  The k-SERVER problem is one of the most prominent problems in online
algorithms with several variants and extensions. However, simplifying
assumptions like instantaneous server movements and zero service time has
hitherto limited its applicability to real-world problems. In this paper, we
introduce a realistic generalization of k-SERVER without such assumptions - the
k-FOOD problem, where requests with source-destination locations and an
associated pickup time window arrive in an online fashion, and each has to be
served by exactly one of the available k servers. The k-FOOD problem offers the
versatility to model a variety of real-world use cases such as food delivery,
ride sharing, and quick commerce. Moreover, motivated by the need for fairness
in online platforms, we introduce the FAIR k-FOOD problem with the max-min
objective. We establish that both k-FOOD and FAIR k-FOOD problems are strongly
NP-hard and develop an optimal offline algorithm that arises naturally from a
time-expanded flow network. Subsequently, we propose an online algorithm
DOC4FOOD involving virtual movements of servers to the nearest request
location. Experiments on a real-world food-delivery dataset, alongside
synthetic datasets, establish the efficacy of the proposed algorithm against
state-of-the-art fair food delivery algorithms.
