Joint production planning, pricing and retailer selection with emission control based on Stackelberg game and nested genetic algorithm

In practice, it is of paramount importance that firms make joint decisions in production planning, pricing and retailer selection while considering emission regulation. This is because the joint decisions can ensure firms to obtain higher profits while contributing to sustainable environments. However, due to the problem complexity, no models facilitating such decision making are available. This study aims to develop a model to help firms make optimal joint decisions. To model the situations where a manufacturer is the leader and the retailers are followers, we adopt the Stackelberg game theory and develop a 0–1 mixed nonlinear bilevel program to maximize the profits of both the manufacturer and his retailers. We further develop a nested genetic algorithm to solve the game model. Numerical examples demonstrate (i) the applicability of the game model and the algorithm and (ii) the robustness of the algorithm. Managerial insights are obtained, suggesting that (i) manufacturers need to identify the capacity ranges (called capacity traps) where capacity increases result in reduced profits when making decisions to optimize profits; (ii) retailers should make suitable, e.g., pricing decisions so that the manufacturers can include them in the supply chains; (iii) both manufacturers and retailers may not need to consider the carbon emission buying (or selling) price when making decisions.