Competitive Analysis of Online Price Discount Replacement Problem

When a paid price discount activity occurs, the decision-maker must decide whether or not and when to pay the additional fees for preferential price in an online fashion. This problem which generalizes the basic leasing problem has been introduced and studied by Fleischer et al. In this paper, we extend the basic model to consider different price discount replacement case and present the optimal deterministic online CA algorithm. Moreover, the risk-reward framework is introduced into the model to allow the decision-makers to manage their risk and utilize their forecasts. We give a new online risk algorithm and derive an improved competitive ratio, which is the function of the risk tolerance lambda and forecast F. It is found that with the competitive risk analysis, the flexible competitive ratio has the decreasing character of the risk tolerance.