Multiple Criteria Public Investment Decision Making By Mixed Integer Programming
Multiple Criteria Public Investment Decision Making By Mixed Integer Programming
Jeremy F Shapiro
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The group G = 2^, Y = {(x, z)|x. = or I, s . = 0, 1, 2, ... U. ) and the corresponding dual problem can be shown to be tlie linear prograiraning relaxation of (7). The k k+1 groups here have the property that G is a subgroup of G, implying directly that ^k+1 supergroup of G . The critical step in this approach to solving the IP problem (7) is that if an optimal solution to the kth dual does not yield an optimal integer solution, then k+1 k+1 k we are able to construct the supergroup G so that Y... c Y . Moreover, the construction eliminates the infeasible IP solutions (x, s) £ Y which are used in combination by the IP dual problen to produce a fractional solution to the optimality conditions. Since the set of feasible solutions to (7) is finite, the process must converge in a finite number of IP dual problem constructions to an ipdual problem yielding an optimal solution to (7) by the optimality conditions. The IP dual problem (9) is actually a large scale linear programming problem, t t T Let Y = {x, s ] be an eniraieration of Y.
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