Readiness and the optimal redeployment of resources

This paper considers the problem of the optimal redeployment of a resource among different geographical locations. Initially, it is assumed that at each location i, i = 1,…, n, the level of availability of the resource is given by a1 ≧ 0. At time t > 0, requirements Rf(t) ≧ 0 are imposed on each location which, in general, will differ from the a1. The resource can be transported from any one location to any other in magnitudes which will depend on t and the distance between these locations. It is assumed that ΣRj > Σat The objective function consideis, in addition to transportation costs incurred by reallocation, the degree to which the resource availabilities after redeployment differ from the requirements. We shall associate the unavailabilities at the locations with the unreadiness of the system and discuss the optimal redeployment in terms of the minimization of the following functional forms: \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{j = 1}^n {kj(Rj - yj) + } $\end{document} transportation costs, Max \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {Max}\limits_j \,[kj(Rj - yj)] + $\end{document} transportation costs, and \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{j = 1}^n {kj(Rj - yj)^2 + } $\end{document} transportation costs. The variables yj represent the final amount of the resource available at location j. No benefits are assumed to accrue at any location if yj > Rj. A numerical three location example is given and solved for the linear objective.