A General VNS Heuristic for a Three-Stage Assembly Flow Shop Scheduling Problem

Abstract

This paper studies a flow shop scheduling problem with three stages. At the first stage, different parts of a job are independently manufactured on m unrelated parallel machines. At the second stage, the manufactured parts are collected and transferred to the assembly stage where the parts are assembled into a final product. In this problem we considered sequence dependent setup times at each stage, and the objective to be minimize is the total tardiness. Motivated by the computational complexity and the practical relevance of the problem, we propose a heuristic based on General Variable Neighborhood Search with random VND (RVND) local search procedure to obtain near-optimal solutions. In the proposed RVND, a neighborhood is selected according to a selection probability that is self-updated with the number of improvements obtained by the neighborhood. As shaking procedure, we use a destruction-construction strategy that is used in the Iterated Greedy meta-heuristic. The effectiveness of the presented heuristic is evaluated by comparing its results to a basic GVNS, a Simulated Annealing proposed in the literature, and the CPLEX solver used to solve the mixed integer programming model of the problem. The obtained results have been statistically analysed.