REFUELING STRATEGIES TO MAXIMIZE THE OPERATIONAL RANGE OF A NONIDENTICAL VEHICLE FLEET

Recently Mehrez et al., Mehrez and Stern and Melkman et al. studied a vehicle fleet refueling problem that arises in military applications a nd is aimed at maximizing the operational range of the fleet. More spe cifically, they investigated the problem of maximizing the range of th e last vehicle from a fleet of n vehicles by employing a pure refuelin g chain strategy. However, the problem is solved only for the vehicles with the same fuel consumption rate or the same fuel capacity. This p aper is aimed at solving the problem of a more general case where vehi cles may have different fuel consumption rates and different fuel capa cities. Based on the analysis of fuel demand and supply curve, a recur sive procedure which requires only O(n) calculations is developed to s olve the linear programming problem of maximizing the operational rang e for a given refueling chain. A pairwise interchange rule is also pro vided to improve the maximum operation range by switching the adjacent vehicles in a refueling chain. Finally, a heuristic approach is sugge sted for finding an optimal refueling chain. Computer simulations show that for n = 6, by using the heuristic approach, the chance of findin g an optimal solution is 72% and the average operational range is 97.8 % of the optimal. Furthermore, employing an O(n) recursive formula, th e solution of a multiple-transfer refueling chain is derived. An illus trative example is demonstrated for a military assessment of the trade -offs between the maximum operational range and the number of fuel tra nsferring operations under the pure and the multiple-transfer chains.