A Novel Approach to Large-Scale Linear Programming Decomposition for National Transportation Network Optimization in Nigeria

National transportation network optimization in Nigeria involves a large-scale linear programming problem of such complexity, spanning tens of thousands of origin-destination pairs, multiple transport modes, commodity types, and time periods, that direct solution using commercial solvers is computationally infeasible for planning-relevant problem scales. This dissertation develops a novel approach to large-scale linear programming decomposition specifically designed for national transportation network optimization problems, with theoretical innovations motivated by the structural characteristics of the Nigerian transport planning context. A mathematical characterization of the national transport network optimization problem is developed using multi-commodity flow formulations that explicitly represent road, rail, and waterway network interactions. A novel decomposition scheme is proposed, extending Dantzig-Wolfe decomposition with commodity and geographic subproblem structures that exploit the problem's block angular constraint matrix. Original convergence results are established for the proposed algorithm under realistic non-degeneracy conditions, including tight bounds on the number of iterations required to achieve epsilon-optimality. The algorithm is implemented and tested on a Nigeria-specific transportation network dataset constructed from Federal Ministry of Works road condition surveys, Nigerian Ports Authority throughput data, and National Bureau of Statistics freight demand data. Computational results demonstrate solution of the full national network problem in under four hours on standard hardware, a capability not achievable with existing algorithms on this problem scale. Policy application of the optimized network solution generates investment prioritization recommendations for the National Integrated Infrastructure Master Plan. Keywords: linear programming, Dantzig-Wolfe decomposition, transportation network, national planning, Nigeria