solution
Four cargo ships will be used for shipping goods from one port to four other ports (labeled 1, 2, 3, 4). Any ship can be used for making any one of these four trips. However, because of differences in the ships and cargoes, the total cost of loading, transporting, and unloading the goods for the different ship-port combinations varies considerably, as shown in the following table: Port 1 2 3 4 Ship 1 2 3 4 $500 600 700 500
$400 600 500 400
$600 700 700 600
$700 500 600 600
The objective is to assign the four ships to four different ports in such a way as to minimize the total cost for all four shipments, (a) Describe how this problem fits into the general format for the assignment problem. c (b) Obtain an optimal solution (e) Reformulate this problem as an equivalent transportation prob- lem by constructing the appropriate parameter table. D.1 (d) Use the northwest comer rule to obtain an initial BF solu- tion for the problem as formulated in part). DI (e) Starting with the initial BF solution from part (d), interac- tively apply the transportation simplex method to obtain an optimal set of assignments for the original problem. DI (1) Are there other optimal solutions in addition to the one ob- tained in part (e)? If so, use the transportation simplex method to identify them.
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