With the fragmentation of markets and the increasing demand variation, chemical companies can no longer confine themselves to just simple network of dedicated processes. They need to introduce more types of chemicals, as well as integrating flexibility, into the existing process network. Moreover, the shortening of product life span and the escalation of demand and pricing uncertainties require chemical companies to consider their optimization model in a stochastic fashion in addition to the traditional deterministic way. The chemical supply chain optimization of continuous process networks is essential for managing the operation of many chemical processing industries. The inclusion of more chemicals and processes complicate the optimization problem, making it larger and more difficult to solve. The introduction of scenarios further enhances the size and complexity, sometimes making the model unsolvable, due to the explosion in the combinatorics that results from multiple scenarios, products, plants, processes, and prolongation of planning horizons. Hence, it requires the use of decomposition methods to break the problem down, so that it could be solved efficiently and effectively.

This work expands the continuous flexible process network model proposed by Bok et al. (2000) by incorporating various scenarios into the multiple periods. Combinations of linking constraints between consecutive time periods and/or different scenarios, such as inventory balance, periodic shortfall, production changeover, and intermittent delivery, are relaxed into the objective function through the Lagrangean relaxation method (Fisher, 1985). Lagrangean decomposition (Guignard and Kim, 1987) is applied to the expanded stochastic model as well as the original deterministic model, decomposing them into sets of smaller and simpler subproblems. The Lagrangean multipliers are updated between consecutive iterations using the modified subgradient optimization method (Fumero, 2001). The resulting computational times and solution values from both models for many instances are then presented and compared.

__________________

Bok, J. K.; Grossmann, I. E.; Park, S., 2000, Supply chain optimization in continuous flexible process networks, Ind. Eng. Chem. Res., 39, 1279-1290.

Fisher, M. L., 1985, An applications oriented guide to Lagrangian relaxation, Interfaces, 15, 2, 10-21.

Fumero, F., 2001, A modified subgradient algorithm for Lagrangean relaxation, Comp. and Oper. Res., 28, 33-52.

Guignard, M.; Kim, S., 1987, Lagrangean decomposition: A model yielding stronger Lagrangean bounds, Mathematical Programming, 39, 215-228.