24th Mediterranean Conference on Control and Automation (MED) June 21-24, 2016, Athens, Greece
PN modelling, simulation, performance evaluation and production forecast of a tanning industry Konstantinos E. Vrontakis, Andreas N. Kampianakis, and George J. Tsinarakis
Abstract In this paper a Petri Net (PN) based methodology for modelling, simulation, performance evaluation and production forecast of a tanning industry processing 5 leather types is presented. The Petri net models of the production procedures are built and simulated in order to calculate specific performance measures. Then exponential smoothing method is applied in order to forecast the overall demand of the upcoming year for each product type. Finally, a scenario concerning partial change of the equipment efficiency is tested and the results obtained are compared to the ones of the initial model.
I. INTRODUCTION The growth in the complexity of modern industrial systems creates numerous problems to be considered by production engineers and cooperating teams. Using accurate and complete system models can help in overcoming many problems efficiently and without loss. In view of capital intensive of industrial systems, design and operation modeling and analysis are used to select the optimal design alternative and operational policy. Another major problem is the distribution and use of limited shared resources through time to meet demand [1]. Flaws in the modeling process contribute significantly to the development time and cost, while operational efficiency may also be affected [2]. Discrete event system models are described at an abstraction level where the time base is continuous, but during a time-span only a finite number of events causing change of system state occurs. Simulation, analysis and optimization of realistic scale discrete event dynamic systems (DEDS), whose reachable states number is typically plentiful, requires large amount of computationally intractable. Inclusion of time information in above formalisms is .-00(!*$ !21" 20$0 , $51/ 0(&,(%(" ,1 (,"/$ 0$ (, +-#$*@0 complexity, leading to reachable state space explosion [3].
II. THE TANNING INDUSTRY Leather process concerns the conversion of raw hide or skin, a highly putrescible material into leather, a stable material which can be used in the production of a wide range of products. In Europe 36.500 enterprises process final leather products and employ 414.000 persons. 70% of tanneries in Europe are small and medium sized enterprises. Annual leather production has increased steadily from 1993 to 2012 up to 33.1% from 10.55*107 to 14.0425*107 pieces. Figure 1, summarizes the growth of worldwide production of heavy cattle leather (in pieces) from 1993 to 2011 [6].
Figure 1.
Annual Cattle Leather Production.
From the previous information, it is obvious that leather industry pays a key role in Europe and worldwide. The motivation to deal with the specific problem was the identification that planning in the majority of tanning industries was traditionally done empirically.
In this paper a tanning industry processing two types of leather and producing five types of final products is studied. In particular, the PN model of the industry is implemented and its parameters are adjusted so that the behavior approximates the real systems values. Certain scenarios are simulated and the results obtained are compared and evaluated.
Konstantinos E. Vrontakis is with the Environmental Engineering School, Technical University of Crete, GR-73100 (+306-985-774-929; email:
[email protected]). Andreas N. Kampianakis is with Department of Management Engineering, Technical University of Denmark (e-mail:
[email protected]). George J. Tsinarakis is with the Production Engineering and Management School, Technical University of Crete (e-mail:
[email protected]). 978-1-4673-8345-5/16/$31.00 ©2016 IEEE
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Figure 2.
The four stages of leather process[7].
Figure 2 presents the four stages of leather process (dashed parallelogram for each stage), an analysis of their main substages and their interconnections. In most of the cases, industries specialize in one or two stages of the overall process. The Emmanouil Vrontakis & Co industry, is located in Chania, Greece and specializes at stages three and four of leather process. During the last 63 years it has increased sixteen times its production level and is considered as one of the biggest tanneries in Greece. In the field of natural (vegetable) tanning, it has one of the highest production volumes in the whole Europe. It produces five types of final leather (kudu, vachetta, sole leather, colored vachetta and colored sole leather), using two types of raw materials (cattle and kudu) and has more than a hundred wholesaling customers. Each product type follows its own sequence of operations. Main differences concern number of operations, durations, capacities, batch sizes and associate raw materials. Figure 0'-40 1'$ #(01/(!21(-, -% (,#201/6@0 -3$/ ** production between the five types of final products. Half of (,#201/6@0./-#2"1(-,"-,"$/,0= -*$$ 1'$/?4'(*$=2#2 *$ 1'$/0? /$1'$0$"-,#+-01.-.2* / leathers.
Figure 3.
Production segmentation.
Figure 4 summarizes the flow of processes that transform each type of raw materials into the corrensponding products. Reader can see that each product follo40(1@0(,#(3(#ual route consisting of different types and number of processes.
Figure 5.
Figure 4.
Leather process sequence for each type of product.
III. PN MODELING
Petri Net model of sole leather and colored sole leather production. 1285
PNs have been proven to be a powerful tool for studying concurrency, sequential, parallel, asynchronous, distributed deterministic or stochastic behavior, resource allocation, mutual exclusion and conflicts [4], [8] < [10]. Most of these features are present in the system studied and this makes PNs an ideal modeling and simulation tool. In this paper timed Petri Nets with arc extensions are used to model and simulate the processes. An Ordinary Petri Net (OPN) is a bipartite directed graph defined as the five-tuple: PN={P, T, I, O, m0}, where P={p1, p2 ... pnp} is a finite set of places, T={t1, t2, ..., tnt} is a finite set of transitions, P U T=V, where V is the set of vertices and . I is an input function and O an output function and m0 the PN initial marking. Places represent conditions; transitions represent events and arcs direct connection, access rights or logical connection between places and transitions. A t-timed PN arises from the corresponding Ordinary PN by associating each transition ti a firing delay that may be constant or follow a given distribution, defined as TPN={P, T, I, O, m0, D} with D representing time delay, a function from the set of nonnegative real numbers } [11], [12], [16]. Standard arcs /$ #/ 4, 0 202 * A 4'(*$ (,'(!(1-/0 /$ /$./$0$,1$# !6 /"04'-0$$,#(0+ /)$#4(1' 0+ **"(/"*$B[12].
p51, p56, p57, p62 p52,p53,p58,p59
PLACES MEANING FOR SOLE LEATHER AND COLORED SOLE LEATHER PN MODEL Places Characteristics
p1 p2,p3,p4,p5,p6,p8,p11,p12,p13,p14,p15,p16,p23,p24, p25,p26,p29,p31,p33,p34,p35,p37,p43 p7 p9,p10 p17,p20,p27,p28 p18,p19,p21,p22 p30
Raw materials buffer
Capacit y 5000
Buffer
300
Buffer Buffer Buffer Buffer Buffer
1 500 150 600 1000
p32
Finished Sole Leather buffer
10000
p36,p38,p41,p42
Buffer Finished Colored Sole Leather buffer Input place for mut. exclusive operations control
120
p44 p45,p47,p49,p63
Meaning
of
winter
1 12 7 8
The overall model consists of 64 places and 56 transitions and is deadlock free, k-bounded and non-persistent due to the presence of conflicted transitions. An interesting part of the model is the drying procedure where the duration varies with respect to the season (in the summer drying is much faster than in the winter). In particular, 3 drying seasons are considered and the change from one to the other (sequential and not random) is achieved through a mutually exclusive PN structure (transitions: 44-54, places: 51-62) where each one enables the following after the production of a certain number of product batches (with respect to realistic data provided from the industry).
The Timed Petri net model of Sole Leather and Colored Sole Leather production is presented in Figure 5 while the exact nodes (places and transitions) meanings as well as their main features (delay and capacity) are shown in Tables I, II.
Sole Leather and Colored Sole Leather model, places
Control place drying process
p54,p55,p60,p61
At this section the PN-models describing the production of the five final leather types, are introduced. In total three PN models are implemented and are simulated to calculate certain efficiency parameters. In particular, the first model describes the production of = -*$$ 1'$/? ,#=-lored Sole $ 1'$/? as their production process is common for the first twenty one processes (the flow of processes as well as their interconnections are analytically shown in Figure 4). Then a sorting procedure, according to the quality of the surface, fo**-404'$/$= -*$$ 1'$/0? ../-5(+ 1$*6 /$"$(3$ eight more processes in order to become final products, while the worst 10%, receive eleven more different processes and 12/,1-=-*-/$# -*$$ 1'$/0? The corresponding stand for the leather types = "'$11 ? (90%) ,# =-*-/$# "'$11 ? (10% due to quality control). The fifth final product is the processed =2#2?*$ 1'$/16.$
TABLE I.
Output place for mut. exclusive operations control Control place of summer drying process Control place of springautumn drying process
p46,p48,p50,p64
TABLE II.
TRANSITIONS MEANING IN SOLE LEATHER AND COLORED SOLE LEATHER PN MODEL
Sole Leather and Colored Sole Leather model, transitions t1 t2
Transition Characteristics min Delay 1.2 0.63
Meaning Partition Fleshing
max Delay 1.7 0.99
t3
Waste Removal
0.76
t4,t7,t13,t31
Drum Input
0
0
t5
Depickling
360
360
t6
0.3
0.33
t11
Drum Output Conversion of items in square meters Tanning Conversion of square meters in pieces Drum Output
t12 t14
t8 t9 t10
0.79
0
0
1330
1630
0
0
0.3
0.33
Sammying
0.7
1.7
Stuffing
180
180
t15,t33
Drum Output
0.18
0.198
t16,t35 t17 t18 t19 t20 t21
Setting Transport Drying Transport Roller Coating Transport
0.48 0.32 720 0.34 1.21 0.34
t22
Sorting
0.14
t23 t24 t25 t26
Buffing Drying Transport Waste Removal
1.64 480 1.03 0.47
0.63 1.82 1440 0.49 1.32 0.49 0.140 7 1.75 480 1.03 0.507
t27 t28 t29,t39 t30,t40
Ironing Sorting Measurement Packing
1.64 0.16 0.13 0.5
1.663 0.183 0.209 0.67
t32
Dyeing
225
225
t34
Sammying
0.72
1.68
t36
Setting
1.08
1.14
t37
Roller Coating
1.21
1.46
t38 t41,t42,t43,t45,t47,t49,t51,t53,t55,t5
Spraying
1.58
1.83
execute process activation
0
0
Drying process, Summer Drying process, SpringAutumn Drying process, Winter
1440
1440
6
t44,t50
10000
t46,t52
1
t48,t54
1286
2880
2880
4320
4320
The exact meaning of sole leather and colored sole leather PN models nodes (places and transitions) is presented in Tables I and II respectively. Place p1 represents the raw material (cow) buffer while places p32 and p44 describe %(,(0'$# = -*$ $ 1'$/? ,# =-*-/$# -*$ $ 1'$/? !2%%$/0 respectively. The majority of transitions representing parts processes do not have a constant delay but their value is randomly distributed between a minimum and a maximum number. In order to generate normally distributed random numbers in the specified interval for each parameter, the following general form is used:
Certain processes are performed using the same equipment. For this reason supervisory control structures have been added to the initial model in order to achieve mutual exclusion of these states. For example t29 and t39, that model the measurement process, which are performed using the same machine, cannot be enabled and fired simultaneously as they both have as input place p64 which has initially one token (one measuring machine available) and also unitary capacity. When measurement finishes, this token is moved in p63 and through firing of immediate transition t56, machine becomes again available.
A x y * rnd ( z)
The respective models for Vachetta and Colored Vachetta and Kudu leathers are presented in Figures 6 and 7.
where:
Their nodes meaning is not presented analytically due to space limitations, but the sequence of operations performed in order to produce each product can be found in Figure 4. While each leather type receives different types and sequence of processes, all models follow common assumptions and only capacity and time data are different.
A : represents the randomly generated value,
x : is the lower bound of A ,
x y * z : the upper bound of A ,
z , this assumption was adopted in cooperation
4(1' (,#201/6@0 0 (1 ./-3(#$0 +-/$ /$ *(01(" results.
Table III summarizes the main structural differences between the production processes of the five leather types, as well as certain critical features.
In such production systems, many of the processes are performed in batches. In order to model this concept, arcs of weight equal to the batch size are used. It must be noted, that not all of them have the same batch size. For this reason the non-unitary arc weights, are presented above them in the model of Figure 5. In addition, the capacities of such arcs input and output buffers are multiples of these weights and are defined in Table I (e.g. t5 represents depickling process that is performed in batches of 150 pieces. Input buffer p5 and output p6 have maximum capacity of 300 pieces, equal to the double size of the respective batch).
Leather Type
Process Differences
Kudu
Vachetta
Colored Colored Sole Vachetta Leather
Overall processes 23
34
29
37
32
Average Surface 0.98 (m2)
1.40
1.40
1.40
1.40
Batch Size
200
150
20
30
TABLE III.
300
DIFFERENCES BETWEEN THE 5 PRODUCT TYPES PROCESSES
Figure 6. Petri Net model of vachetta and colored vachetta production. 1287
Sole Leather
Figure 7. Petri Net model of kudu leather production.
IV. SIMULATION RESULTS Initially the models parameters were adjusted using the real batch production time for each raw material and final product combination. After the verification, a scenario concerning the annual production for each product type was considered (base scenario). The production volume for each one of the five final types was estimated with respect to previous years demand data, using sophisticated mathematical tools. Multiple forecasting methods were tested and with respect to the results -!1 (,$#/-4,@0$5.-,$,1( * smoothing method was chosen. Table IV summarizes the calculation of the most popular error indicators, using different forecast models [13] for the best-selling product of the firm, Sole Leather. The results of Table IV ensure this choice. The values of the indicators [14] for the rest products behave similarly. TABLE IV.
Production forecast of 2015 (orange line) arising from ..*(" 1(-, -% /-4,@0 $5.-,$,1( * 0+--1'(,& +$1'-# %-/ each final product type as well as demand for years 20112014 (blue line) are shown in Figures 8-12.
Figure 9.
Vachetta demand (2011-2014) and forecast using Browns smoothing.
ERROR INDICATORS FOR ALTERNATIVE FORECASTING MODELS Forecasting Method
Sole Leather
Mean Error Mean Absolute Deviation Mean Squared Error Mean Percentage Error
Simple Moving Average
Double Moving Average
Exponential Smoothing
348.075
417.778
211.326
367.754
426.495
315.323
199365.771
272369.042
151027.372
1.324
2.752
1.351
Figure 10. Sole Leather demand (2011-2014) and forecast using Browns smoothing.
Figure 8. Kudu demand (2011-2014) & forecast using Browns smoothing. 1288
Figure 11. Colored Vachetta demand (2011-2014) and forecast using Browns smoothing.
TABLE VI. Simulation Results Kudu Vachetta Sole Leather Colored Vachetta Colored Sole Leather
According to forecast results, the annual quantities for each product were calculated and were respectively: 3300 pieces of Kudu leather, 1800 Vachetta leather pieces, 7290 Sole leather pieces, 200 Colored Vachetta pieces and 810 Colored Sole leather pieces. Then, for each product type, sets of eight simulations were performed in order to minimize the overall randomness and obtain more representative results. Table V presents the calculated results of this scenario.
Simulation Results Kudu Vachetta Sole Leather Colored Vachetta Colored Sole Leather
BASE SCENARIO CALCULATIONS
3300 1800 7290 200 810
Mean time (min)
67685.6 59589.03 97058.3 64116.9 100481.6
35374.7 33824.3 84130.3 35386.9 84648.9
Mean time per piece (min)
10.720 18.791 11.541 176.935 104.505
Reduction (%)
47.74 43.24 13.32 44.81 15.76
The operation and production forecast of a tanning industry is studied. PNs are used to model and simulate the operation of the line, while forecasting methods are applied to calculate the yearly demand. A scenario concerning partial change of the equipment (use of a drying machine) is studied. REFERENCES [1] -#/:&2$7 ;*3$7 ,# $/0$&2$/ =, 1'e Performance
[2]
Calculations Pieces
Calculations Mean time (min)
V. CONCLUSION
Figure 12. Colored Sole Leather demand (2011-2014) and forecast using Browns smoothing.
TABLE V.
SCENARIO 1 CALCULATIONS AND COMPARISON
Mean time per piece (min)
[3]
20.511 33.105 13.314 320.585 124.051
[4]
In addition, simulation produces diagrams showing the $3-*21(-, -% $ "' (,1$/, * !2%%$/@0 *$3$* in order to detect machines that cause deadlocks in certain systems parts. Figure 13 shows the inventory of P16 (Sole Leather). This buffer has maximum capacity 300 pieces and it was full for 44.32% of overall simulation time. This indicates that in the specific part of the industry there is a deadlock.
[5]
[6]
[7] [8] [9] [10]
Figure 13. Inventory of P16 internal buffer.
Because of this fact, a new scenario (scenario 1) concerning the installation of an advanced drying machine was considered. In particular, this equipment would reduce the duration of drying process in winter, from 4320min to 2880 mins. A set of eight simulations for the same quantities of final products, was performed for the updated model. The results as well as the comparison with the base scenario are shown on Table VI. From this it is obvious that such an investment reduces significantly the mean production times of all products (from 13-48%). Moreover such a change increases the overall production capability of the industry about 30% and should be further studied with respect to its financial viability.
[11] [12] [13] [14] [15]
[16]
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21-/( *?, IEEE Transactions on Industrial Electronics, Vol. 41, No. 6, December 1994. Beek van D., Rooda J., Muyzenberg van den M., Specification of combined continuous-time / discrete-event models, in Modelling and Simulation 1996 < Proceedings of the 1996 European Simulation Multiconference, Budapest, pp. 219
