Joint optimization of pricing and planning decisions in divergent supply chain

In divergent supply chains, such as in the oil industry, processing raw materials results in an outflow of multiple products. Final products are stored at international depots, from where they are ready to be shipped to the markets. Even if one company controls the entire chain, when production and sales organizations are decoupled, a relevant problem is to determine the internal prices of products at depots for achieving coordination. We propose an optimization model involving pricing and production decisions, and several constraints commonly used in divergent chains. In our approach, the producer incorporates the sellers' behavior by expressing demand as a function of the internal price. As a result, our model serves as a coordination mechanism in trying to get an overall coordinated integrated solution in a decoupled reality. Numerical examples in single and multiple periods problems show the advantages of our approach over cost-based methods.