ps6sol - 1.203J / 6.281J / 13.665J / 15.073J / 16.76J /...

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1.203J / 6.281J / 13.665J / 15.073J / 16.76J / ESD.216J Logistical and Transportation Planning Methods Problem Set 6 Due: December 6, 2006 Problem 1
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1.203J / 6.281J / 13.665J / 15.073J / 16.76J / ESD.216J Logistical and Transportation Planning Methods
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1.203J / 6.281J / 13.665J / 15.073J / 16.76J / ESD.216J Logistical and Transportation Planning Methods Problem 2 Problem 3 (a) As suggested, we can prove the results by contraposition. Let’s suppose that the set of nodes T contains no solution to the 1-median problem. Then, the solution one of S’s nodes. Let y S be that node. Then J(y) = T j j y d j h ) , ( ) ( + S j j y d j h ) , ( ) ( = + T j j t d t y d j h )] , ( ) , ( )[ ( + S j j y d j h ) , ( ) ( = ) , ( ) ( t y d T H + T j j t d j h ) , ( ) ( + S j j y d j h ) , ( ) ( ) , ( ) ( t y d S H + T j j t d j h ) , ( ) ( + S j j y d j h ) , ( ) ( = T j j t d j h ) , ( ) ( + + S j t y d j y d j h )] , ( ) , ( )[ ( = T j j t d j h ) , ( ) ( + S j j t d j h ) , ( ) ( = J(t) This implies that the 1-median could be located at T t , which contradicts our initial assumption. Therefore, the set of nodes T contains at least one solution to the 1-median problem on G(N,A).
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1.203J / 6.281J / 13.665J / 15.073J / 16.76J / ESD.216J Logistical and Transportation Planning Methods (b) From part (a), we know that there is an optimal solution in T. T
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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ps6sol - 1.203J / 6.281J / 13.665J / 15.073J / 16.76J /...

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