Many actual rental activities present online rental problems with multiple units of assets or equipment whose use can be continuous,separable,or discrete.Using online algorithms and competitive analysis,continuous mul...Many actual rental activities present online rental problems with multiple units of assets or equipment whose use can be continuous,separable,or discrete.Using online algorithms and competitive analysis,continuous multiple online rental problems have obtained the optimal risk control strategy and the optimal competitive ratio.For multiple online rental problems with discrete assets,first,we present an approximation algorithm for a risk control strategy and the upper bound of the optimal competitive ratio.Moreover,in practical applications,the approximation algorithm of the discrete online problem provides the approximate rental quantities in each period and the solution principle for the approximate competitive ratio.Second,we present the approximate optimal rental quantities and the correction algorithm to obtain a better competitive ratio based on the approximation algorithm.Finally,we compare the approximation algorithm with the correction algorithm by real data.Our findings show that when the approximate solution is used to replace the corrected solution,the resulting approximation error is usually less than the magnitude of 1/ms where m is the total units of certain assets or equipment and s is the price to buy one unit in each period.展开更多
基金We would like to thank the anonymous referees and the senior/associate editors for their comments,which have significantly strengthened this paper.The authors would like to acknowledge the financial support of National Natural Science Foundation of China(71471065,71720107002)Guangdong Province Science and Technology Plan Project(2017A070706004)The Fundamental Research Funds for the Central Universities(2018YBXMPY09).
文摘Many actual rental activities present online rental problems with multiple units of assets or equipment whose use can be continuous,separable,or discrete.Using online algorithms and competitive analysis,continuous multiple online rental problems have obtained the optimal risk control strategy and the optimal competitive ratio.For multiple online rental problems with discrete assets,first,we present an approximation algorithm for a risk control strategy and the upper bound of the optimal competitive ratio.Moreover,in practical applications,the approximation algorithm of the discrete online problem provides the approximate rental quantities in each period and the solution principle for the approximate competitive ratio.Second,we present the approximate optimal rental quantities and the correction algorithm to obtain a better competitive ratio based on the approximation algorithm.Finally,we compare the approximation algorithm with the correction algorithm by real data.Our findings show that when the approximate solution is used to replace the corrected solution,the resulting approximation error is usually less than the magnitude of 1/ms where m is the total units of certain assets or equipment and s is the price to buy one unit in each period.
