A BRANCH-AND-BOUND APPROACH FOR SPARE UNIT ALLOCATION IN A SERIES SYSTEM

This paper analyzes a spare unit allocation model for the availability of a system (composed of multiple stages in series) under some struct ural constraints where each stage is allowed to carry many spare units in addition to a single operating unit having exponentially-distribut ed failure time but generally-distributed repair times, and all the st ages are stochastically independent. In the model, the system availabi lity is derived as a 0-1 knapsack program with an infinite number of v ariables involved, for which an efficient branch-and-bound solution pr ocedure is constructed on the basis of a bounding procedure exploited in a fathoming mechanism. The bounding procedure determines both the l ower bound and the upper bound of the number of spare units so as to m ake the solution search easier. The overall solution procedure is test ed for its efficiency with various numerical examples.