Author:
Christine Markarian
Affiliation:
Department of Engineering and Information Technology, University of Dubai, Dubai, U.A.E.
Keyword(s):
Online Non-metric Facility Location, Service-quality Costs, Optimization, Online Algorithms, Competitive Analysis, Randomized Algorithms, Rounding.
Abstract:
In this paper, we study the Online Non-metric Facility Location with Service-Quality Costs problem (Non-metric OFL-SQC), a generalization of the well-known Online Non-metric Facility Location problem (Non-metric OFL), in which facilities have, in addition to opening costs, service-quality costs. Service-quality costs are determined by the quality of the service provided by each facility so as the higher the quality, the lower the service-quality cost. These are motivated by companies wishing to incorporate the quality of third-party services into their optimization decisions. Clients are scattered around facilities and arrive in groups over time. Each arriving group is composed of a number of clients at different locations. Non-metric OFL-SQC asks to serve each client in the group by connecting it to an open facility. Opening a facility incurs an opening cost and connecting a client to a facility incurs a connecting cost, which is the distance between the client and the facility. Mor
eover, for each group, the algorithm needs to pay the sum of the service-quality costs associated with the facilities serving the clients of the group. The aim is to serve each arriving group while minimizing the total facility opening costs, connecting costs, and service-quality costs. We develop the first online algorithm for non-metric OFL-SQC and analyze it using the standard notion of competitive analysis, in which the online algorithm’s worst-case performance is measured against the optimal offline solution that can be constructed optimally given all the input sequence in advance.
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