Lower bounds for the multislope ski-rental problem

H. Fujiwara, Y. Konno, T. Fujito
2013 11th International Symposium on Operations Research and its Applications in Engineering, Technology and Management 2013 (ISORA 2013)   unpublished
The multislope ski-rental problem is an extension of the classical ski-rental problem, where the player has several options of paying both of a per-time fee and an initial fee, in addition to pure renting and buying options. Damaschke gave a lower bound of 3.62 on the competitive ratio for the case where arbitrary number of options can be offered. In this paper we propose a scheme that for the number of options given as an input, provides a lower bound on the competitive ratio, by extending the
more » ... o, by extending the method of Damaschke. This is the first to establish a lower bound for each of the 5or-more-option cases, for example, a lower bound of 2.95 for the 5-option case, 3.08 for the 6-option case, and 3.18 for the 7-option case. Moreover, it turns out that our lower bounds for the 3-and 4-option cases respectively coincide with the known upper bounds. We therefore conjecture that our scheme in general derives a matching lower and upper bound.
doi:10.1049/cp.2013.2252 fatcat:ayxnhbsqk5ev5myvfhdrb5jsfa