Stochastic inventory management for tactical process planning under uncertainties: MINLP models and algorithms

Abstract

We address in this article the mid-term planning of chemical complexes with integration of stochastic inventory management under supply and demand uncertainty. By using the guaranteed service approach to model time delays in the flows inside the network, we capture the stochastic nature of the supply and demand variations, and develop an equivalent deterministic optimization model to minimize the production, feedstock purchase, cycle inventory, and safety stock costs. The model determines the optimal purchases of the feedstocks, production levels of the processes, sales of final products, and safety stock levels of all the chemicals. We formulate the model as a mixed-integer nonlinear program with a nonconvex objective function and nonconvex constraints. To solve the global optimization problem with modest computational times, we exploit some model properties and develop a tailored branch-and-refine algorithm based on successive piecewise linear approximation. Five industrial-scale examples with up to 38 processes and 28 chemicals are presented to illustrate the application of the model and the performance of the proposed algorithm. © 2010 American Institute of Chemical Engineers AIChE J, 2011