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Unformatted text preview: Thai Naval Transportation Problem Hern an Abeledo The George Washington University Abeledo (GWU) Thai Naval Transportation Problem 1 / 16 The Problem I Thailand inducts naval draftees at three drafting centers. Then the draftees must each be sent to one of three naval bases for training. The cost of transporting a draftee from a drafting center to a base is given in Table 1. Each year, 1,000 men are inducted at center 1; 600 at center 2; and 700 at center 3. Base 1 can train 1,000 men a year, base 2, 800 men, and base 3, 700 men. After the inductees are trained, they are sent to Thailands main naval base (B). They may be transported on either a small ship or a large ship. It costs $5,000 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. Formulate an IP that will minimize the total cost of transporting men from drafting centers to their bases, and from the training bases to the main base. Table: Transportation Costs per Trainee To ($) From Base 1 Base 2 Base 3 Center 1 200 200 300 Center 2 300 400 220 Center 3 300 400 250 Abeledo (GWU) Thai Naval Transportation Problem 2 / 16 The Problem II Table: Boat Tours Tour Number Locations Visited Miles Traveled 1 B1B 370 2 B12B 515 3 B23B 665 4 B2B 460 5 B3B 600 6 B13B 640 7 B123B 720 Abeledo (GWU) Thai Naval Transportation Problem 3 / 16 The Problem, version 1 1 2 1 3 2 1 B Main Base Training Bases Induction Centers 1 Ships 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 x cb Pick bs T st Tours Abeledo (GWU) Thai Naval Transportation Problem 4 / 16 Formulation Phase I Formulate stage 1 of the problem like a transportation problem. Let x cb the number of trainees transported from center c to base b , with c = 1 , 2 , 3, and b = 1 , 2 , 3. The cost of a given transportation will be Stage 1 Cost = X c X...
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 Fall '08
 HernanAbeledo

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