This thesis is concerned with the analysis of a Rectilinear Distance Location Allocation Problem, where the costs are directly proportional to rectilinear distances and the amount shipped. The problem is formulated as a Mixed Integer Bilinear Programming Problem and as a Discrete Location Allocation Problem. Using linear programming relaxations constructed via the Reformulation-Linearization Technique (RLT), the latter formulation is shown to provide stronger lower bounds and is therefore adopted for implementation. In addition, cutting planes are developed to further strengthen the linear programming relaxation. The special structure of the resulting linear program is exploited in order to get a quick lower bound via a suitable Lagrangian dual formulation. This lower bounding scheme is embedded within a finitely convergent Branch and Bound algorithm that enumerates over the location decision variable space. An illustrative example and computational experience are provided to demonstrate the efficacy of the proposed algorithm.