Showing papers by "Aalto University published in 1977"
TL;DR: The bounds on variables are used to compute bounds on the optimal value when the problem is being solved by the simplex method, and the latter bounds may then be used as a termination criteria for the simples iterations for the purpose of finding a “sufficiently good” near optimal solution.
Abstract: Consider a standard linear programming problem and suppose that there are bounds available for the decision variables such that those bounds are not violated at an optimal solution of the problem (but they may be violated at some other feasible solutions of the problem). Thus, these bounds may not appear explicitly in the problem, but rather they may have been derived from some prior knowledge about an optimal solution or from the explicit constraints of the problem.
In this paper, the bounds on variables are used to compute bounds on the optimal value when the problem is being solved by the simplex method. The latter bounds may then be used as a termination criteria for the simples iterations for the purpose of finding a “sufficiently good” near optimal solution. The bounds proposed are such that the computational effort in evaluating them is insignificant compared to that involved in the simplex iterations. A numerical example is given to demonstrate their performance.
10 citations
TL;DR: The contribution of the paper lies in its unification of existing decomposition approaches and in showing that they can be generalized to apply to what the authors call arborescent linear programs.
Abstract: We apply what we call sequential projection to reformulate certain linear programs as recursive optimization problems. We then apply the standard idea of approximating the return function at each stage of the recursion by using inner (or outer) linearization, and iteratively refining the approximation until the original linear program has been solved. The contribution of the paper lies in its unification of existing decomposition approaches and in showing that they can be generalized to apply to what we call arborescent linear programs.
7 citations
TL;DR: Transport via the Siberian railway in trade between West Europe and Japan is clearly advantageous compared with sea transport as mentioned in this paper. But whether the Siberian transport route is productive for the Soviet Union measured by Western standards is difficult to say.
Abstract: Transport via the Siberian railway in trade between West Europe and Japan is clearly advantageous compared with sea transport. Whether the Siberian transport route is productive for the Soviet Union measured by Western standards is difficult to say. Some Western experts at least have expressed their doubts.
4 citations