Abstract

GUILLEN-BURGUETE, S.; SANCHEZ-LARIOS, H.  and  VAZQUEZ-VAZQUEZ, J.G.. An Optimal Transportation Schedule of Mobile Equipment. J. appl. res. technol [online]. 2012, vol.10, n.5, pp.713-723. ISSN 2448-6736.

Motivated by a problem faced by road construction companies, we develop a new model to obtain an optimal transportation schedule of mobile machines which have to travel to execute tasks. In this problem, each task is characterized by the location where it is to be executed, a work-content in terms of machine-time units, and one or more time intervals within which it can be performed. The machines can be transported from one location to another at any time, thus the problem has an indefinite number of variables. However, this indefinite number of variables can be reduced to a definite one because, as we prove, the problem has an optimal solution in which the arrivals of machines occur only at certain time instants. The objective is to minimize the total transportation cost such that all the tasks are executed within their time intervals. The constraints ensuring that the tasks are processed within their prescribed time intervals are nonlinear; nevertheless, due to the sets of the possible arrival times of the machines forming bounded convex polyhedra, our problem can be transformed into a mixed integer linear program by the same device used in the decomposition principle of Dantzig-Wolfe.

Keywords : transportation schedule; generalized linear programming; bounded convex polyhedron; work-content.

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