Risk strategy analysis for an online rental problem of durable equipment with a transaction cost. (April 2021) - Xin, Chunlin; Zhang, Jianwen; Wang, Ziping
This study introduces the second-hand market into the famous ski-rental model, presents an online rental problem of durable equipment with a transaction cost, and designs an optimal deterministic competitive strategy. The traditional competitive analysis is based on the worst-case scenario; hence, its results are too conservative. Even though investors want to manage and control their risks in reality, in some cases, they are willing to undertake higher risk to obtain greater benefits. Considering this situation, this study designs a risk strategy combining the decision makers' risk tolerance with certain and probabilistic forecasts. Numerical analysis shows that the proposed risk strategy can improve the competitive ratio. This study introduces the idea of risk compensation into traditional competitive analysis and designs strategies for online rental of durable equipment based on forecast. The decision maker selects a strategy according to risk tolerance and forecast. If the forecast is correct, then a reward is obtained; otherwise, the risk is guaranteed to be within the decision maker's risk tolerance. The optimal restricted ratio, that is, the competitive ratio of a risk strategy, is less than the optimal competitive ratio of a deterministic strategy. Therefore, the performance of the proposed risk strategy is better than a deterministic strategy. At the same time, the risk strategy based on the probabilistic forecast represents an extension of the strategy based on a certain forecast. In other words, the risk strategy based on a certain forecast is a special case of the risk strategy based on the probabilistic forecast.