Discrete Event Dynamic Systems Framework for Analysis and Modeling of Real Manufacturing System J. Zelenka* *
Institute of Informatics / Slovak Academy of Sciences, Bratislava, Slovakia e-mail:
[email protected]
Abstract — This article refers to possibility of utilization of modeling of a manufacturing system sense as a discrete event system by the optimization of a job schedule. Using software tools we can create a model, which allows simulation of system behaviour at varying parameters. The example of the manufacturing system model created by the SimEvents toolbox of software tools Matlab is illustrated.
I. INTRODUCTION The goal is focused on research and development of new approaches to optimize control and job scheduling of applied research on plastic recycling manufacturing system in the field of unconventional methods of control with the main attention on specific manufacturing line for recycling-based polymerization. The manufacturing system itself consists of several different lines recycling plastic materials. As a result of the process low-density polyethylene (LDPE) film is obtained, which serves as a base material for waste bags production. For more detailed description see the fourth part of this paper. The optimization is aimed at increased flexibility, reduced cost and improved product quality. Currently, a job scheduler is able to create short-time job schedules only, about 5 – 7 days, due to intuitive human decision. Therefore it is necessary to map all downtimes, to create uniform clue to simplification of the job schedule, which will be applied into software product. In creating the process optimization stochastic algorithms should be applied namely Tabu search [2], Hill-climbing [7], Simulated annealing, Genetic algorithm [3][4][5] [6], Bayes reasoning or others, which are capable of finding a suboptimal solution to our problem. One of these algorithms will be verified by the manufacturing system model. The paper is organized as follows. The next section gives the presentation of manufacturing line as a discrete event system. The third section describes SimEvents toolbox which allows modeling and simulating discreteevent systems. Current state of the model is described in the fourth part of the paper. The simulation results are given in the fifth section. Conclusion and outline on future works are presented in the sixth section. II. MANUFACTURING LINE AS A DISCRETE EVENT SYSTEM Discrete systems can be controlled by time (timedriven) or event (event-driven), i.e. the system state changes depend on time or event. This article deals with discrete event system (DES; the discrete systems
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controlled by events). Reference [1] characterized discrete event system by the state space S (a countable set), set of asynchronous event E (a countable set), which correspond to the transition between states and a transition function D (D: S × E → S ∪ Λ, where Λ denotes a null element used to indicate that the transition is undefined).Then the discrete event system can be defined as follows:
∑ = (S , E , D ) .
(1)
This model of DES contains no timing information, such as state holding times or event occurrence rates, which are often of interest (e.g. downtime …). In the case when the information on occurrence of the kth event ek at time tk ({ek, tk}k=0,1,…) is known, we think of timed DES. In order to properly define a timed DES, we need to specify the mechanism for generating all tk in the sequence ({ek, tk}k=0,1,…), and equip (S, E, D) with all necessary additional information. The timed DES are defined as follows: ∑ = (S , E , D, F )
(2)
F = {Fe (τ e ) : e ∈ E}
(3)
where
is the distribution function probability set associated with event types. The random variable τe characterized by Fe(τe) is called the event lifetime. The set F refers to the event lifetime generator for the DES ∑. The possibility of the manufacturing system with a continuous process describes how a discrete event system is necessary to specify what will represent the state and the event. In this case, the event represents producing or processing of a product and the state represents the manufacturing line which is producing or processing product. III. MODEL OF DISCRETE EVENT SYSTEM CREATED BY SIMEVENTS TOOLBOX OF MATLAB SOFTWARE TOOLS The SimEvent toolbox extends utilization of Simulink® whitch is a part of Matlab software tools for modeling and simulating a discrete-event system. With SimEvents we can create a model of discrete event systems to simulate passing of entities through a model created by queues, servers and other event based blocks.
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INES 2010 • 14th International Conference on Intelligent Engineering Systems • May 5–7, 2010 Las Palmas of Gran Canaria, Spain
Figure 3. Granulate line part of the manufacturing system model
Figure 1. Blocks of SimEvents toolbox
A discrete-event simulation (event-based simulation) permits the system’s state transition to be ruled by asynchronous discrete incidents called events. By contrast, a simulation based solely on differential equations in which time is an independent variable is a time-based simulation because state transitions depend on time. Simulink is designed for time-based simulation, while SimEvents is designed for discrete-event simulation. Discrete-event simulations involve discrete items of interest. These items are called entities in SimEvents. As noted previously, entities can pass through a network of queues, servers, gates, switches, etc. “Fig. 1” shows blocks of the SimEvents toolbox. Event occurrences cannot be represented by graphically, but their occurrence can be assessed by observation of the consequences of using the Scope blocks (e.g. Instantaneous Event Counting Scope). In SimEvent, models are created by the “drag and drop” method. SimEvents uses two types of connection line, an entity and a signal connection line. The difference is ensured by the different type of port at block input and output. Interconnection of entity and signal connections is excluded. Before we start to create a model, the setting of Simulink must be changed to simulation of discrete-event system by the command “simeventsstartup(‘des’)” in Matlab command line. If we need to combine discreteevent simulation with a continuous system we have to use the hybrid setting through the command “simeventsstartup(‘hybrid’)” [8]. The use of SimEvents block will be illustrated on the manufacturing system which produces waste bags from LDPE film.
Figure 2. Block diagram of the manufacturing system
Figure 4. Blowing line part of manufacturing system model
IV. DESCRIPTION OF THE MANUFACTURING SYSTEM AND ITS MODEL CREATED MAKING USE OF SIMEVENTS TOOLBOX A. Manufacturing System The manufacturing system is dealing with recycling of so-called soft plastics, producing of LDPE film and producing of waste bags from LDPE film. Block diagram of the manufacturing system is shown in “Fig. 2”. The system consists of three main parts: - granulate line: the polymerization process of waste plastics leads to production of different color granulates (“wet way” production); - blowing line (extruder): the polymerization process using granulates and other input additives produces LDPE film of desired shape, thickness, width and color (four different types of blowing line extruder are available); the film is reeled into rolls (maximum weight of roll depends on blowing line type); - scroll line: LDPE film is welded, punched and scrolled to desired size (two different scroll line types are available). B. Optimization Problem The goal of optimization is to create uniform clue to simplification of the job schedule. 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 [9]. By creating of the convenient criterion we can figure with: - material loss minimization by color change (from dark to light color change by granulate or LDPE film production is used); - material loss minimization by parameters change (it is possible to width, thickness or color modification during LDPE film production, but the material loss is increasing); - downtime minimization; - production time minimization (we can divide one order on two or more lines and thus to reduce the production time); - power consumption minimization; In this paper we target the downtime minimization on scroll line.
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J. Zelenka • Discrete Event Dynamic Systems Framework for Analysis and Modeling of Real Manufacturing System
b)
a)
Figure 5. Graphical user interface and simulation results
C. Description of the Manufacturing System Model Because, the manufacturing system model is too large, only a part of the model is described here. “Fig. 3” shows the granulate line model. The entity generator “Waste input” generates entities (each time unit an entity is generated). Every entity contains information about weight of delivered plastic waste (it is assumed that every generated entity will have the same information about weight). The FIFO queue “Waste storage” works as storage of plastics waste before processing, because the waste plastics may be fed in faster than processed. Gate 1, gate 2 and server “Capacity KV” ensure that the number of processed entities will not be higher than the granulate line capacity. The output switch transports entities to next FIFO queues. All of these blocks are controlled by the Granulate Control block, which ensures transport of entities from server to FIFO queues intended for granulates (depending on color). Blowing line model (see “Fig. 4”) can be created in a similar way. Input and output switches ensure transport of entities from FIFO queue of granulate (depending on color) from which the LDPE film will produced. The Granulate Control block (“Fig. 3”) or the Control Extruder 1 block (“Fig. 4”) control and ensure correct run of the manufacturing system model. Control of these blocks was necessary to create the graphical user interface GUI (see “Fig. 5a”). Through the graphical user interface the input information (customer orders) are loaded and processed, the job scheduling for all manufacturing lines is created and signals for control gates and switches of the model are generated. By using of the scope block we can see the simulation result of transmission of entities. For example, “Fig. 5b” shows the simulation result of the state of waste store (second block of the model in “Fig. 3”).
Figure 6. Recasted graphical user interface
A disadvantage of this model is input information. The input information includes data on color and weight of the required quantity of granulates. On the basis of this data the software of GUI reserves the quantity of entities which will be removed by all models as one order (taking into account the capacity of individual manufacturing lines). It is necessary to know the conversion rate between the weight of film and the weight of granulate. In fact, the order contains information on waste bag size, width, thickness, color, quantity, etc. This is why the graphical user interface was recast (see “Fig. 6”) into a shape, able to reserve the information about order (size, width, thickness, color, quantity, type of blown film, etc.) and the SimEvents model will be used for scheduling of production of individual orders. The results of new graphical user interface are shown as graphs of processing time of a line per a day. V. SIMULATION AND RESULTS “Fig. 7” shows the result of the recast SimEvents model. This model compares two ways of LDPE film processing. The entity generated by the entity generator “Blowing line 1” in “Fig. 7” represents the blowing line product (LDPE film roll). The production time of LDPE film roll depends on blown film width and thickness and on blowing line type. Then the film roll is processed on the scroll line. With the first way of processing a film roll is processed on the scroll line immediately after being produced. When the processing time of the scroll line is less than the production time of the blowing line, the scroll line must wait for the production of film roll. TABLE I. SIMULATION RESULTS OF TWO WAYS OF FILM ROLL PROCESSING TRS1
TDRS1
x
TRS2
TDRS2
ΔDT
ΔDY
43,0 h
47,5 h
1
43,0h
47,5 h
0h
0h
43,0 h
47,5 h
2
38,5h
47,5 h
4,5h
0h
43,0 h
47,5 h
3
34,0 h
47,5 h
9,0h
0h
43,0 h
47,5 h
4
29,5 h
47,5 h
13,5h
0h
43,0 h
47,5 h
5
25,0 h
47,5 h
18,0h
0h
43,0 h
47,5 h
6
25,0 h
52,0 h
18,0h
-4,5h
43,0 h
47,5 h
7
25,0 h
56,5 h
18,0h
-9,0h
43,0 h
47,5 h
8
25,0 h
61,0 h
18,0h
-13,5h
43,0 h
47,5 h
9
25,0 h
65,5 h
18,0h
-18,0h
43,0 h
47,5 h
10
25,0 h
70,0 h
18,0h
-22,5h
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INES 2010 • 14th International Conference on Intelligent Engineering Systems • May 5–7, 2010 Las Palmas of Gran Canaria, Spain
Figure 7 Model in SimEvents
a)
b)
c)
d)
Figure 8. Simulation results
Scroll line will be unnecessarily reserved (downtime originated, which must be reduced). Reality is that the processing time of the scroll line is less than the production time of the blowing line. The second way of processing a film roll is that the film roll will be processed on the scroll line after production of the xth film roll on the blowing line. The results of simulating the production of ten LDPE film rolls and their processing on the scroll line are shown in “Fig. 8”. The graph in “Fig. 8a” shows roll film production on the blowing line (each dot in the figure represents production LDPE film roll). “Fig. 8b (c, d)” shows the result of the first (second) way of roll film processing on the scroll line (each dot in the figure represents processing LDPE film roll). The results of this simulation are summarized in Table 1, where TRS1 is production time of the tenth product on the scroll line (first way), TRS2 is production time of tenth product on the scroll line after production of the xth roll film on the blowing line (second way), TDRS1 is processing finish time on the scroll line (firs way), TDRS2 is processing finish time on the scroll line (second way).In the last but one column of the table ΔDT (the difference between the first
and the second production time) is given; this difference represents downtime. In the last column ΔDY (the delay of the second way of film roll processing with respect to the first one) is given. It is evident from the results in Table 1 that the second way of film roll processing on the scroll line is better than the first way. For example, when the scroll line starts to process the roll film after six produced film roll (the seventh row in Table 1), then the production time is reduced to eighteen hours. On the other hand, the processing finish is prolonged by four and half hours. Using the second way the operating costs are reduced, but the process on the scroll line is longer. The best job schedule can be found in the fifth row of Table 1. In this case the production time is reduced to eighteen hours and the roll film processing finishes at the same time as with the first way of production. Using second way we can reduce production time by 58% compared to the first way. Result of this simulation is shown in the “Fig. 8c”. Now a company starts processing LDPE film roll on the scroll line after produced of the last film roll (“Fig. 8d” or the eleventh row in Table 1). In this case downtime does not originate, but finish time of rolls processing on the scroll line is by 46% greater than finish time of the first way.
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J. Zelenka • Discrete Event Dynamic Systems Framework for Analysis and Modeling of Real Manufacturing System
VI. CONCLUSION AND FUTURE WORK The task of manufacturing system analysis and modeling is to analyze the system behaviour and to create the model, which will represent the behaviour of the system. With this model created we can easily find the answer to the question, which would be hard without simulation. The possibility of the model created by SimEvents interconnected with the state diagram created by Stateflow toolbox makes the Matlab software tools stronger for modeling of event system. Addition of next blocks from Simulink to the model results in simple modeling of complex hybrid systems. It is evident from the simulation of two ways that the second way is better than the first one, but, only if the processing time on the scroll line is shorter than the production time of the blowing line, and if the processing of film roll can start on the scroll line after having produced the xth roll film on the blowing line. Accordingly, it is possible to divide one order on two blowing lines, and thus to reduce the production time. However, job scheduling with short production time is not necessarily the optimal solution from the point of view of finances; therefore it is necessary to find the optimal (suboptimal) job scheduling solution satisfying all conditions (production time, downtime, finance, power consumption of all lines, etc.) The next parameter which will influence the production is represented by free days (weekend, holiday), as well as by unforeseen failure. Thus, the next step will create a model, which allows simulation of production on work days only, with additional criteria added to job scheduling.
ACKNOWLEDGMENT This work has been supported by the APVV scientific grant agency, grant No. 0168-09 “Optimalizácia recyklačných výrobných liniek aplikovaním nekonvenčných metód riadenia” and by VEGA scientific grant agency, grant No. 2/0197/10 “Moderné metódy a techniky pre integrované inteligentné riadenie výrobných systémov”. REFERENCES [1]
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