ORIGINAL CONTRIBUTION A Genetic Algorithm for Flow Shop Scheduling with Assembly Operations to Minimize Makespan A. S. Bhongade • P. M. Khodke Received: 24 September 2012 / Accepted: 24 April 2014 / Published online: 6 May 2014 Ó The Institution of Engineers (India) 2014 Abstract Manufacturing systems, in which, several parts are processed through machining workstations and later assembled to form final products, is common. Though scheduling of such problems are solved using heuristics, available solution approaches can provide solution for only moderate sized problems due to large computation time required. In this work, scheduling approach is developed for such flow-shop manufacturing system having machin- ing workstations followed by assembly workstations. The initial schedule is generated using Disjunctive method and genetic algorithm (GA) is applied further for generating schedule for large sized problems. GA is found to give near optimal solution based on the deviation of makespan from lower bound. The lower bound of makespan of such problem is estimated and percent deviation of makespan from lower bounds is used as a performance measure to evaluate the schedules. Computational experiments are conducted on problems developed using fractional factorial orthogonal array, varying the number of parts per product, number of products, and number of workstations (ranging upto 1,520 number of operations). A statistical analysis indicated the significance of all the three factors consid- ered. It is concluded that GA method can obtain optimal makespan. Keywords Scheduling  Genetic algorithm  Heuristics  Flow shop List of symbols ConSetOpr Set of connected operations O k for a part Job_seq Set of products in a particular sequence Makespan Completion time for all products makespan_h Completion time for product h considered alone P(J hi ,w j ) Processing time of part J hi on workstation w j S_M_h Set of scheduled operations on workstations for product h ST_FT_J Start time and finish time of operation on workstation w j for part J hi W Total number of workstations for machining and assembly Introduction In many manufacturing systems, products are made from several parts and/or subassemblies, and require a series of machining operations in the first stage and assembly operations at a later stage. Scheduling problem in such manufacturing system is more complicated as the final assembly or sub assembly may have to wait, not only for machines, but also for its mating parts. This complexity is greatly influenced by the product structure, which shows relationship among parts or subassemblies and product in a hierarchical manner. Product structure may be flat, tall, or complex depending on product requirements as shown in Fig. 1. In job-shop, each part has a separate flow pattern. In a flow shop, all parts are processed by a series of ‘m’ machines in exactly the same order [1]. The production scheduling problem for job-shop and flow-shop with machining and assembly operations may be respectively termed as assembly job-shop problem (AJSP) and assem- bly flow-shop problem (AFSP). A. S. Bhongade (&) Rajiv Gandhi Institute of Technology, Versova, Andheri (W), Mumbai 400053, India e-mail: ajay_bhongade@rediffmail.com P. M. Khodke Government College of Engineering, Karad, India 123 J. Inst. Eng. India Ser. C (April–June 2014) 95(2):89–96 DOI 10.1007/s40032-014-0111-7