Amariei O.I., Hamat C.O., Coman L., Burian R. Robotica & Management, 18-2 / 2013 39 MINIMIZING MAKESPAN IN JOB SHOP PRODUCTION USING A NETWORK APPROACH Teach. Assist. Eng. Olga Ioana Amariei*, Prof. Dr. (Ph.D.) Eng. Codruţa Oana Hamat*, Assist. Prof. Dr. Liviu Coman*, MSc MBA Renate Burian** *Eftimie Murgu University of Reşiţa, Faculty of Engineering and Management Piaţa Traian Vuia, N 0 1-4 , Reşiţa, Romania e-mail : c.hamat@uem.ro, o.amariei@uem.ro, l.coman@uem.ro **European Training and Research Institute, Schaufelberg 63, A-8380, Jennersdorf, Austria e-mail: burian@cere.com Abstract: This paper aims at solving a job shop scheduling problem of 3 tasks with different execution sequences of operations on 3 machines. The Shortest Processing Time rule is used, because this rule minimizes the average proccesing time of a set of tasks. It is then converted to a CPM network. The software Lekin is used for establishing the execution launch sequence of tasks, and for solving the CPM problem, the WinQSB software. Keyword: job shop scheduling, Gantt graph,CPM, dispatching rules, Lekin. 1. Introduction Organizing production systems are of particular interest to industrial enterprises, regardless of their size, job shop scheduling of production is one of the most difficult problems of organization [2]. Job shop scheduling of production is conducting a series of calculations that establish the order of startup of tasks [2]. The problem of job shop scheduling of n tasks on m machines is the most complex and for this many complex studies have been conducted. It can be divided in 2 sub problems [4]: 1. Job shop scheduling of n tasks with the same sequence of executing component operations, for which there are no deadlines, on m machines whose initial release moments are known; 2. Job shop scheduling of n tasks with different execution sequences of operations for which there expected delivery times on m machines. 2. Problem Data Considering we have a job shop problem with 3 machines, noted M1÷M3 and 3 tasks, noted J1÷J3. Processing times (in minutes) of each task on each machine are given in table 1, and in figure 1 are represented the technological flow path of the 3 tasks. Tab. 1 Fig. 1. Technological flow path of the three tasks 3. Dispatching Rules The dispatch order of the tasks is well established, based on some dispatching rules. The total processing times of the tasks on machines, are shown in the information windows of the Lekin software (tab.2). Tab. 2 Conway and Maxwell have been the first researchers that focused their studies on rule SPT