Towards implementing a total capital cost budgeting constraint in MILP-based approximations to MIFP problems

Budgeting the total capital cost of a chemical engineering project is integral to its future financial success. It is often difficult to know beforehand how costly a project will be, but if the final price grows larger than an internal budget, problems can arise. The project may have to be prematurely cancelled, reflecting a large lost sunk cost. Alternatively, the project could be completed, but at the cost of shelving other pursuits. Neither result is desirable. Capping the total estimated capital cost of the project in preliminary optimisation studies could pre-emptively circumvent some of these problems. This work explores the challenge of integrating a capital cost budgeting constraint into a nonconvex, MIFP chemical process network unit production cost minimisation model, and introduces a novel solution strategy and algorithm to find the globally optimal solution. The algorithm incorporates an inexact parametric algorithm based on Newton's method with successive piecewise linear approximations and NLP subproblems to guarantee feasibility of the nonconvex objective function. The result is an MILP problem with NLP subproblems. The efficiency of the proposed algorithm is demonstrated by minimising the unit production cost of a large chemical conversion network. The problem is solved with several general purpose MINLP solvers in addition to the proposed method. Computational results show that the proposed method shows promise to outperform general-purpose MINLP solvers when solving large MIFP network optimisation problems.