(701e) Optimal Procurement Contract Selection with Price Optimization Under Uncertainty for Process Networks

Calfa, B. A., University of Wisconsin at Madison
Grossmann, I., Carnegie Mellon University

Manufacturing enterprises deal with uncertainty from both internal and external sources. Internally, production variability due to unplanned events may prevent the company to achieve its demand-driven production targets. Externally, fluctuations in supply and demand as well as market economic conditions pose challenges to efficient operation of the supply chain. One way to reduce the level of uncertainty on both the supply and the customer sides, and that is typically used by companies, is by making contractual agreements (Tsay, Nahmias, & Agrawal, 1999). In the context of this paper, a contract is a binding agreement in which the seller provides the specified product and the buyer pays for it under specific terms and conditions.

A different approach to managing uncertainty is pricing analytics (Phillips, 2005; Bodea & Ferguson, 2014), also known as price optimization. In formulating such a problem, selling prices become decision variables, and the demand of a product is modeled as a function of its price. Nonetheless, this still typically does not completely eliminate uncertainty, since stochastic environmental, economic, and market conditions remain uncontrollable by the manufacturing company.

In this paper, we combine the aforementioned uncertainty management strategies in a two-stage stochastic optimization model for multi-period, multi-site tactical production planning. Uncertain parameters include raw material and finished product price and availability/demand. We propose a manufacturer-centric approach in which the purchase contract structures are set by suppliers, and it is the manufacturer's decision to select which contract, if any, to sign. In addition, the manufacturer sets the selling price of its main products that may be used to design sales contracts with its customers. However, it is the customer's decision to select the sales contracts, if any, designed by the manufacturer. The contract design problem is not addressed in this paper, but is discussed as a future work. We demonstrate how different pricing models, linear and nonlinear, can be used within the proposed optimization framework. Throughout this paper, we refer to price as unit price (e.g., $/kg, $/t etc.). 

More specifically, we use three quantity-based contract models (Park et al., 2006): discount after a certain purchased amount, bulk discount, and fixed duration contracts. With regards to pricing models, we argue that general regression models can be used 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. Uncertainty is considered and modeled in both supply (e.g., raw material spot market price) and demand (random nature of the residuals of the regression models). The proposed method is illustrated with two numerical examples of chemical process networks. 


Bodea, T., and Ferguson, M. 2014. Segmentation, Revenue Management and Pricing Analytics. Routledge – Taylor & Francis. New York, NY. USA.

Park, M.; Park, S.; Mele, F. D.; and Grossmann, I. E. 2006. Modeling of Purchase and Sales Contracts in Supply Chain Optimization. Industrial & Engineering Chemistry Research. 45(14):5013–5026.

Phillips, R. L. 2005. Pricing and Revenue Optimization. Stanford Business Books – Stanford University Press. Palo Alto, CA. USA.

Tsay, A. A.; Nahmias, S.; and Agrawal, N. 1999. Modeling Supply Chain Contracts: A Review. In Tayur, S.; Ganeshan, R.; and Magazine, M., eds., Quantitative Models for Supply Chain Management, volume 17 of International Series in Operations Research & Management Science. Springer US. 299–336.