Effective Approach to Job Scheduling in the Recycling Process with Diferent Type of Manufacturing Machines

Currently, materials flow optimization and creating of optimal job scheduling are one of the main tasks of all company for increase of competitiveness. A schedule problem in a manufacturing company is characterized as jobs sequence and allocation on machines during a time period. The first part of this article is focused on dynamic scheduling and its methods. The second part describes a case study of dynamic scheduling in a manufacturing company on recycling of plastic materials realized by APVV project number VMSP 0168/09. The manufacturing company described in this article is focused on recycling-based polymerization of plastic waste and on plastic waste bags production. A multi machine job shop scheduling problem is to assign each operation to a machine and to find a sequence of jobs (operations) on machines that the maximal production time is minimized [1]. 1 Mathematical formulation of a schedule task For solving a schedule task must be defined mathematical formulation of the schedule task. The schedule task can be defined by three sets: set of jobs J = {1, 2, ..., n}; set of machines M = {1, 2, ..., m}; set of operations O = {1, 2, ..., N}. Finite sequence of operations which must be made within one order represents one job. One operation is a basic unit of technological process, and it is characterized by type and processing time. In case that the operation can be made on several machines, processing time for all machines must be determined. Creation of job schedule must meet some restrictions, which we divide to hard and soft restrictions. Hard restrictions represent the technological process. They describe restrictions of individual operation time dependence, manufacturing machine capacity and other manufacturing machine characteristics. Soft restrictions represent the preferences which need not be fulfilled, but from the scheduling point of view it is convenient to fulfil them. The correct definition of soft restrictions we can reduce the searching space and find better solution of the job schedule. Preferences are an operation sequence which can minimize downtime or the waste due to changing of manufacturing parameters. The time continuity of several operations is expressed by the preference j i O O p , where operation Oj cannot start earlier than the operation Oi finishes. Other technological restrictions of processing of operations on machines can be described as follows: an operation can be made on one machine only; an operation can be atomic, it means the producing process of operation cannot interrupted by an arrival of other operation; it is specified in several processes, that two operations cannot be made on one machine at one time unit. Every job can be specified by next input information (Mičunek 2002): operations Oi processed on machines; processing time pijk is the time to process j operation, i job on k machine; ri is the time when it is possible to start processing job Ji; di is the required end time of job Ji; ai is maximal allowed time of a job in the system ai = di – ri; wi is the weight of job importance Ji. Output information of a scheduling problem represents the data, which can be calculated for every job Ji of the job schedule. The information consists of the following data: Ci is the end time of job Ji; Fi is the processing time of job Ji; Wi is the waiting time of job Ji in the system; Li is the delay calculated by Li = Ci – di; Ti is the maximal {0, Li} delay of job Ji ; Ei is the maximal {0, -Li} advance of job Ji; Ui = 0, if Ci <= di, else Ui = 1 is penalty function of job Ji. The task defined in this way belongs to the optimization field. Optimal (suboptimal) solution of the job schedule is found if several criterions and restrictions are valid. Traditional approach of static schedule assumes static environment and does not assume failure of machine. Real manufacturing system assumes several types of unpredictable events that result in the creation of a new job schedule. According to (Vieira et al., 2003) in manufacturing systems there are two types of events in real time: events related to source (failure of source, material ageing, human operator, etc.); events related to job (new jobs arrival, changing job priorities, changing job deadline, etc.); According to (Metha and Uzsoy, 1999; Vieira et al., 2000a, 2003; Aytug et al., 2005; Leus and Herroelen, 2005), dynamic scheduling is divided into four basic types: reactive scheduling; predictive-reactive scheduling; predictive-reactive (robust) scheduling; proactive (robust) scheduling. Solution of dynamic scheduling problem can be broken into a series of static problems to be dealt with static scheduling methods. Depending on when we need to create a new job schedule, we use scheduling at regular intervals (rescheduling), upon arrival of new event (event rescheduling), or the hybrid way, when new job schedule is created periodically but in case urgent event arrives for job scheduling new job schedule is created. Dynamic scheduling uses five basic approaches for job scheduling: dispatching rules; heuristics; meta-heuristics (Tabu search, simulated annealing, genetic algorithm); artificial intelligence (neural networks, case-based reasoning, fuzzy logic, Petri nets); Multi-agents systems. Dispatching rules the literature describes several types of rules, from simple to very complex rules. No set of rules can capture the complexity of scheduling requirements in dynamic environment. Therefore, to verify the efficiency and effectiveness of the rules simulation techniques are used. Experimental results show that the correct choice of rules depends not only on the characteristics of the manufacturing machines, but also on other factors, such as material flow, etc. Heuristics – this is a frequently used approach in dealing with scheduling tasks. In combination with the set of dispatching rules, it very significantly may contribute to finding appropriate solution to scheduling tasks. Meta-heuristics this technique includes methods such as Tabu search, simulated annealing or genetic algorithms. All methods have been used successfully to solve different types of scheduling tasks. Artificial intelligence – this field includes methods such as knowledge-based systems, neural networks, case reasoning, fuzzy logic, Petri nets, etc. The use of the technology is very successful in the field of machine learning and adaptive learning. Multi-agent systems MAS technologies are among the most progressive evolving technologies, from which we expected major benefits in addressing the job scheduling. Initial expectations have caused frustration and certain scepticism in the application of this theory into practice. Nevertheless, this approach is still a current topic, especially in research toward the development of comprehensive, robust and cost-effective solutions for businesses new generation. The following part of the article describes an approach to solving job scheduling based on a real manufacturing company problem. 2 Description of the real manufacturing system The manufacturing system which is the carrier of the APVV project No. 0168/09, with significant share in Slovak market, is dealing with producing of recycled low-density polyethylene (LDPE) film. Recycling capacity is 180 tons per month. The manufacturing company is one of the three largest companies in Slovakia from the point of view of recycling waste film. Manufacturing machines for recycling of soft plastics are used as a pilot application for the output of research carried out in cooperation with the Institute of Informatics of Slovak Academy of Sciences (II SAS) in a joint applied research project. This project resulted from years of research in modeling and simulation of manufacturing machines at the II SAS. The manufacturing system itself consists of several different machines recycling plastic materials and producing waste bags from LDPE film. Block diagram of the manufacturing system is shown in Figure 1. The system consists of three main parts: granulation machine: polymerization of waste plastics leads to production of different color granulates (“wet production”); blowing machine (extruder): the polymerization process using granulates and other input additives produces LDPE film of desired shape, thickness, width and color (four different blowing machine types – extruders are available); the film is scrolled into rolls (maximum roll weight depends on blowing machine type); scroll machine: LDPE film is welded, punched and scrolled to desired size (two different scroll machine types are available). Figure 1: Block diagram of the manufacturing system The manufacturing system is defined by the following set of jobs:  = , , ; where Jgran represents granulate production, Jfol represents the production of LDPE film roll and Jvrec represent the production of waste bags from LDPE film. Every job is defined by the following operations:  → ;  → ,;  → ,, , ; which can be divided into the following set of machines:  → ;  → , , , ;  → , ;  → .