Computational Trends and Effects of Approximations in an MILP Model for Process Planning

As several mixed-integer linear programming (MILP) optimization models have been developed in the past few years for design, planning, and scheduling of chemical processes, questions arise about their sensitivity to uncertainties in the problem data and modeling assumptions. This paper presents a study of the effects of time horizon discretization and inaccurate data on the quality of the MILP solution. The results provide information on how detailed discretizations and how accurate forecasts are required in order to obtain good-quality solutions with the MILP model. The studies indicate that the LP relaxation gap of the MILP reduces as the number of time periods of the planning model is increased. Another interesting finding of this study is that, for all the problems solved, uncertainty in prices and demands does not seem to have any major impact on the quality of the solution of the MILP model as long as plan revision is allowed through adjustment of production levels and amounts of purchases and sales. In the course of this investigation, we also develop an efficient solution method for the planning problem and demonstrate its superiority to a popular MILP package.