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Design of cellular networks with diversity and capacity constraints

This paper presents three mathematical models for network design of cellular networks. The models reflect varying degrees of complexity. Model 1 is a 1-period fixed-link capacity model. Three heuristics are used for solving this problem. All the heuristics first use linear programming relaxations to yield the near-optimal integer solution, then use clever rounding-schemes to find the final solution. The three heuristics are compared with an integer branch-and-bound algorithm to show the efficacy of the heuristics and the speed with which they achieve their solution. The first heuristic is the best. An appendix presents a detailed algorithmic description of the first heuristic. Model 2 allows the capacities of the links to vary. This is a much more difficult mathematical programming problem, yet certain features of the problem reveal valuable characteristics of the linear programming relaxations. Two heuristics are generated; the first heuristic is superior to the second. The heuristics are compared with an optimal branch-and-bound algorithm. Model 3 presents a multi-period demand problem. This is a very complex problem and, while no heuristics are developed and no computational experiments are shown, the structure of the final problem is similar to models 1 and 2; thus linear programming relaxations should be a viable strategy for its solution.