abstract
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Recently , Mehrez et al. (Mehrez and S tern [1983, 1985], Melkman et al. [1986 ]) have studied a vehicle fleet refueling problem that arises in military applications and is aimed to maximize the operational range of the fleet. More specifically, they investigated the problem of maximizing the range of the last vehicle from a fleet of n vehicles by employing a sequential refueling chain strategy. The strategy of maximizing the range of the last vehicle is an important criterion to be considered under war conditions. This problem has its own elegant solution which demonstrates how a specific military Operations Research problem may reveal interesting results due to its unique structure. The approach recommended here to solve the problem indicates that numerical computations rather than an analytical approach may result in knowing less about the problem solution. The purpose of this paper is: (i) To construct an ordering rule for n = 2, which contradicts the conjecture of Mehrez et al. that even for the case of n = 2 a simple ordering rule does not exist. (ii) To suggest a recursive procedure which requires only O(n) calculations to solve the linear programming problem of maximizing the operational range for a given refueling chain. (iii) To suggest a new approach, which is based on the derivation of supply and demand curves for each refueling operation, to solve scheduling problems. It is shown how the analysis of these curves provides important information regarding the nature of the optimal solution which was treated by Mehrez et al. for some special cases of fleet configurations. The analysis supports the idea of solving the problem of determining the optimal refueling chain by a enumerative search for n sufficiently small. Finally, 2 for n = 2 and 3, an analysis is shown by which inferior refueling chains may be eliminated for the vehicle fleet refueling problem.