The capacitated facility location problem with random input data

Abstract

Under study is the capacitated facility location problem (CFLP) with random input data. The transportation costs are assumed to take random values according to the uniform discrete distribution on the integer segment [1, r]. For CFLP with uniform capacity constraints, we construct an algorithm of time complexity O(n log m) and establish conditions for asymptotic optimality (where n is the number of consumers and m is the number of facilities). For CFLP with varying capacities, we construct an algorithm of time complexity O(n 2(1-θ) m) and establish conditions for asymptotic optimality for certain θ < 1/2.