Geometric approach for logistics outsoursing contracting

In this paper, we extend our geometric approach to study the optimal logistics outsourcing contract in the problem with more complex distributions. We propose an approximate method to explore the problem, by using piecewise uniform distributions to approximate the original distributions. With appropriate number of cutting, the approximation hardly leads to any deterioration in the solution, showed by three cases. By using this approach, we provide a numerical comparison for the LCSCR contract and nonlinear cost-sharing contract, which shows that the LCSCR contract performs well when the moral hazard dominates the problem. When the adverse selection dominates, the performance of LCSCR contract becomes worse. In contrast, the nonlinear cost sharing contract performance great in most situation.