Optimizing vehicle routing via Stackelberg game framework and distributionally robust equilibrium optimization method

Abstract

In this paper, we study the vehicle routing problem (VRP) with multiple firms in depot with focus on the carbon cap-and-trade policy. By establishing the upper-level carbon trading revenue model from the government’s perspective and the lower-level model from the firm’s perspective, we describe the VRP based on the Stackelberg game framework. In addition, a traffic density objective is put forward. As a consequence, the lower-level model is a double objective optimization model including transportation cost and traffic density. Due to the influence of uncontrollable factors, the batches of distributed vehicles are uncertain and characterized as random fuzzy variables with uncertain credibility distribution. To address this situation, we propose a new distributionally robust equilibrium optimization (DREO) method, in which it describes the existence range of the real credibility distribution by constructing the uncertainty distribution set. For a given specific uncertainty distribution set, we derive its equivalent formulation for the proposed method. Moreover, given the single-period, we reduce the derived model to a single-layer multi-criteria optimization model by using the parameter-driven approach, so as to avoid solving the complicated original model. Besides, we analyze dynamic process of the multi-period Stackelberg game model. Finally, we apply a lexicographic optimization algorithm to solve the proposed model under the single-period, thereby verifying its effectiveness and also obtaining some promising results.