This thesis investigates three different optimization problems in designing multimedia communication networks. The problems are formulated as integer programming models to investigate analytically where the objective functions are expressed in the operation and/or installation cost of the associated networks. The first model considers a multicast routing problem to find the minimum cost tree where the whole communication link delay on each path(route) of the tree is subject to a given delay allowance. The problem is formulated as an integer programming problem by using path variables. An associated problem reduction property is then characterized to reduce the solution space. Moreover, a polynomial time column generation procedure is exploited to solve the associated linear programming relaxation with such solution space reduced. Therewith, a branch-and-price algorithm is derived to obtain the optimal integer solution(tree) for the problem. Computational results show that the algorithm can solve practical size problems in a reasonable time. The second model considers the problem of locating the wavelength converter in an optical Wavelength Division Multiplexing(WDM) network. The problem is formulated as an integer programming problem by using path variables. In order to solve the associated linear programming relaxation which has exponentially many variables, a polynomial time column generation procedure is exploited. Therewith, an LP-based branch-and-bound algorithm is derived to obtain the optimal integer solution for the problem. Computational results show that the algorithm can solve practical size problems in reasonable time. The last model considers an optimal video file allocation problem in a video-on-demand (VOD) network which is inatwo-level hierarchical topology with the higher level sub-network for distributed servers and the lower level sub-network for local servers. The objective of the problem is to find an optimal video allocation strategy, giv...