Linear Programming Algorithm with Mixed Real-Integer Variables in MATLAB Environments

Efficient numerical procedures for solving general Linear Programming (LP) problems with mixed real-integer variables are developed in this work. The proposed algorithms employ the revised dual simplex with Branch and Bound (B&B) algorithms, with special procedures for limited search of subsequent branches. Computational time can be significantly reduced by incorporating the updated inverse formulas into the developed procedures. Both generic LP problems and deterministic pavement maintenance and rehabilitation (M&R) problems are used in this study to vaiidate the developed procedures. Medium to large-scale examples ( 11 pavement M&R) presented in this work have demonstrated that the developed numerical procedures consistently offer superior performance (I.5x to 49.2x faster) as compared to Matlab built-in function bintprog