Combining Optimisation and Simulation Using Logic-Based Benders Decomposition

TL;DR

This paper introduces a novel logic-based Benders decomposition method that integrates simulation directly into the optimization process, enabling exact solutions for complex stochastic resource allocation problems.

Contribution

The paper presents a new approach that combines simulation with optimization using logic-based Benders cuts, allowing for exact solutions to complex stochastic problems previously only approximately solvable.

Findings

Successfully solved realistic instances exactly within reasonable time

Derived strong, valid Benders cuts for all problems of the given form

Handled up to 100 scenarios for sample average approximations

Abstract

Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to evaluate the true objective value of one or more solutions. We propose a new approach to integrating simulation into the optimisation model itself. The idea is to run the simulation at each incumbent solution to the master problem. The simulation data is then used to guide the trajectory of the optimisation model itself using logic-based Benders cuts. We test the approach on a class of stochastic resource allocation problems with monotonic performance measures. We derive strong, novel Benders cuts that are provably valid for all problems of the given form. We consider two concrete examples: a nursing home shift scheduling problem, and an airport check in counter allocation problem. While previous papers on these applications could only approximately solve realistic instances, we are able to solve them exactly within a reasonable amount of time. Moreover, while those papers account for the inherent variance of the problem by including estimates of the underlying random variables as model parameters, we are able to compute sample average approximations to optimality with up to 100 scenarios.