Программные продукты и системы

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 pharmaceuti- cal 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 manufacturing. 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, M0)                                            (1)

where P = {p1, p2, ..., pn} is a finite set of places; T = {t1, t2, ..., tm} is a finite set of transitions; A Í (P×T) È (T×P) is a set of arcs; W: A → {1, 2, ...} is a weight function; M0 : 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 antioxidants. 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:

Nt=(P, T, F, M0, t¢, t¢¢),                                           (2)

where Р={pi} is a finite set of positions; T= {tj} is a finite set of transitions; F ⊆ (P×T)È(T× P) is a set of arcs (or flow relations); M0, P → {0, 1, 2, …} is a the initial token; t¢={t¢1, t¢2, ..., t¢j} is a finite set of times for minimum delay for transitions; t¢¢={t¢¢1, t¢¢2, ..., t¢¢j} is a finite set of times for the maximum delay for transitions.

This paper developed a detailed model of a manufacturing 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:

O1 – a batch of raw material arrives at the input of a vibrating sieve machine;

O2 – vibration sieve is free (empty) and is in a standby mode;

O3 – 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;

O4 – a batch of sifted materials is off-loaded from the vibration sieve into a holding repository for transportation to the next stage of manufacturing;

O5 – a batch of sieved pharmaceutical ingredients, which were off-loaded from the sieving machine, arrives at the input of the mixer;

O6 – the mixer  is free (empty) and is in a standby mode;

O7 – 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;

O8 – a batch of mixed ingredients is off-loaded from the mixer into a holding container for transportation to the next stage of manufacturing;

O9 – a batch of  the mixed ingredients, which was off-loaded from the mixer, arrives at the input of the granulator;

O10 – the granulator is free (empty) and is in a standby mode;

O11 – 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;

O12 – wet granules are poured out of the granulator into a holding container to be transported to the next stage of manufacturing;

O13 – a batch of wet granule arrives at the input of the dryer;

O14 – the dryer is free (empty) and is in a standby mode;

O15 – 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;

O16 – the cooling process in the dryer;

O17 – dried granules are off-loaded from the dryer to be transported to next stage of production;

O18 – a batch of dried granules of the pharmaceutical ingredients arrives at the input of the tablet press machine;

O19 – the tablet press machine is free (empty) and is in a standby mode;

O20 – the tablet press presses the granules into tablets in accordance with given shape and weight;

O21 – A batch of tablets are released from the tablet press and kept in appropriate containers to be transported to the next stage;

O22 – a batch tablets arrives at the input of the packaging machine;

O23 – the tablet packaging machine is free (empty) and is in a standby mode;

O24 – the packaging machine undergoes the process of packaging tablets into defined sets;

O25 – 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 – maceutical 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:

t1 – 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;

t8 – end of granulation process;

t9 – the completion of the operation on transportation of wet granules  from the granulator machine to the dryer;

t10 – start of the drying process;

t11 – end of the drying process;

t12 – completion of the cooling process;

t13 – the completion of the operation on transportation of dried granules from the dryer  machine to the tablet press machine;

t14 – start of table press process;

t15 – end of tablet press process;

t16 – the completion of the operation on transportation of formed tablets from the tablet press machine to the packaging machine;

t17 – start of packaging process;

t18 – 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. 1). 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 2

Input and output conditions

Table 3

A Petri net in a tabular form

The finite set of positions P and the finite set of transitions T are:

P={p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, p12, p13, p14, p15, p16, p17, p18, p19, p20, p21, p22, p23, p24, p25};

T={t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18}.

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 equa- tions 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 columns 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:

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:

Multiplication of the matrix is performed according to the rule:

.                                                       (4)

The incidence matrix C for the analysis of the manufacturing system can be represented as follows:

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 D1 (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: A1, A2, A5 and A6. 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:

P1 (Ibuprofen): {A1, A2, A5, A6};

P2 (Malar-2 Forte): {A1, A2, A3, A5, A6};

P3 (Citramon): {A1, A2, A3, A4, A5, A6}.

The technological process of manufacturing product D3 (Citramon) consists of six operational steps carried out in the sequence in the equipment: A1, A2, A3, A4, A5 and A6. The first stage consists of loading operations of a batch of raw materials into the equipment A1 (vibration sieve). After loading the equipment A1  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 A2 (mixer).

The second stage of the manufacturing process includes loading a batch of defined proportions of the in- gredients 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 A3 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 A4 (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 A5 (tablet press machine).

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. A5 is switched off and the formed tablets are col- lected and kept in containers to be transported to the next stage of the production in the equipment A6 (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 A4, 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: A1, A2, A3, A5 and A6. Sieving of the ingredients in A1 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 A3. 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 D1 (Ibuprofen). The Equipment A3, which was previously connected to equipment A5, 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: A1, A2, A5 and A6. It starts with Sieving of the ingredients in A1, followed by mixing of the ingredients for the product D1 in equipment A2. After that the manufacturing process continues in A5 with the tablet pressing process, after which they are packaged in A6 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: A1, A2, A3, A4, A5 and A6.

The analysis of the Petri net model (fig. 1) of the manufacturing system and the timeline chart (fig. 4) shows that the only equipment busy within the time in- terval [0, t1] 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 t1 and continues until time t2. The sieving process ends at time t2; the sieved materials are off-loaded from A1 and transported to the next stage of the manufacturing in the equipment A2.

Time t3 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 A2. At that same time the loading of equipment A2 with all the ingredients to be mixed begins. Time t4 shows the be- ginning of mixing the ingredients for the product D3. The process of mixing ends at t5 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 [t3, t4] 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 t4 to produce the product D2.

At the time t6 the off-loading and transportation of the entire mass of mixed ingredients from A2 to the equipment A3 is completed. At the same moment t6 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 t7 and the equipment A3 starts the technological process (wet granulation). Time t8 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 t9. At the same moment the operation of loading A4 starts. The loading operation is completed at the time t10 and A4 begins the process of drying wet granules.

However, at time t9 to t11 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 t11.

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 [t17, t18] 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 [t23, t24] and on the time interval [t27, t28] 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, t28] the structure of the manufacturing system 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.

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