Journal of Manufacturing Systems 32 (2013) 700–714 Contents lists available at ScienceDirect Journal of Manufacturing Systems j ourna l ho me p age : www.elsevier.com/locate/jmansys Technical Paper A new optimization approach for nozzle selection and component allocation in multi-head beam-type SMD placement machines S.A. Torabi a,∗ , M. Hamedi a , J. Ashayeri b a School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran b Department of Econometrics & Operations Research, Tilburg University, Tilburg, The Netherlands a r t i c l e i n f o Article history: Received 3 April 2011 Received in revised form 25 August 2013 Accepted 22 September 2013 Available online 19 October 2013 Keywords: PCB assembly Multi-head beam-type SMD machine Augmented epsilon-constraint method Particle Swarm Optimization Taguchi Method a b s t r a c t This paper addresses a highly challenging scheduling problem faced in multi-head beam-type surface mounting devices (SMD) machines. An integrated mathematical model is formulated aiming to balance workloads over multiple heads as well as improving the traveling speed of the robotic arm by incorpo- rating the appropriateness factors in the model to evaluate the compatibility of component-nozzle pairs. The proposed model is a bi-objective mixed integer nonlinear programming one, which is first converted into a linearized model and then directly solved by using the augmented epsilon constraint method for small problem instances. As the model is turned out to be NP-hard, we also develop a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to solve the model for medium and large-sized prob- lem instances. The parameters of the proposed MOPSO are tuned by using the Taguchi Method and corresponding numerical results are provided. © 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. 1. Introduction The growing demand for electronic devices has made the man- ufacturing of printed circuit boards (PCBs) a promising industry over the last decades. As the demand for printed circuit boards increases, the industry becomes more dependent on highly auto- mated assembly processes using surface mounting devices (SMD). Surface mount technology (SMT) has displaced through-hole tech- nology as the primary means of assembling PCBs. It has also made it easy to automate the PCB assembly process. The component placement machine is probably the most important piece of man- ufacturing equipment on a surface mount assembly line (Hardas et al. [1]). As SMT becomes popular, different types of placement machines have arisen. For a well-organized classification of place- ment machines based on their operational methods the reader is referred to Ayob and Kendall [2]. Among the component place- ment machines, multi-head of gantry-type machines are becoming increasingly popular because they provide high mounting speed with relatively low cost. A gantry robot, which moves components between the components feeder racks and the PCB, nowadays are equipped with multiple heads to reduce the number of pick-and- place cycles. The heads are sequentially arranged on a beam or a rotating wheel at the gantry robot. The former is called beam-type ∗ Corresponding author. Tel.: +98 21 88335605. E-mail addresses: satorabi@ut.ac.ir (S.A. Torabi), mhamedy@ut.ac.ir (M. Hamedi), j.ashayeri@uvt.nl (J. Ashayeri). while the latter is called collect-and-place type (Sun and Lee [3]). Both types of these machines can have single or multiple arms. Production planning and control of SMT facilities can be consid- ered as involving a hierarchy of six fundamental types of decision problems, which can be grouped into three distinct, yet interdepen- dent, levels. The machine level of the hierarchy deals with decisions focusing on making the best use of the capabilities of an individual machine (Rogers and Warrington [4]). McGinnis et al. [5] summa- rizes optimization problems for an SMD machine (at the machine level) as feeder assignment and placement sequencing. The proper assignment of component types to feeders in placement machines and the placement sequence of components on the PCB are the main factors greatly affecting the production cycle time of each machine and the whole SMT line (Crama et al. [6]). These problems are highly interrelated and very difficult to solve them simultaneously. There- fore, during the last decade, most research on minimizing the PCB assembly time has focused on solving these problems separately by decoupling one from the other (Lee et al. [7]). Many research works have been devoted to these complex problems by devel- oping various mathematical models and solution approaches. For example, Ball and Magazine [8] modeled the sequencing problem in a sequential pick-and-place machine as a directed postman prob- lem. They suggested that the balance and connect heuristic can be applied to this problem. Leipala and Nevalainen [9] dealt with the placement sequencing sub-problem in the same machine of [8] as a three dimensional asymmetric traveling salesman problem whilst the feeder assignment sub-problem was modeled as a quadratic assignment problem. Khoo and Loh [10] modeled the problem of 0278-6125/$ – see front matter © 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmsy.2013.09.005