A study on robust revenue optimization problem with uncertainty

Abstract

Uncertainty is ubiquitous in the real-world system when decision makers attempt to find an optimal revenue solution. The corresponding risk has been the subject of much speculation. Robust optimization is defined as an approach to find a solution whose objective value is close to that of the optimal solution for all scenarios. In our study, we attempt to discuss several real-world problems in the context of robust optimization. In the first part, we propose a network robust optimization model for professional services firms’ revenue management under an uncertain environment. Our model helps arrive at a decision about order processing focused on capacity allocation of multi-functional professionals. In the second part, the optimal car rental problem is considered. Mathematical programming formulations are defined to address the problem under substitution, using the basic concepts of the revenue management theory. In the third part, we present a robust optimization formulation for dealing with production cost and government administered price uncertainty in a kind of quasi-public goods market scenario. Participants in the market face price administration by government but uncertain production costs, at the same time. We show that the robust optimization formulation, based on a nominal problem, may be articulated as a variational inequality involving control and state variables. This convenient approach may be applied for computation of optimal solutions, which can help manufactories dramatically and rapidly alter production and distribution schedules, in order to compete in the market successfully. In the last part, the robust optimization formulation for dealing with production cost uncertainty in an oligopolistic market scenario is considered. When production costs fluctuate and yet, at the same time, selling price can not be adjusted because it is determined by the equilibrium of the entire market, at the aggregate level, where different players have different cost advantages in different products and processes. We show that the variational inequality approach is suitable for dealing with this differential game. A robust optimization formulation is built, based on a nominal problem, to overcome the influence of variable cost. We provide detailed numerical examples, which demonstrate the efficiency of the robust model.