Problem 4 Thailand inducts naval draftees at three drafting centres. Then the draftees must
each be sent to one of three naval bases for training. The cost of transporting a draftee from a
drafting centre to a base in given in Table 1. Each year, 1000 men are inducted at centre 1; 600
at centre 2 and 700 at centre 3. Base 1 can train 1000 men a year, base 2, 800 men; and base
3, 700 men. After the inductees are trained, they are sent to Thailand's main naval base (B).
They may be transported on either a small ship or a large ship. It costs $5000 plus $2 per mile
to use a small ship. A small ship can transport up to 200 men to the main base and may visit
up to two bases on its way to the main base. Seven small and five large ships are available.
It costs $10,000 plus $3 per mile to use a large ship. A large ship may visit up to three bases
on its way to the main base and may transport up to 500 men. The possible " tours" for each
type of ship are given in Table 2. Assume that the assignment of draftees to training bases
is done using the transportation method. Then, formulate an IP that will minimize the total
cost incurred in sending the men from the training bases to the main base. (Hint: Let y;j =
number of men sent by tour i from base j to main base (B) on a small ship, ry = number of
men sent by tour i from base j to B on a large ship, S; = number of times tour i is used by a
small ship and L; = number of times tour i is used by a large ship).
Table 1: The cost of transporting a draftee from a drafting centre to a base
To
From
Base 1 Base 2 Base 3
Centre 1
$200
$200
$300
Centre 2
$300
$400
$220
Centre 3
$300
$400
$250
Table 2: The possible "tours" for each type of ship
Tour Number Locations Visited Mile Travelled
1
B-1-B
370
B-1-2-B
515
B-2-3-B
665
B-2-B
460
B-3-B
600
B-1-3-B
640
B-1-2-3-B
720