Optimal procurement contract selection with price optimization under uncertainty for process networks

In this work, we propose extending the production planning decisions of a chemical process network to include optimal contract selection under uncertainty with suppliers and product selling price optimization. We use three quantity-based contract models: discount after a certain purchased amount, bulk discount, and fixed duration contracts. We propose the use of general regression models to describe the relationship between selling price, demand, and possibly other predictors, such as economic indicators. For illustration purposes, we consider three demand-response models (i.e., selling price as a function of demand) that are typically encountered in the literature: linear, constant-elasticity, and logit. We develop a mixed-integer nonlinear two-stage stochastic programming that accounts for uncertainty in both supply (e.g., raw material spot market price) and demand (random nature of the residuals of the regression models) for the planning of the process network. The proposed method is illustrated with two numerical examples of chemical process networks.