An Optimal Transportation Schedule of Mobile Equipment

Abstract

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