An analytical and computer simulation approach to the problem of replenishing task forces at sea

Abstract

An analytical approach to the problem of replenishing task forces at sea is investigated, using a random walk model. The type of replenishment operations considered consists of two replenishment ships of different types, each replenishing L combatant ships of different types. The combatant ships are initially distributed into queues of length M and N between the two replenishment ships. As each combatant ship completes its first replenishment, it then enters the queue of the other replenishment ship. Thus each combatant ship is replenished by both replenishment ships. Replenishment times for the combatant ships are assumed to be independent, positive valued random variables whose distributions are dependent upon both replenishment ship type and combatant ship type. The replenishment of the task force is completed whenever 2L replenishments, two for each combatant ship, are completed. The total replenishment time is shown to be the maximum of certain partial sums of the individual replenishment times. A general expression for the distribution function of the total replenishment time is sought by various methods of analysis. A computer simulation is used to gain a better understanding of the form of the distribution function of total replenishment time for a specific underway replenishment operation. Some examples are discussed.