain a 4×5 (
) matrix or a 5×4 (
) matrix, where the extra row or column corresponds to a fictional center.