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 structural constraints where each stage is allowed to carry many spare units in addition to a single operating unit having exponentially-distributed failure time but generally-distributed repair times, and all the stages are stochastically independent. In the model, the system availability is derived as a 0–1 knapsack program with an infinite number of variables involved, for which an efficient branch-and-bound solution procedure is constructed on the basis of a bounding procedure exploited in a fathoming mechanism. The bounding procedure determines both the lower bound and the upper bound of the number of spare units so as to make the solution search easier. The overall solution procedure is tested for its efficiency with various numerical examples.