Authors:
Christine Markarian
and
Claude Fachkha
Affiliation:
Department of Engineering and Information Technology, University of Dubai, U.A.E.
Keyword(s):
Combinatorial Optimization, Online Algorithms, Competitive Analysis, Facility Location, Leasing.
Abstract:
Leasing has become one of the most widely spread business models in almost all markets. The online algo- rithmic study of leasing was initiated in 2005. Unlike classical algorithms, online algorithms are not given the entire input sequence at once. A portion of the input sequence is revealed in each step and the online algorithm is required to react to each step while targeting the given optimization goal against the entire input sequence. In a leasing setting, resources are leased and expire once their lease duration is over. Many well- known optimization problems are defined and studied in the leasing setting. In this paper, we continue the online algorithmic study of leasing by addressing the so-called Online Non-metric Facility Leasing problem (ONFL), the leasing variant of the non-metric Online Facility Location problem (non-metric OFL). Given a collection of facility and client locations. Facilities can be leased using a fixed number of lease types, each characterized by length
and price. Lease types respect the economy of scale, such that longer leases cost more but are cheaper per unit of time. In each step, a client appears. The algorithm needs to promptly connect it to a facility that is leased at the current time step. To this end, it needs to decide which facility locations to lease, the start of their lease, and the lease duration. Connecting a client to a facility incurs a cost equal to the distance between the facility and the client. The goal is to minimize the total connecting and facility leasing costs. In this work, we develop the first deterministic algorithm for ONFL and evaluate it using the notion of competitive analysis, a worst-case performance analysis in which the solution of the online algorithm is compared, over all instances of the given problem, to the optimal solution of the offline variant of the problem.
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