Combining simulation with a GRASP metaheuristic for solving the permutation flow-shop problem with stochastic processing times

Abstract

Greedy Randomized Adaptive Search Procedures (GRASP) are among the most popular metaheuristics for the solution of combinatorial optimization problems. While GRASP is a relatively simple and efficient framework to deal with deterministic problem settings, many real-life applications experience a high level of uncertainty concerning their input variables or even their optimization constraints. When properly combined with the right metaheuristic, simulation (in any of its variants) can be an effective way to cope with this uncertainty. In this paper, we present a simheuristic algorithm that integrates Monte Carlo simulation into a GRASP framework to solve the permutation flow shop problem (PFSP) with random processing times. The PFSP is a well-known problem in the supply chain management literature, but most of the existing work considers that processing times of tasks in machines are deterministic and known in advance, which in some real-life applications (e.g., project management) is an unrealistic assumption.