CC BY
43
Received 16.11.15
DOI: 10.15827/0236-235X.113.170-179
MODELING OF THE TIME-CYCLE CONTROL SYSTEM FOR TECHNOLOGICAL PROCESSES EQUIPMENT IN PHARMACEUTICAL SOLID DOSAGE MANUFACTURING BASED
ON PETRI NETS
Okai G.E. Y., Postgraduate Student (Tver State Technical University, Nikitin Quay 22, Tver, 1 70026, Russian Federation), Lecturer (Presbyterian University College, Ghana); Klyushin A. Yu., Ph.D. (Engineering), Associate Professor; Bogatikov V.N., Ph.D. (Engineering), Professor (Tver State Technical University, NNikitin Quay 22, Tver, 1 70026, Russian Federation)
Abstract. The key purpose of this research is to develop an approach to modeling batch manufacturing of a system of pharmaceutical solid dosage forms using a mathematical tool called Petri net. This possibility can be provided by a model that can be easily understood by a System Analyst and Technological engineers.
This paper describes a system analysis and a model of manufacturing processes of pharmaceutical solid dosage forms with much emphasis on tablets. It also provides a brief classification of technological processes within the manufacturing system of solid-based dosage forms. The system analysis was done with much focus on manufacturing processes and equipment used at each stage of a manufacturing system. The paper briefly considers the development of a Petri net model for manufacturing processes of pharmaceutical solid dosage forms. A Petri net model was implemented and analyzed using the PIPE tool (Platform Independent Petri net Editor 4.3) for Windows
The authors also developed and analyzed a timeline chart for the analysis of technological routes for manufacturing of three different solid dosage forms.
The resulting Petri net model and the timeline chart helped to create a clearer picture of the technological processes in the manufacturing system. The Petri net model developed in this paper can be used to solve the problem of choosing an optimal manufacturing model or optimal technological routes. It can also be used to improve the efficiency of using a set of equipment in the manufacturing system of pharmaceutical solid dosage forms.
Keywords: Petri net, manufacturing process, modeling, pharmaceutical manufacturing, system analysis, solid dosage, technological process, pharmaceutical industry, technological route.
Manufacturing of pharmaceutical solid dosage forms (tablets, capsules, pills etc.) usually involves a batch production system. In this case the product in question is manufactured stage by stage using a set of predefine equipment that can also accommodate different batches of products. The processes within most manufacturing systems are carried out sequentially in a defined set of stages from one to another reaching a desirable or a specified stage. Each product goes through its own manufacturing stages until it reaches completion or the final stage [1]. Recently the pharmaceutical industry has experienced significant changes in connection with prevailing economic situations. There is also lots of competition among the manufacturers of generic pharmaceutical products. Therefore, there is the need for constant research to optimize the use of equipment in pharmaceutical industries to face modern day challenges [2-4].
The objective of this paper is to develop a Petri net model for modeling the equipment of periodic action of a solid dosage manufacturing system with much focus on the technological processes of manufacturing tablets. This paper will also create an optimal timeline to analyze technological routes for a manufacturing system of pharmaceutical solid dosage forms. The analysis will emphasize both manufacturing processes and equipment or machines used at each stage of man-
ufacturing. The paper analyzes and discusses the development of a Petri net model for a manufacturing system of pharmaceutical solid dosage forms.
A Petri net was chosen as a tool for modeling a manufacturing system of solid dosage forms because it offers a strong theoretical and powerful mathematical method for the purpose of modeling and analysis of a manufacturing system. The analysis can be done to underline the properties such as safeness, boundedness, conservation, liveness etc. Invariants can be also determined to analyze markings in a Petri net model.
A Petri net is a mathematical modeling language to depict distributed systems or a complex system. A Petri net is a directed bipartite graph, in which the nodes represent transitions (i.e. events that may occur, signified by bars) and places (i.e. conditions, signified by circles). The directed arcs describe which places are pre-and/or post conditions for which transitions (signified by arrows). Petri nets were invented in August 1939 by Carl Adam [5-7].
A Petri net is a five-tuple
PN = (P, T, A, W, Mo) (1)
where P = {pi, p2, ..., pn} is a finite set of places; T = {ti, t2, ..., tm} is a finite set of transitions; A Π(PxT) u (TxP) is a set of arcs; W: A ^ {1, 2, ...} is a weight function; Mo : P ^ {0, 1, 2, ...} is the initial marking.
A Manufacturing Process of Solid-Based Pharmaceutical Dosage Forms
Technological processes of manufacturing pharmaceutical products are done in batches through a series of technological processes transforming active pharmaceutical ingredients into suitable products before they are brought to humans and animals. Active pharmaceutical ingredients are carefully combined with the pharmaceutical excipients, such as binders, fillers, bulking agents and flavouring, preservatives and anti-oxidants. These raw materials may be dried, milled, blended, compressed and granulated to achieve the desired properties before they are manufactured as a final formulation. Tablets and capsules (solid dosage form drugs) are the most common oral dosage forms. The technological processes of manufacturing solid dosage products consist of the following generalized operations: weighing and dispensing of raw materials; preparation of a binder; mixing active drug substances with a binder; wet granulation; drying; dry granulation; dusting; tableting and packaging [8-10].
The technological processes of manufacturing solid dosage forms can be divided into four main technological stages.
1. The technological stage of getting raw materials into a powder form;
2. The technological stage of obtaining the correct texture and mixture for a dosage form;
3. The technological stage of obtaining the finished solid dosage;
4. The technological stage of packaging and labeling.
A specific type of equipment is used at each stage of the solid dosage manufacturing process [10]. A developed classification of the technological stages with needed equipment is shown in table 1.
Table 1
Classification of the technological stages and the equipment used at each stage
Development of a Petri net Model for the Manufacturing Process
of Solid-Based Pharmaceutical Dosage Forms
This paper focuses on Petri nets with time constraints to analyze the technological processes of manufacturing solid dosage forms. Real industrial processes have a finite duration that can be represented graphically with time schedules [11].
The manufacturing process of solid-based pharmaceutical dosage runs sequentially in a predefined set of equipment. So, we were inspired to use Petri nets to model and conduct system analysis of a manufacturing system. The aim for developing a Petri net model and the subsequent analysis of the model is to obtain important information about the structure and dynamic behaviour of the manufacturing system. This information can be used to evaluate the modeled system and to develop proposals for its improvement.
Graphically, a Petri net is denoted as follows. Positions are represented by circles, transitions are represented by thickened lines, tokens are represented by dots inside circles. In this paper a timed Petri net was considered for the model. A timed Petri net is a bipartite directed graph with arcs and vertices, which are represented with positive integers [5, 12]. Mathematically it is defined as:
N=(P, T, F, Mo, t', t"), (2)
where P={p,} is a finite set of positions; T= {tj} is a finite set of transitions; F c (PxT)u(T* P) is a set of arcs (or flow relations); Mo, P ^ {0, 1, 2, ...} is a the initial token; t'={t':, t'2, ..., t',} is a finite set of times for minimum delay for transitions; t''={t'' 1, t'' 2, ..., t' ' ,} is a finite set of times for the maximum delay for transitions.
This paper developed a detailed model of a manu-factoring system of solid-based pharmaceutical dosage using Petri nets. The finite set of operations and places for manufacturing processes are described in the following paragraphs.
Definitions of manufacturing operations (conditions) are the following:
01 - a batch of raw material arrives at the input of a vibrating sieve machine;
02 - vibration sieve is free (empty) and is in a standby mode;
03 - after being loaded with a defined amount of pharmaceutical ingredients the sieving machine is switched on to undergo a technological process (sieving) until the completion of the process;
04 - a batch of sifted materials is off-loaded from the vibration sieve into a holding repository for transportation to the next stage of manufacturing;
05 - a batch of sieved pharmaceutical ingredients, which were off-loaded from the sieving machine, arrives at the input of the mixer;
06 - the mixer is free (empty) and is in a standby mode;
No. Technological stage Manufacturing process Equipment
1 Getting raw materials into a powdered form Grinding/milling Pharmaceutical grinding machine
Sieving Pharmaceutical sieving machine
2 Obtaining the correct texture and mixture for the solid dosage form Mixing Granulator/mixer
Wet granulation Granulator
Dry granulation Granulator
Drying Pharmaceutical powder dryer
3 Obtaining the finished solid dosage Tablet pressing Tablet press machine
Capsule filing Capsule filling machine
Tablet de-dusting Tablet de-dusting machine
4 Packaging and labeling. Tablet packaging Tablet packaging machine
Capsule packaging Capsule packaging machine
Oi - after being loaded with defined proportions of the pharmaceutical ingredients the mixer is switched on to undergo a technological process (mixing) until the completion of the process;
08 - a batch of mixed ingredients is off-loaded from the mixer into a holding container for transportation to the next stage of manufacturing;
09 - a batch of the mixed ingredients, which was off-loaded from the mixer, arrives at the input of the granulator;
010 - the granulator is free (empty) and is in a standby mode;
011 - after being loaded with defined proportions of the mixture ingredients the granulator is switched on to undergo a technological process (granulation) until the completion of the process;
012 - wet granules are poured out of the granulator into a holding container to be transported to the next stage of manufacturing;
013 - a batch of wet granule arrives at the input of the dryer;
014 - the dryer is free (empty) and is in a standby mode;
015 - after being loaded with a batch of the wet granules the dryer is switched on to undergo a technological process (drying) until the completion of the process;
016 - the cooling process in the dryer;
O11 - dried granules are off-loaded from the dryer to be transported to next stage of production;
018 - a batch of dried granules of the pharmaceutical ingredients arrives at the input of the tablet press machine;
019 - the tablet press machine is free (empty) and is in a standby mode;
020 - the tablet press presses the granules into tablets in accordance with given shape and weight;
021 - A batch of tablets are released from the tablet press and kept in appropriate containers to be transported to the next stage;
022 - a batch tablets arrives at the input of the packaging machine;
023 - the tablet packaging machine is free (empty) and is in a standby mode;
024 - the packaging machine undergoes the process of packaging tablets into defined sets;
025 - the packaged tablets are collected and sent to the storage.
Further there are notations and descriptions of the finite set of Petri net positions (status of the manufacturing operations):
P1 - a batch of raw material arrives at the input of the vibrating sieve;
P2 - vibration sieve is free (empty) and in a standby mode;
P3 - after being loaded with a defined amount of pharmaceutical ingredients the sieving machine is switched on to undergo a technological process (sieving) until completion of the process;
P4 - the batch of sifted materials are off-loaded from the vibration sieve into a holding repository for transportation to the next stage of manufacturing;
P5 - a batch of sieved pharmaceutical ingredients, which were off-loaded from the sieving machine, arrives at the input of the mixer;
P6 - the mixer is free (empty) and in a standby mode;
P7 - after being loaded with defined proportions of the pharmaceutical ingredients the mixer is switched on to undergo a technological process (mixing) until the completion of the process;
P8 - the batch of mixed ingredients are off- loaded from the mixer into a holding container for transportation to the next stage of manufacturing;
P9 - a batch of the mixed ingredients, which was off-loaded from the mixer, arrives at the input of the granulator;
P10 - the granulator is free (empty) and in a standby mode;
P11 - after being loaded with defined proportions of the mixture ingredients the granulator is switched on to undergo a technological process (granulation) until the completion of the process;
P12 - wet granules are poured out of the granulator into a holding container to be transported to the next stage of manufacturing;
P13 - a batch of wet granules arrives at the input of the dryer;
P14 - the dryer is free (empty) and in a standby mode;
P15 - after being loaded with a batch of the wet granules the dry is switched on to undergo a technological process (drying) until the completion of the process;
P16 - the cooling process in the dryer;
P17 - dried granules are off-loaded from the dryer to be transported to the next stage of production;
P18 - a batch of dried granules of the phar - maceu-tical ingredients arrives at the input of the tablet press machine;
P19 - the tablet press machine is free (empty) and in a standby mode;
P20 - the tablet press presses the granules into tablets in accordance with the given shape and weight;
P21 - a batch of tablets are released from the tablet press and kept in appropriate containers to be transported to the next stage;
P22 - a batch tablets arrives at the input of the packaging machine;
P23 - the tablet packaging machine is free (empty) and in a standby mode;
P24 - the packaging machine undergoes the process of packaging the tablets into defined sets;
P25 - the packaged tablets are collected and sent to the storage.
Notations and descriptions of the finite set of Petri net transitions (status of the equipment in manufacturing operations) are the following:
Table 2
Input and output conditions
Equipment Status of system (Event) Input conditions (Operation) Output conditions (Operation)
Vibration sieve Si (start of event ) Ol, O2 O3
S2 (end of event) O3 O2, O4
Transport cart S3 O4 O5
Mixer S4 (start of event) O5, O6 O7
S5 (end of event) O7 O6, O8
Transport cart S6 O8 O9
Granulator S7 (start of event) O9, Oio O11
S8 (end of event) On O10, O12
Transport cart S9 Ol2 O13
Tray Dryer Sio (start of event) Ol3, Ol4 O15
Sii (end of event) Ol5 O16
Si2 Ol6 O14, O17
Transport cart Si3 Ol7 O18
Tablet Press Machine Si4 (start of event) Ol8, Ol9 O20
Si5 (end of event) O20 O19, O21
Transport cart Si6 O2l O22
Packaging machine Si7 (start of event) O22, O23 O24
Sis (end of event) O24 O23, O25
t\ - start of the sieving process; t2 - end of the sieving process; t3 - the completion of the operation on transportation of processed raw material from sieving machine to the mixer;
t4 - start of the mixing process; t5 - end of the mixing process; t6 - the completion of the operation on transportation of mixed ingredients from the mixer machine to the granulator;
t7 - start of granulation process; tg - end of granulation process; t9 - the completion of the operation on transportation of wet granules from the granulator machine to the dryer;
tio - start of the drying process; tn - end of the drying process; ti2 - completion of the cooling process; ti3 - the completion of the operation on transportation of dried granules from the dryer machine to the tablet press machine;
ti4 - start of table press process; ti5 - end of tablet press process; ti6 - the completion of the operation on transportation of formed tablets from the tablet press machine to the packaging machine;
ti7 - start of packaging process; tig - end of packaging process. In the development of a Petri net model for the batch manufacturing system of solid dosage forms, positions represent the individual operations in the manufacturing process or the status of the production system. The presence of a token in any of the positions corresponds to the execution of certain technological operations. Transitions correspond to events showing the beginning or the end of simulated operations. Therefore, the model will be based on pre-defined assumptions of a Petri net having notational symbols as shown earlier.
The definition of states, thus, the beginning and the end of a manufacturing process are represented in a table of input and output conditions (see table 2).
The manufacturing process was modeled according to the Petri net, which is presented in a tabular form (table 3), and graphically (fig. i). According to the earlier described definitions of manufacturing operations (conditions), there is a one-to-one relationship between the process operations and the positions of the Petri net as well as between the system status and transitions of the Petri net: {O} ~ {P}; {S} ~ {t}; {Technological Operations} ^ {Petri net Position}; {Status of the Equipment} ^ {Petri net Transition}.
The transitions correspond to the events showing the beginning or the end of simulated manufacturing operations. Positions correspond to technological operations reflecting the input and output conditions of the simulated manufacturing operations.
Table 3
A Petri net in a tabular form
Equipment Status of system (event) Input condition (operation) Output condition (operation)
Vibration sieve tl Pl, P2 P3
t2 P3 P2, P4
Transport cart t3 P4 P5
Mixer t4 P5, P6 P7
t5 P7 P6, P8
Transport cart t6 P8 P9
Granulator t7 P9, Pl0 Pll
t8 Pll Pl0, Pl2
Transport cart t9 Pl2 Pl3
Tray Dryer tl0 Pl3, Pl4 Pl5
tll Pl5 Pl6
tl2 Pl6 Pl4, Pl7
Transport cart tl3 Pl7 Pl8
Tablet Press Machine tl4 Pl8, Pl9 P20
tl5 P20 Pl9, P2l
Transport cart tl6 P2l P22
Packaging machine tl7 P22, P23 P24
tl8 P24 P23, P25
The finite set of positions P and the finite set of transitions T are:
P=(pi, p2, P3, P4, P5, P6, P7, P8, P9, Pl0, Pll, Pl2, Pl3, Pl4, Pl5, Pl6, Pl7, Pl8, Pl9, P20, P2l, P22, P23, P24, P25}
T={tl, t2, t3, Î4, Î5, Î6, Î7, t8, t9, tl0, tll, tl2, tl3, tl4, tl5,
tl6, tl7, tl8}.
Fig. 1. A detailed Petri net model of the solid dosage manufacturing system
Development of the Petri Net Model for the Manufacturing System of Solid Dosage Form
Taking into consideration the sequential technological processes in line with different machines or equipment used in the system, the Petri net model of the manufacturing system of the solid dosage form has been developed. In this case the state, in which the manufacturing process will be found at any given time, was determined by the equipment that is either busy or redundant. Within the same equipment, the state of manufacturing can also have sub states while the processing is going on. Based on these defined parameters the Petri net model of the manufacturing system was designed as shown in figure 1.
Analysis of the Petri net and results
It should be noted that in order to develop a model for a manufacturing system, the static structure of the system was established as well as the rules for the dynamic behaviour of the system. The Petri net model developed both asynchronous and synchronous execution, because some transitions can be fired at the same time and others can be fired only after the execution of other transitions. The presented Petri net model can be developed by means of linear algebra techniques. The authors used the PIPE tool (Platform Independent Petri net Editor 4.3) for Windows for the purposes of analysis.
P-Invariant analysis results associated with the developed Petri net model are presented in the table 4.
Since the Petri net is covered by positive P-Invari-ants, it is bounded. The results of the P-Invariant equations associated with the Petri net are presented below:
• M(P1) + M(P11)+M(P12) + M(P13) + M(P15)+ + M(P16) + M(P17) + M(P18) + M(P20) + M(P21) + + M(P22) + M(P24) + M(P25) + M(P3) + M(P4) + M(P5)+ + M(P7) + M(P8) + M(P9) =1
• M(P10) + M(P11) = 1
• M(P14) + M(P15) + M(P16) = 1
• M(P19) + M(P20) = 1
• M(P2) + M(P3) = 1
• M(P23) + M(P24) = 1
• M(P6) + M(P7) = 1
The forwards incidence matrix (I+), backwards incidence matrix (I-) and the combined incidence matrix (I) were also analyzed in the developed model. The analysis of the developed Petri net showed that it is bounded, not safe and there is a possibility of a deadlock. The shortest path to a deadlock: T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18.
The initial markings associated with the developed Petri net model for the manufacturing system are presented in the table 5.
Development of a timeline and an analysis of technological routes for manufacturing of three different tablets
A busy level or a level of redundancy of equipment in the manufacture of three different tablets range taking into consideration the three major methods of manufacturing tablets. They can be determined using a matrix. The authors used a matrix with the rows representing the type of product to be manufactured and the col-
Table 4
P-Invariant analysis results associated with the developed Petri net model
P1 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P2 P20 P21 P22 P23 P24 P25 P3 P4 P5 P6 P7 P8 P9
1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
Table 5
The initial markings associated with the developed Petri net model for the manufacturing system
Marking P1 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P2 P20 P21 P22 P23 P24 P25 P3 P4 P5 P6 P7 P8 P9
Initial 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0
Current 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0
umns representing the set of equipment. The elements of the matrix B have a value of 0 if the equipment Aj is not used or redundant for the manufacture of the product Di, and the elements of the matrix B have a value of 1 if the equipment Aj is used for the manufacture of the product Di [13]. Figure 2 and Figure 3 defined the matrix B as:
Ai A2 A3 A4 A5 A6 Di 1 1 0 0 11 D2 1 1 1 0 11 D3 1 1 1 111
B =
To determine the total number of general equipment for manufacture of three different tablets, the algorithm of an incidence matrix can be used as follows:
C=B*BT, (3)
where BT is the transpose matrix of the matrix B. Matrix BT will have the following form:
D3
D1 D2
A1 1 1
A2 1 1
A3 0 1
A4 0 0
A5 1 1
A6 1 1
Multiplication of the matrix is performed according to the rule:
Cj=Ё ЬЛ •
(4)
k=1
RD1 A1 > > J A2 h E A4 IH E 1 > A6
1 >
RD2 The structure of the route of technological processes of the manufacturing system for Ibuprofen \f
FDi
A1 A2 Ы 1 A4 I 1 A5 > A6
> \ f
Шъ The structure of the route of technological processes of the matrufachmng system for Malar-2 Forte FD h
A1 A2 A3 N. A4 A5 A6
I
The structure of the route of technological processes of the manufacturing system for Citramon FDi
Fig. 2. The manufacturing systems with a reconfigurable structure: Ai - sieving machine; RDi -flow of raw materials for Ibuprofen; A2 - mixer; RD2 - flow of raw materials for Malar-2 Forte; A3 - granulator; RD3 - flow of raw materials for Citramon; A4 - tray dryer; FDi - finished product (Ibuprofen); A5 - tablet press; FD2 - finished product (Malar-2 Forte); Aö - packaging machine; D3-finished product (Citramon)
RDi
Fig. 3. Combined routing of manufacturing systems technological processes: Ai - sieving machine; RDi - flow of raw
materials for Ibuprofen; A2 - mixer; RD2 - flow of raw materials for Malar-2 Forte; A3 - granulator; RD3 - flow of raw materials for Citramon; A4 - tray dryer; FDi - finished product (Ibuprofen); A5 - tablet press; FD2 - finished product (Malar-2 Forte); Aö - packaging machine; FD3-finished product (Citramon)
The incidence matrix C for the analysis of the manufacturing system can be represented as follows:
Di D2 D3
Di 4 4 4
D2 4 5 5
D3 4 5 6
This paper considers the elements of the matrix C represent the number of general equipment needed for the manufacture of three different products (tablets). The incidence matrix is the basis for finding combinations of products that could be manufactured simultaneously. It can also be used to analyze which products can be obtained in the form of parallel combination of equipment or the series combination of equipment [9].
The analysis of the incidence matrix showed that the products Di (Ibuprofen), D2 (Malar-2 Forte) and D3 (Citramon) have 4 general equipment out of a total of six equipment. The analysis showed that the common equipment is: Ai, A2, A5 and Ae. Figure 2 shows the reconfigurable manufacturing system.
This paper gives the set of equipment used in the manufacture of the range of three different products under consideration as follows:
Pi (Ibuprofen): {Ai, A2, A5, Ae};
P2 (Malar-2 Forte): {Ai, A2, A3, A5, Ae};
P3 (Citramon): {Ai, A2, A3, A4, A5, Ae}.
The technological process of manufacturing product D3 (Citramon) consists of six operational steps carried out in the sequence in the equipment: Ai, A 2, A3, A4, A5 and Ae. The first stage consists of loading operations of a batch of raw materials into the equipment Ai (vibration sieve). After loading the equipment Ai is switched on to start the technological process of sieving till the end of the process, resulting in the formation
of sifted raw materials. The equipment is switched off and sieved raw materials are off-loaded and kept in containers for transportation to the next stage of manufacturing in equipment A 2 (mixer).
The second stage of the manufacturing process includes loading a batch of defined proportions of the ingredients for the product Citramon in equipment A2 (mixer). After loading the equipment A2, it is switched on to start the technological process (mixing) in a predetermined time, which results in the formation of a homogeneous mixture of wet mass of Citramon. The equipment is switched off and the homogeneous mixture formed is off-loaded into containers and transported to the next stage of manufacturing in equipment A3 (granulator).
The third stage of the manufacturing process includes loading a batch of a wet homogeneous mixture (wet powder) into the fixed cylinder of equipment A3 (granulator). After loading the equipment A 3 it is switched on to start the technological process (wet granulation) till the end of the process resulting in the formation of wet granules. The equipment is switched off and the wet granules are off-loaded into containers for transportation to the next stage of manufacturing in the equipment A4 (tray dryer).
The fourth stage of the manufacturing process includes loading a batch of wet granules on trays, which are then placed in the chamber of A 4 (tray dryer). A4 is switched on to start the technological process of drying. The process occurs by heating wet granules at 50-55° C for 16 hours, which results in formation of dried granules. A4 is switched off and the dried granules are off-loaded from A4 for transportation to the next stage of production in the equipment A 5 (tablet press machine).
Equipment
D3
Ai A2
D2
Di
A3
A4
A5
A6
tl Ь Î3 Î4 ts t6 Î7 Î8 Î9 tio til ti2 ti3 ti4 tis ti6 ti7 tig ti9 Î20 toi Î22 Î23 Î24 Î25 Î26 hl Î28
Fig. 4. A timeline chart for technological processes
0
The fifth stage of the manufacturing process includes loading a batch of dried granules of the ingredients of Citramon into the equipment A5 (tablet press machine). After loading A5 it is switched on to start the technological process (tablet pressing) until the end of the process resulting in the formation of Citramon tablets. A 5 is switched off and the formed tablets are collected and kept in containers to be transported to the next stage of the production in the equipment A 6 (Packaging equipment).
The sixth stage of the manufacturing process includes loading a batch of the formed tablets into the equipment A6 (Packaging equipment). After loading A6 it is switched on to carry out the technological process of packaging until the end of the process. The production of the product D3 ends at the packaging stage. The packaged products are collected together in large boxes and transported to the storage facility.
The general equipment are washed and reconfigured according to a new scheme for the manufacture of the next range of product D2 (Malar-2 Forte). The Equipment A3, which was previously connected to equipment A 4, is now connected in series with the general equipment A5 and A6 since A4 will not be needed in the production of D2.
The manufacture of product D2 starts after washing and configuring the equipment. The technological processes for the manufacture of the product D2 consist of five stages, which are carried out sequentially in the following equipment: Ai, A2, A3, A5 and A6. Sieving of the ingredients in Ai is followed by mixing of the ingredients for the product D2 in equipment A2. After that the mixture is sent for dry granulation process in A 3.
The manufacturing process continues in A5 with the tablet pressing process. After that they are packaged in A6 and sent to the storage facility.
Once again, the general equipment are washed and reconfigured in a new scheme for manufacturing a new range of product Di (Ibuprofen). The Equipment A3, which was previously connected to equipment A 5, is changed with the connection of equipment A2 in series with the general equipment A5 and A6.The technological process for the production of the product D2 consist of four technological processes, which are carried out sequentially in the following equipment: Ai, A2, A5 and A6. It starts with Sieving of the ingredients in Ai, followed by mixing of the ingredients for the product Di in equipment A 2. After that the manufacturing process continues in A5 with the tablet pressing process, after which they are packaged in A 6 and sent to the storage facility.
Development and analysis of a timeline chart for the technological processes of manufacturing three different products (tablets)
The developed manufacturing timeline chart (fig. 4) shows the duration of the sequence of technological processes and their relative positions in a particular stage of the manufacturing system. The analysis of the subsystem of solid dosage manufacturing consists of six main equipment represented by: Ai, A2, A3, A4, A5 and A6.
The analysis of the Petri net model (fig. i) of the manufacturing system and the timeline chart (fig. 4) shows that the only equipment busy within the time in-
terval [0, /1] was A1. Within the indicated time interval a batch of raw materials is loaded into the equipment A1 to start the first stage (sieving of powdered ingredients) of manufacturing the product D3. The process of sieving starts at time /1 and continues until time /2. The sieving process ends at time /2; the sieved materials are off-loaded from A1 and transported to the next stage of the manufacturing in the equipment A2.
Time /3 on the time chart indicates the completion of the off-loading and transportation of the entire mass of the sieved materials from A1 to the equipment A 2. At that same time the loading of equipment A2 with all the ingredients to be mixed begins. Time /4 shows the beginning of mixing the ingredients for the product D3. The process of mixing ends at /5 and the off-loading of the resulting homogenous mixture from A2 begins. The mixture is transported to the next stage of the manufacturing in the equipment A3.
However, within the time interval [/3, /4] the equipment A1, which was previously configured for the manufacture of D3, is cleaned and reconfigured for the manufacturing D2. The loading of a batch of raw material into A1 starts at the time /4 to produce the product D2.
At the time /6 the off-loading and transportation of the entire mass of mixed ingredients from A2 to the equipment A3 is completed. At the same moment /6 begins the loading of the equipment A3 with a batch of the mixture of ingredients for the product D3. The loading operation finishes at time /7 and the equipment A3 starts the technological process (wet granulation). Time /g shows the ending of the wet granulation process and beginning of off-loading of the wet granules from A3 into containers for transportation to the next stage of equipment A4 production.
The off-loading and transportation of the whole mass of wet granules from A3 to A4 finishes at the time /9. At the same moment the operation of loading A4 starts. The loading operation is completed at the time /10 and A4 begins the process of drying wet granules.
However, at time /9 to /11 the equipment A1 is simultaneously cleaned up and prepared for service. The operation of loading a batch of raw material for the manufacture of another range of product D1 starts at time /11.
The analysis of the Petri net model and the time chart to accommodate the manufacture of three ranges of products revealed that during the time interval [/17, /18] the manufacture of product D3 ends. The product is discharged from equipment A6 for transportation to the warehouse of finished products. Also, on the time interval [/23, /24] and on the time interval [/27, /28] the manufacture of products D1 and D2 is also completed. The products are off-loaded from the equipment A6 for transportation to the storage facility of finished products. The timeline analysis showed that during the time interval [0, /28] the structure of the manufacturing sys-
tem changed many times to accommodate the simultaneous manufacture of three completely different ranges of products. The changes in the structure of the manufacturing systems are not caused only by multi-stage manufacturing operations, but also by the change in the product range of three different products.
Conclusion
As indicated earlier, a Petri net model is a graphical and mathematical tool, which can be used to design models of complex and distributed systems that can be easily understood by a system analyst and technological engineers. The developed model in this research can be used to analyze the concurrent, asynchronous, distributed and parallel system structures of manufacturing system. This can help to optimize the issues of redundancy of the equipment in the manufacturing system. As a basis for selecting optimal technological routes it can also accommodate the manufacture of a range of products simultaneously.
References
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УДК 658.5 Дата подачи статьи: 16.11.15
DOI: 10.15827/0236-235X.113.170-179
МОДЕЛИРОВАНИЕ СИСТЕМЫ УПРАВЛЕНИЯ ВРЕМЕННЫМИ ЦИКЛАМИ ОБОРУДОВАНИЯ ТЕХНОЛОГИЧЕСКИХ ПРОЦЕССОВ ИЗГОТОВЛЕНИЯ ФАРМАЦЕВТИЧЕСКИХ ТВЕРДЫХ ЛЕКАРСТВЕННЫХ ФОРМ НА ОСНОВЕ СЕТИ ПЕТРИ Окаи Д.Э.Я., аспирант, okai.george@mail.ru; Клюшин А.Ю., к.т.н., доцент, klalex@inbox.ru;
Богатиков В.Н., д.т.н., профессор, vnbgtk@mail.ru (Тверской государственный технический университет, наб. Аф. Никитина, 22, г. Тверь, 170026, Россия)
Основной целью данного исследования является разработка подхода к моделированию системы серийного производства фармацевтических твердых лекарственных форм с использованием сетей Петри. Эту возможность обеспечивает модель, которую могут легко понять системный аналитик и технологические инженеры.
В статье проведен системный анализ разработанной модели процессов производства фармацевтических твердых лекарственных форм с большим акцентом на таблетки. Также приводится краткая классификация технологических процессов в системе производства твердых лекарственных форм. Системный анализ в основном касается производственных процессов и оборудования, используемых на каждом этапе производственной системы. Кратко описано развитие чистой модели сети Петри для процессов производства фармацевтических твердых лекарственных форм. Чистая модель сети Петри была реализована и проанализирована с инструментом PIPE (Platform Independent Petri net Editor 4.3) для ОС Windows.
Проанализирована временная шкала диаграммы для анализа технологических маршрутов изготовления трех различных твердых лекарственных форм.
Из разработанной модели сети Петри и временного графика получена более четкая картина технологических процессов производственной системы. Чистая модель сети Петри, описанная в данной статье, может быть использована для решения проблемы выбора оптимальной модели производства или оптимальных технологических маршрутов. Ее применение целесообразно для повышения эффективности использования комплекта оборудования в системе производства фармацевтических твердых лекарственных форм.
Ключевые слова: сети Петри, производственный процесс, моделирование, производство фармацевтических средств, системный анализ, твердая лекарственная форма, технологический процесс, фармацевтическая промышленность, технологический маршрут.
Литература
1. Kim N., Shin D., Wysk R.A., Rothrock L. Using Finite State Automata for Formal Modeling of affordances in Human-Machine Cooperative Manufacturing System. Int. Journ. of Production Research. 2010, vol. 48, no. 5, pp. 1303-1320.
2. Suresh P., Basu P.K. Improving pharmaceutical product development and manufacturing: Impact on cost of drug development and cost of goods sold of pharmaceuticals. J. Pharm. Innov. 2008, vol. 3, pp. 175-187.
3. Shah N. Pharmaceutical supply chains: Key issues and strategies for optimisation. Comput. Chem. Eng. 2004, vol. 28, pp. 929-941.
4. McKenzie P., Kiang S., Tom J., Rubin A.E., Futran M. Can pharmaceutical process development become high tech? AIChE J. 2006, vol. 52, no. 12, pp. 3990-3994.
5. Котов В.Е. Сети Петри. М.: Наука, 1984, 160 с.
6. Peterson J.L. Petri Net Theory and the Modeling of Systems. Prentice Hall Publ., 1981, 288 p.
7. Petri C.A., Reisig W. Scholarpedia. 2008, vol. 3, no. 4, p. 6477. Safety. URL: http://www.Scholarpedia.org/arti-cle/Petri_net (дата обращения: 19.10.2015).
8. Погорелов В.И., Степанова Э.Ф., Мичник Л.А. [и др.]. Фармацевтическая технология: учеб. пособие. Р-н-Д: Феникс, 2002. 467 с.
9. Ажгихин И.С., Гендель В.Г. Избранные лекции по курсу технологии лекарств заводского производства. М., 1972. Ч. 2. 189 с.
10. Tait K. Pharmaceutical Industry, Encyclopedia of Occupational Health and Safety. 2011. URL: http://www.ilo.org/oshenc/part-xii/pharmaceutical-industry/item/385-pharmaceutical-industry#PHC_fig2 (дата обращения: 19.04.2014).
11. Федосеев А.А. Модель производства лекарственных препаратов с использованием теоретико-множественного описания и временных сетей Петри // Радиоэлектронные и компьютерные системы. 2012. № 6 (58). С. 224-228.
12. Зайцев Д.А. Инварианты временных сетей Петри // Кибернетика и системный анализ. 2004. № 2. С. 92-106.
13. Кафаров В.В., Макаров В.В. Гибкие автоматизированные производственные системы в химической промышленности. М.: Химия, 1990. 320 с.
