ORIGINAL ARTICLE A mixed integer programming formulation for scheduling of virtual manufacturing cells (VMCs) Saadettin Erhan Kesen & Sanchoy K. Das & Zulal Gungor Received: 6 April 2009 / Accepted: 20 July 2009 / Published online: 12 August 2009 # Springer-Verlag London Limited 2009 Abstract We present a multi-objective mixed integer programming formulation for job scheduling in virtual manufacturing cells (VMCs). In a VMC, machines are dedicated to a part family as in a regular cell, but machines are not physically relocated in a contiguous area. Cell configurations are therefore temporary, and assignments are made to optimize the scheduling objective under changing demand conditions. We consider the case where there are multiple jobs with different processing routes. There are multiple machine types with several identical machines in each type and are located in different locations in the shop floor. The two scheduling objectives are makespan minimization and minimizing total traveling distance. Since batch splitting is permitted in the system, scheduling decisions must tell us the (a) assignment of jobs to the machines, (b) the job starting time at each machine, and (c) the part quantity processed on different machines due to batch splitting. Under these decision variables, the objective function is to minimize the sum of the makespan and total traveling distance/cost. Illustrative examples are given to demonstrate the implementation of the model. Keywords Virtual manufacturing cells (VMCs) . Scheduling . Mathematical model . Flexible manufacturing systems 1 Introduction Like any other sector, manufacturing sector nowadays has been striving to survive against the economic downturn surrounding all over the world. Hence, firms look for more options to decrease their production costs. Undoubtedly, one of the most effective cost reduction strategies is reconfiguration of the production facilities [1]. Many types of production configurations have been proposed and built in the manufacturing industry. If demand structure is characterized by high volume and less variety, a product type layout is the most efficient. In the case of low to medium volume and unstable demand, a functional type layout is suggested because of its flexibility. It is well known that while a product type layout limits flexibility, a functional type layout suffers from efficiency. In the 1960s, cellular manufacturing systems (CMS), based on group technology (GT) principles, were introduced to cope with the drawbacks of product type and functional type layouts. In CMS, parts with similar processing requirements are grouped together to form part families, and machines with different processing capabilities are grouped to create machine cells. The production operations are therefore simplified by processing a family through only one cell. Because of its processing advantages, CMS provides the basis for implementing more sophisticated manufacturing methods such as flexible manufacturing systems, computer- aided design/computer-aided manufacturing, just-in-time production, Robotics, etc. [14, 27, 28]. The performance of CMS, though, depends significantly on the stability of S. E. Kesen (*) Department of Industrial Engineering, Selcuk University, 42075, Campus, Konya, Turkey e-mail: sekesen@gazi.edu.tr S. K. Das (*) Department of Industrial & Management System Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA e-mail: das@njit.edu Z. Gungor (*) Department of Industrial Engineering, Gazi University, 06570, Maltepe, Ankara, Turkey e-mail: zulalg@gazi.edu.tr Int J Adv Manuf Technol (2010) 47:665–678 DOI 10.1007/s00170-009-2231-4