Online Metric Facility Service Leasing with Duration-Specific Dormant Fees

Abstract

Inspired by the COVID-19 pandemic, a new online facility model, known as the Online Facility Service Leasing problem (OFSL), has been recently introduced. In OFSL, services at different (health) facility locations are leased for different durations and costs. Each service at each facility is associated with a dormant fee that needs to be paid for each day on which the service is not leased at the facility. Clients arrive over time, each requesting a number of services, and need to be served by connecting them to multiple facilities jointly offering the requested services. The aim is to decide which services to lease, when, and for how long, in order to serve all clients as soon as they appear with minimum costs of leasing, connecting, and dormant fees. In this paper, we study a generalization of OFSL in which we are additionally given a parameter d, such that, should the service be not leased for more than d consecutive days, a dormant fee is to be paid (d = 0 in the case of OFSL). We call this variant the Online Facility Service Leasing with Duration-Specific Dormant Fees (d-OFSL). We particularly focus on the metric version of the problem in which facilities and clients reside in the metric space. We refer to it as metric d-OFSL and design the first online algorithm for the problem. The latter is a deterministic algorithm based on a primal-dual approach. We measure its performance by comparing it to the optimal offline solution for all instances of the problem. This performance analysis is known as competitive analysis and is the standard to evaluate online algorithms. Copyright © 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved