Supply chain competition on shelf space and pricing for soft drinks: A bilevel optimization approach

We develop a bilevel optimization model with two manufacturers at the top level and a common retailer at the bottom level to analyze the merits of integrated vs. non-integrated supply chains. The resulting model is an instance of an equilibrium problem with equilibrium constraints (EPEC), a notoriously computationally challenging model to solve. We provide a closed-form expression for the approximate solution to the lower-level problem determining the retail prices and the allocated shelf spaces. This solution then is incorporated into the manufacturers' profit resulting in a single-level optimization problem which is easier to solve. Numerical results from a real soft drink supply chain involving two beverage suppliers selling their major products through a common retailer shows the applicability of the proposed model for supply chain planning. We then analyze the integrated model where the manufacturers and the retailer work together to maximise profit without any competition between the manufacturers. Comparing the profits in the integrated and non-integrated supply chains finds that centralization benefits all of the players if the two brands are almost identical, but it hurts the weaker brand if the two brands exhibit different characteristics in terms of costs or brand loyalty. In addition, we run several sensitivity analyses with regard to variations in the exogenous parameters including the price and shelf-space elasticities and explore the changes in the profits in both non-integrated and integrated supply chains.