Abstract
The residual value of the equipment is an important and inevitable issue for any decision-making process of equipment leasing. In this paper, we present an on-line financial leasing problem considering the second-hand transaction issue, i.e. the equipment can be sold in the secondary market when it is no longer needed. Using competitive analysis, the optimal deterministic strategies are given to deal with the financial leasing problem. Finally, to test the performance of the proposed on-line financial leasing strategies, several numerical experiments are conducted.







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03 October 2022
The two identical errors in the equations with the incorrect symbol “gt;” has been updated with the correct symbol “>”.
References
Al-Binali S (1999) A risk-reward framework for the competitive analysis of financial games. Algorithmica 25(1):99–115. https://doi.org/10.1007/PL00009285
Azar Y, Bartal Y, Feuerstein E, Fiat A, Leonardi S, Rosén A (1999) On capital investment. Algorithmica 25:22–36. https://doi.org/10.1007/PL00009281
Chen X, Xu W (2017a) A risk-reward model for on-line financial leasing problem with an interest rate. In: Xiao M, Rosamond F (eds) Frontiers in algorithmics, vol 10336. Springer, Cham, pp 68–78. https://doi.org/10.1007/978-3-319-59605-1_7
Chen X, Xu W (2017) Risk-reward strategies for the non-additive two-option online leasing problem. Int J Innovative Comput Inf Control 13(6):2051–2065
Chen X, Xu W (2018) A risk-reward model with compound interest rate for non-additive two-option ski rental. Inf Process. Lett 135:9–13. https://doi.org/10.1016/j.ipl.2018.02.013
Dai W, Dong Y, Zhang X (2016) Competitive analysis of the online financial lease problem. Eur J Oper Res 250(3):865–873. https://doi.org/10.1016/j.ejor.2015.10.020
El-Yaniv R, Kaniel R, Linial N (1999) Competitive optimal on-line leasing. Algorithmica 25(1):116–140. https://doi.org/10.1007/PL00009279
Epstein L, Zebedat-Haider H (2015) Rent or buy problems with a fixed time horizon. Theory Comput Syst 56(2):309–329. https://doi.org/10.1007/s00224-014-9552-x
Feng X, Chu C (2020) Online leasing problem with price fluctuations and the second-hand transaction. J Combin Optim, pp 1–18, https://doi.org/10.1007/s10878-020-00640-x
Feng X, Xu Y, Ni G, Dai Y (2018) Online leasing problem with price fluctuations under the consumer price index. J Combin Optim 36(2):493–507. https://doi.org/10.1007/s10878-018-0305-7
Fujiwara H, Kitano T, Fujito T (2016) On the best possible competitive ratio for the multislope ski-rental problem. J Combin Optim 31(2):463–490. https://doi.org/10.1007/s10878-014-9762-9
Fujiwara H, Shibusawa K, Yamamoto K, Yamamoto H (2020) Bounds for the multislope ski-rental problem. IEICE Trans Inf Syst 103(3):481–488. https://doi.org/10.1587/transinf.2019FCP0001
Hu M, Xu W (2017) A better bound of randomized algorithms for the multislope ski-rental problem. RAIRO-Theor Inform Appl 51(2):91–98. https://doi.org/10.1051/ita/2017009
Karp R (1992) On-line algorithms versus off-line algorithms: how much is it worth to know the future? vol 1, pp 416–429
Levi A, Patt-Shamir B (2015) Non-additive two-option ski rental. Theor Comput Sci 584:42–52. https://doi.org/10.1016/j.tcs.2015.01.038
Wu B, Bao W, Yuan D (2021) Competitive analysis for two-level ski-rental problem. In: Proceedings of the AAAI conference on artificial intelligence, vol. 35, pp 12034–12041
Xu Y, Xu W, Li H (2007) On the on-line rent-or-buy problem in probabilistic environments. J Global Optim 38(1):1–20. https://doi.org/10.1007/s10898-006-9079-z
Yang X, Zhang W, Zhang Y, Xu W (2012) Optimal randomized algorithm for a generalized ski-rental with interest rate. Inf Process Lett 112(13):548–551. https://doi.org/10.1016/j.ipl.2012.04.006
Zhang Y, Zhang W, Xu W, Li H (2011) Competitive strategy for on-line leasing of depreciable equipment. Math Comput Model 54(1):466–476. https://doi.org/10.1016/j.mcm.2011.02.036
Zhang Y, Xian J, Huang M (2020) Online leasing strategy for depreciable equipment considering opportunity cost. Inf Process Lett 162:105981. https://doi.org/10.1016/j.ipl.2020.105981
Funding
This research was supported by the Humanities and Social Science Foundation of the Ministry of Education of China (No. 21YJA630117, 19YJC790146), the Philosophy, Social Sciences Planning Project of Guangdong Province (GD19CGL06), and the Scientific Developing Foundation of Tianjin Municipal Education Commission (No. 2017SK055).
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Zhang, Y., Li, J., Yang, X. et al. Lease or financial lease? Deterministic strategies for on-line financial lease problem with the second-hand transaction. J Comb Optim 44, 1248–1264 (2022). https://doi.org/10.1007/s10878-022-00886-7
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DOI: https://doi.org/10.1007/s10878-022-00886-7