On capital investment

Yossi Azar, Yair Bartal, Esteban Feuerstein, Amos Fiat, Stefano Leonardi, Adi Rosén

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


We deal with the problem of making capital investments in machines for manufacturing a product. Opportunities for investment occur over time, every such option consists of a capital cost for a new machine and a resulting productivity gain, i.e., a lower production cost for one unit of product. The goal is that of minimizing the total production and capital costs when future demand for the product being produced and investment opportunities are unknown. This can be viewed as a generalization of the ski-rental problem and related to the mortgage problem [3]. If all possible capital investments obey the rule that lower production costs require higher capital investments, then we present an algorithm with constant competitive ratio. If new opportunities may be strictly superior to previous ones (in terms of both capital cost and production cost), then we give an algorithm which is O(min{log C, log log P, log M}) competitive, where P is the ratio between the highest and the lowest capital costs, Ρ is the ratio between the highest and the lowest production costs, and Μ is the number of investment opportunities. We also present a lower bound on the competitive ratio of any on-line algorithm for this case which is (formula pesented). This shows that the competitive ratio of our algorithm is tight (up to constant factors) as a function of C, and not far from the best achievable as a function of P and M.

Original languageAmerican English
Title of host publicationAutomata, Languages and Programming - 23rd International Colloquium, ICALP 1996, Proceedings
EditorsFriedhelm Meyer auf der Heide, Burkhard Monien
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540614400, 9783540614401
StatePublished - 1996
Externally publishedYes
Event23rd International Colloquium on Automata, Languages, and Programming, ICALP 1996 - Paderborn, Germany
Duration: 8 Jul 199612 Jul 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Colloquium on Automata, Languages, and Programming, ICALP 1996

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1996.


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