Optimization algorithm study : mixed integer linear programming

Abstract

In the present, many petrochemical and petroleum products (engine fuel, solvent, plastic and synthetic rubber. etc.) are important. They are transported by ship, pipe line or train every day. So, minimizing transportation cost and time or maximizing profit is an important key of every company. In this optimization process, the optimal supply chain must be well developed in mathematical programming with the objective function of minimum cost or maximum profit and be solved by using optimization solvers. Objective functions and their constraints are solved by suitable types of optimization solvers: Linear programming (LP) and mixed integer linear programming (MILP). MILP is one of the most widely used optimization technique for designing supply chain, and developed by using linear programming and branch-and-bound technique. In this research, MILP algorithm is studied and developed on FORTRAN 4.0 to study MILP procedure, and then it is applied with case study of biofuel production supply chain. Finally, the results are validated with solver in Microsoft Excel. The result shows that the MILP algorithm can show many solutions with one optimum point for multiple optimum problems for benefit of alternative solutions, while only one solution is obtained from solver in Microsoft Excel. Moreover, the optimal SCNPV from the algorithm is close to one from Microsoft Excel. It shows that the MILP algorithm is high efficient for accuracy solution and benefit for alternative of suitable solutions in optimizing supply chain problems.