(607g) Simultaneous Design and Planning of a Multiproduct Batch Plant Under Demand Uncertainty: Comparison of Rigorous and Hybrid Techniques

In this work two techniques for optimization under parametric uncertainty are applied to the problem of simultaneous design and planning of a multiproduct batch, which has to comply with a priori unknown products demands.

Product demands are not known to the decision maker with certainty, but it is assumed that the uncertainty can be modeled with a probability distribution and/or represented by a set of scenarios. Each scenario has a known probability that reflects the likelihood of each scenario to take place. Also, these scenarios are described through lower and upper bounds on product demand levels in each time period. The amounts of raw materials consumed are determined by mass balances. Costs and availability of raw materials vary from period to period and are assumed to be known. Also, prices of final products in each time period, and maximum available storage capacities, are problem data.

The two techniques utilized for solving this problem were a rigorous two-stage stochastic programming and a hybrid simulation-based optimization. Both techniques divide the decision variables in two stages. The first stage corresponds to variables that do not change once the uncertain parameters values have been realized, while the second-stage resolves those affected by the uncertainty. For the model utilized in this work first-stage decisions consist of design variables that allow determining the batch plant structure. Second-stage decisions consist of planning variables (continuous variables) to determine the production, purchases, and inventories of raw materials and products for each period throughout the time horizon under each scenario, given the plant structure decided at the first-stage. The objective function of the model is the maximization of the Expected Net Present Value (ENPV).

The rigorous two-stage stochastic programming results in a large MILP problem that is it difficult to solve in reasonable time. In the other hand, the hybrid technique subdivides the solving of the second-stage variables into smaller LP problems and uses a genetic algorithm to explore the decision space of the first-stage. Therefore, the computing requirements are lower but can lead to sub-optimal solutions.

A comparison between the performances of both techniques in presented in terms of computing time and quality of the solution.