ORIGINAL ARTICLE Two meta-heuristics for three-stage assembly flowshop scheduling with sequence-dependent setup times Sara Hatami & Sadalah Ebrahimnejad & Reza Tavakkoli-Moghaddam & Yasaman Maboudian Received: 16 November 2009 / Accepted: 10 February 2010 / Published online: 9 April 2010 # Springer-Verlag London Limited 2010 Abstract In this paper, we consider a three-stage assembly flowshop scheduling problem with bi-objectives, namely the mean flow time and maximum tardiness. This problem can be considered as a production system model consisting of three stages: (1) different production operations are done in parallel, concurrently and independently, (2) the manu- factured parts are collected and transferred to the next stage, and (3) these parts are assembled into final products. In this paper, sequence-dependent setup times and transfer times are also considered as two important presumptions in order to make the problem more realistic. We present a novel mathematical model for a production system with a new lower bound for the given problem. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. Thus, we propose two meta-heuristics, namely simulated annealing and tabu search, to solve a number of test problems generated at random. Finally, the computational results are illustrated and compared in order to show the efficiency of the foregoing meta-heuristics. Keywords Assembly flowshop scheduling . Mean flow time . Maximum tardiness . Sequence-dependent setup times . Simulated annealing . Tabu search 1 Introduction Global competition and the ability to respond to the changing demand markets, while keeping the costs down, are some of the key elements in designing effective production systems. Assembly flowshop is a combinatorial production system, in which different sets of parts are manufactured independently on parallel production lines (or machines), and then they are assembled into final products. These production-assembly systems can be used as a way to produce a variety of goods by assembling and combining different sets of parts and subassemblies. From the scheduling perspective, these systems are modeled as a two-stage assembly flowshop scheduling problem (AFSP) [1]. In this problem, jobs (or products) are performed in two stages. At the first stage, parts of each job are manufactured concurrently on parallel machines, and at the second stage, they are assembled to make the final product. This model does not consider the required operation for collecting and transporting the manufactured parts from production site to assembly site. To have a more realistic model, another stage can be considered as a middle stage between the production and assembly stages, called transportation stage, in which parts and subassemblies are collected and transferred from production stage to assembly stage. This stage is important S. Hatami Department of Industrial Engineering, Islamic Azad University-Ghazvin Branch, Ghazvin, Iran S. Ebrahimnejad (*) Department of Industrial Engineering, Islamic Azad University-Karaj Branch, Karaj, Iran e-mail: ibrahimnejad@kiau.ac.ir R. Tavakkoli-Moghaddam Department of Industrial Engineering and Center of Excellence for Intelligence Based Experimental Mechanics, College of Engineering, University of Tehran, Tehran, Iran Y. Maboudian Department of Industrial Engineering, Khaje Nasir University of Technology, Tehran, Iran Int J Adv Manuf Technol (2010) 50:1153–1164 DOI 10.1007/s00170-010-2579-5