First Approximation for Uniform Lower and Upper Bounded Facility Location Problem avoiding violation in Lower Bounds

TL;DR

This paper introduces the first constant factor approximation algorithm for the uniform bounded facility location problem that avoids violating lower bounds while only violating upper bounds by a factor of 2.5, addressing a key challenge in e-commerce platform optimization.

Contribution

It provides the first approximation algorithm for the problem with both bounds, violating only the upper bounds, and transforms the problem to a capacitated facility location instance to eliminate lower bound violations.

Findings

Achieves a constant factor approximation for the problem.

Violates upper bounds by a factor of 2.5, no violation of lower bounds.

Transforms the problem into a capacitated facility location instance.

Abstract

With growing emphasis on e-commerce marketplace platforms where we have a central platform mediating between the seller and the buyer, it becomes important to keep a check on the availability and profitability of the central store. A store serving too less clients can be non-profitable and a store getting too many orders can lead to bad service to the customers which can be detrimental for the business. In this paper, we study the facility location problem(FL) with upper and lower bounds on the number of clients an open facility serves. Constant factor approximations are known for the restricted variants of the problem with only the upper bounds or only the lower bounds. The only work that deals with bounds on both the sides violates both the bounds [8]. In this paper, we present the first (constant factor) approximation for the problem violating the upper bound by a factor of (5/2) without violating the lower bounds when both the lower and the upper bounds are uniform. We first give a tri-criteria (constant factor) approximation violating both the upper and the lower bounds and then get rid of violation in lower bounds by transforming the problem instance to an instance of capacitated facility location problem.