استراتژی رقابتی برای لیزینگ آنلاین تجهیزات مستهلک شدنی

This paper studies the problem of on-line leasing of depreciable equipment. We first discuss deterministic strategies for the problem for situations with and without interest rates, respectively. Competitive ratios are used to evaluate the performance of on-line algorithms. The optimal competitive ratio of the deterministic strategy is therefore obtained. As randomization can boost performance, the randomized strategy for on-line leasing of depreciable equipment with oblivious adversary is further proposed. The main difference between the deterministic algorithm and the randomized algorithm is that the introduction of an interest rate decreases the optimal deterministic competitive ratio while it increases that of the latter. By comparison, we find that the introduction of a depreciation factor improves the competitive performance and the model is more practical for on-line leasing of depreciable equipment. Finally, we conclude that the competitive ratio is closely related to the transaction costs and the profitability in the leasing business.

In recent years, it is a hot topic to use competitive analysis and on-line algorithms to study financial optimization problems [1], [2] and [3]. Competitive analysis compares the performance of on-line algorithms to that of the optimal off-line algorithm and uses a competitive ratio to evaluate the performance of on-line algorithms. Competitive analysis [4] and [5] has been gaining recognition for being a complementary approach in the analysis of algorithmic decision making under uncertainty. In this approach one assumes that the events are generated by an adversary and the performance of an on-line strategy in which the decision maker has no knowledge about the future events is compared with a corresponding strategy with full knowledge about the entire future events and operates optimally. The problems that the on-line algorithms intend to solve usually have typical dynamic characteristics, which are called on-line problems. Thus, the strategies solving on-line problems are called on-line strategies.

Under the assumption that there exists a secondary market, this paper has employed competitive analysis to study the on-line leasing of depreciable equipment. The deterministic strategy and randomized strategy are both presented. The analysis about the two on-line strategies also takes the interest rate into consideration. We show that using a simple randomized algorithm the on-line player can obtain fairly low competitive ratios. As discussed in this paper, the basic assumptions are that the life expectancy of the equipment is large enough and the number of periods to use the equipment is finite (smaller than the life expectancy of the equipment). Therefore a set of new equipment can meet the need of the on-line player. The generalization of this on-line leasing problem to the situation of limited life expectancy of equipment, which can be seen as a multi-stage on-line leasing of depreciable equipment, will be considered in our future research. In addition, in this paper the pure competitive analysis completely ignores the partial knowledge that the on-line player may have. Therefore, it would be very interesting to generalize our results to the situation of risk management. The consideration of price uncertainty, taxes, etc. are also of great interest.