Demand allocation with latency cost functions

TL;DR

This paper presents a specialized branch and bound algorithm for solving a resource allocation MINLP with convex latency costs, achieving superior performance over standard solvers through innovative bounds, branching, and heuristics.

Contribution

The authors develop a novel branch and bound method with efficient bounds, n-ary branching, and a strong heuristic, significantly improving solution times for demand allocation problems.

Findings

The proposed algorithm computes bounds in O(nlog n) time.

N-ary branching scheme improves efficiency over binary schemes.

The method outperforms CPLEX MIPQ in computational tests.

Abstract

We address the exact resolution of a MINLP model where resources can be activated in order to satisfy a demand (a partitioning constraint) while minimizing total cost. Cost functions are convex latency functions plus a fixed activation cost. A branch and bound algorithm is devised, featuring three important characteristics. First, the lower bound (therefore each subproblem) can be computed in O(nlog n). Second, to break symmetries resulting in improved efficiency, the branching scheme is n-ary (instead of the "classical" binary). Third, a very affective heuristic is used to compute a good upper bound at the root node of the enumeration tree. All three features lead to a successful comparison against CPLEX MIPQ, which is the fastest among several commercial and open-source solvers: computational results showing this fact are provided.