Online Quantity Flexibility contract model and its competitive analysis

The literatures related to online quantity flexibility contract model (or various applications) is quite extensive. The common denominator of all previous theoretical work on the subject is based on the traditional ldquoaverage case analysisrdquo. In other word, analyses are typically made under the assumption that the market demand function follows a particular stochastic process that may or may not be known to the online player. But in some situation this leads to the very difficult questions as to how the distribution was selected and what evidence suggests that this distribution is either typical or representative. In this paper we use the competitive ratio optimality criterion to restudy this model and some interesting results are obtained. We present a QF strategy and get the optimal competitive ratio.