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Let a polyhedral convex set be given by a finite number of linearinequalities and consider the problem to project this set onto a subspace. Thisproblem, called polyhedral projection problem, is shown to be equivalent tomultiple objective linear programming. The number of objectives of the multipleobjective linear program is by one higher than the dimension of the projectedpolyhedron. The result implies that an arbitrary vector linear program (witharbitrary polyhedral ordering cone) can be solved by solving a multipleobjective linear program (i.e. a vector linear program with the standardordering cone) with one additional objective space dimension.

Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming