Approximation algorithms for the Transportation Problem with Market Choice and related models

TL;DR

This paper develops approximation algorithms for the transportation problem with market choice, reducing it to facility location problems, and achieves constant-factor approximations in metric cases and logarithmic approximations generally.

Contribution

It introduces polynomial-time reductions from the transportation problem with market choice to facility location, enabling new approximation algorithms.

Findings

Two constant-factor approximation algorithms for the metric case

A logarithmic-factor approximation for the general case

Polynomial-time reductions to facility location problems

Abstract

Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into served clients, paying the transportation cost to serve them. We give polynomial-time reductions from this problem and variants to the (un)capacitated facility location problem, directly yielding approximation algorithms, two with constant factors in the metric case, one with a logarithmic factor in the general case.