Optimal integration of third-parties in a coordinated supply chain management environment

• Different approximation models are proposed to estimate 3rd parties price policies.
• The pricing approximation lead to mathematical complexities (LP, NLP and MINLP).
• The selection of a pricing model significantly affects the tactical decisions.
• The average price approximation leads to the worst real decisions.

A generic tactical model is developed considering third party price policies for the optimization of coordinated and centralized multi-product Supply Chains (SCs). To allow a more realistic assessment of these policies in each marketing situation, different price approximation models to estimate these policies are proposed, which are based on the demand elasticity theory, and result in different model implementations (LP, NLP, and MINLP). The consequences of using the proposed models on the SCs coordination, regarding not only their practical impact on the tactical decisions, but also the additional mathematical difficulties to be solved, are verified through a case study in which the coordination of a production–distribution SC and its energy generation SC is analyzed. The results show how the selection of the price approximation model affects the tactical decisions. The average price approximation leads to the worst decisions with a significant difference in the real total cost in comparison with the best piecewise approximation.