A reward-penalty stochastic pricing and advertising model under demand uncertainty

This paper aims in assessing the effects of governmental policies on a maximal covering location problem facing stochastic demand which is sensitive to both the retail price and facility advertising effort. A reward-penalty two-stage stochastic programming model is proposed to formulate the problem as a supportive approach in a mixed integer non-linear programming form. In particular, a stochastic pricing and advertising dependent demand model in a facility location configuration is developed which sets the retail price for each opened facility and various advertising effort levels based on the zone’s attractiveness. To promote customer welfare and satisfaction, the legislative counterpart of the reward-penalty model is introduced. The legislative model assigns the minimum satisfaction demand level to the model as a constraint. In both models, the firm tries to maximize its net profit according to government decisions. An analytical method based on the L-shaped algorithm is provided to determine the best solutions of the first and second stages with coping nonlinearity term of the proposed models. Finally, numerical examples are developed to illustrate the governmental policies impacts to reach to the most social welfare as well as the least reward-penalty legislation.