Many classical facility location models, like the uncapacitated fixed-charge location problem (known as UFLP), implicitly assume that the facilities will operate well all the time. However, in fact, facilities may fail sometimes due to natural or economic factors. The reliability fixed-charge location problem (RFLP) is based on the UFLP, taking failures into account. Both the UFLP and the RFLP assume that facilities are uncapacitated, which is obviously not true in reality. Capacity limits in reality may mean that customers have to be served from facilities much farther than their egularly assigned facilities at dierent levels. In this thesis, we present a model for choosing facility locations to minimize expected cost, while also taking into account both the possible failures and the capacity of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable under capacity constraints. This capacitated reliability approach is new in the facility location literature. We formulate a capacitated reliability model based on the RFLP and present an exact Lagrangian relaxation algorithm to solve it.
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