# RAS - TAU - (RAS November7,2010 Team:TAUIE Mor Kaspi...

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Railway Application Section (RAS) P bl S l i C titi Problem Solving Competition November 7, 2010 Team: TAU IE Team: TAU IE Mor Kaspi and Tal Raviv*, Tel Aviv University, Israel

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Solution Method f l i MILP formulation + Specialized cuts and Domination rules Commercial Solver 2
Quality of results obtained S l i l 11 399 670 88\$ Solution value: 11,399,670.88\$ Absolute optimality gap: 0.30\$ (Relative gap: 2 63E 8) (Relative gap: 2.63E 8) Best known solution and 0.01% gap found in less than five minutes 3

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MIP Formulation Subject to
Cuts No Contract > No Fueling Fixed Cost 5

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Cuts Stops Subsequences inequalities 1000 2000 1000 1000 1000 0 2 3 1 5 4 L T V 4500 ocomotive ank olume = 4500 gallons 6
Cuts Yards Subsequences Inequalties 1000 2000 1000 1000 1000 3 2 3 4 1 1 + + 1 y 2 y 3 y 4 y 3 + y 4 1 7

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Cuts Minimal number of fuels per locomotive A tight lower bound can be calculated in polynomial time by casting each locomotive problem as shortest path problem 8 TR1
Slide 8 TR1 אמגוד Tal Raviv, 24/10/2010

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Cuts Enough Fuel To Reach the Next Station 9
Cuts Locomotive decomposition 10

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