Subscriber access provided by UNIV OF NEW ENGLAND ARMIDALE
Process Systems Engineering
Decision support method for the choice between batch and continuous technologies in solid drug product manufacturing Kensaku Matsunami, Takuya Miyano, Hiroaki Arai, Hiroshi Nakagawa, Masahiko Hirao, and Hirokazu Sugiyama Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05230 • Publication Date (Web): 11 Apr 2018 Downloaded from http://pubs.acs.org on April 16, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
1
Decision support method for the choice between
2
batch and continuous technologies in solid drug
3
product manufacturing
4 5
Kensaku Matsunami, † Takuya Miyano, ‡ Hiroaki Arai, ‡ Hiroshi Nakagawa, ‡ Masahiko Hirao, †
6
and Hirokazu Sugiyama*, †
7 8
†Department of Chemical System Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-
9
ku, Tokyo, 113-8656, Japan
10
‡Formulation Technology Research Laboratories, Pharmaceutical Technology Division, Daiichi
11
Sankyo Co., Ltd., 1-12-1, Shinomiya, Hiratsuka, Kanagawa, 254-0014, Japan
12 13 14
Corresponding Author
15
*Tel.: +81 3 5841 7227. Fax: +81 3 5841 7227. E-mail:
[email protected].
ACS Paragon Plus Environment
1
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 48
16
ABSTRACT: This work presents a decision support method for the choice between batch and
17
continuous technologies in solid drug product manufacturing based on the economic evaluation.
18
The method consists of four steps: (I) modeling of operating costs, (II) evaluation, (III)
19
sensitivity analysis, and (IV) interpretation, with iterations. For a given design situation,
20
manufacturing processes are modeled and evaluated with consideration for the characteristics of
21
the two technologies. The sensitivity of the input parameters is analyzed; after interpreting all
22
results, the economically preferable technology is suggested. As a case study, the method was
23
applied to a situation where a new product was in the late development stage, and one of the two
24
technologies needs to be chosen. After executing the four steps, the comparison result of the net
25
present cost was obtained as the decision support information.
26 27
ACS Paragon Plus Environment
2
Page 3 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
28
Industrial & Engineering Chemistry Research
1.
Introduction
29
In the pharmaceutical industry, continuous manufacturing technology is attracting the attention
30
of numerous researchers as well as industrial experts.1 Conventionally, pharmaceuticals are
31
produced in batch processes where the product quality is controlled by sampling, offline
32
laboratory analyses, and product release to the next process. This classical approach is nowadays
33
being complemented by quality-by-design, along with the development of process analytical
34
technology (PAT), the online sensing technology. Many of the PATs apply near-infrared (NIR)
35
methods for continuous measuring of critical attributes that affect product quality, such as water
36
content,2 blend uniformity,3 or bulk density.4 Other spectroscopic techniques such as Raman
37
spectroscopy,5 UV–vis,6 and Terahertz spectroscopy7 are also implemented in the pharmaceutical
38
manufacturing processes. The advancement of PAT enables drug producers to achieve real-time
39
release of the product, and moreover, continuous manufacturing. The application of continuous
40
technology is not limited to mass production of inexpensive products, but is also possible in
41
small-scale production, which is in line with personalized healthcare, a recent trend in the
42
pharmaceutical industry.
43
Continuous technology has already become an actual alternative for producing solid drug
44
products such as tablets and capsules. In July 2015, the US Food and Drug Administration
45
(FDA) gave an approval to Vertex to adopt continuous technology in the manufacturing line of
46
Orkambi®. Next, in April 2016, the FDA approved a change from batch to continuous
47
manufacturing for Prezista® produced in a Janssen facility in Puerto Rico. In the literature,
48
numerous contributions are found for granulation, the key unit operation for converting inlet
49
powder materials to granules. Recent research shows experimental results on granule size
50
distribution,8,9 drug hydrophobicity,10 or dissolution11 in order to present the performance of
ACS Paragon Plus Environment
3
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 48
51
continuous granulation. Other unit operations are also studied: e.g., application of modeling
52
approaches such as the population balance model to a drying process,12,13 or the use of the
53
discrete element method in a mixing process,14 and a coating process.15 Some contributions
54
investigated the entire process of continuous manufacturing. Sundaramoorthy et al.16,17
55
demonstrated mathematical capacity planning under clinical trials uncertainty; Boukouvala et
56
al.18 presented dynamic flowsheet modeling and sensitivity analysis. Research on PAT in solid
57
drug product manufacturing is moving forward. For instance, Muteki et al.19 proposed a
58
calibration-free/minimum approach for predicting mixture component; Singh et al.20–24
59
conducted design/implementation of new control systems. Continuous technology is studied for
60
other types of pharmaceutical products, such as sterile drug products of biopharmaceuticals25 or
61
active pharmaceutical ingredients (APIs).26–28
62
Now that continuous technology is becoming real for the industry, it is necessary to evaluate
63
the actual merits of introducing the new technology as compared to the conventional batch
64
technology. Some authors reflected such a need in the comparative studies on both technologies.
65
Järvinen et al.29 compared product quality of granules and tablets through experiments, and
66
investigated the similarity and differences in quality for the two technologies. With the aim of
67
environmental comparison, Lee et al.30 conducted life-cycle assessment on the synthesis of 4-D-
68
erythronolactone; De Soete et al.31 performed an exergy-based sustainability assessment on tablet
69
manufacturing. Regarding economic performance, Schaber et al.32 estimated the production cost
70
of both batch and continuous tablet manufacturing processes starting from an organic
71
intermediate. The authors calculated capital and operating expenditure considering raw material,
72
labor, quality assurance, utilities, and waste disposal costs, and concluded that continuous
73
technology was economically advantageous in the case study. With a focus on API
ACS Paragon Plus Environment
4
Page 5 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
74
manufacturing, Denčić et al.33 compared total production cost and other process performance
75
such as yield, solvent waste, and feasibility aspects of batch and continuous technologies. Further
76
on API manufacturing, Jolliffe and Gerogiorgis presented continuous manufacturing processes of
77
ibuprofen34 and artemisinin,35 and presented a comprehensive economic comparison with the
78
batch processes.36 To support the actual decision-making on the technology choice, it is desired
79
to advance the methodological development beyond studying individual cases.
80
In this work, we present a decision support method for the choice between batch and
81
continuous technologies in solid drug product manufacturing based on economic evaluation. The
82
method consists of four steps: (I) modeling of operating costs, (II) evaluation, (III) sensitivity
83
analysis, and (IV) interpretation, and includes iterations. The final output of the method is the
84
comparison result of the net present cost after the product launch, which serves as decision
85
support information. As a basis for execution of the method, we developed a set of standard
86
models to calculate annual operating cost, and defined the points to incorporate in the calculation
87
model of the annual production amount. To demonstrate the proposed method, a case study was
88
performed assuming a design situation where the choice of either technology is made
89
considering the peak demand and the price of the API. The data used for the calculation were
90
provided and reviewed by the industrial coauthors. In this paper, all the equations and parameter
91
values are reported (see also Supporting Information) so that the presented results can be
92
reproduced, and also that the method can be executed using different input values. An earlier
93
version of this work was partly presented in the 27th European Symposium on Computer-Aided
94
Process Engineering.37
95
2.
96
2.1. Method overview
Method
ACS Paragon Plus Environment
5
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 48
97
Figure 1 shows the proposed method. The initial input of step I is a design situation, in which
98
either technology, batch or continuous, needs to be chosen, e.g., for a new tablet product in the
99
late development stage. In step I, models of operating costs are created for the processes using
100
each technology, so that the characteristics of the two technologies in the manufacturing stage
101
are reflected in the evaluation. Using these models, an economic evaluation is conducted in step
102
II. In step III, a sensitivity analysis is performed to quantify the effect of the input parameter
103
values on the evaluation results. Finally, in step IV, the results of the evaluation and the
104
sensitivity analysis are interpreted to explore the necessity of iterating the previous steps. The
105
final outcome of the method is the decision support information on the choice of the technology.
106
2.2. Technology overview
107
Before describing the details of the method, this section provides the overview of the two
108
technologies. Figure 2 shows a general scheme of pharmaceutical tablet manufacturing using wet
109
granulation, which consists of weighing, granulation, blending, compression, and coating
110
processes. In batch technology, each process is performed batchwise with a specific batch size
111
such as 300 kg/lot, whereas in continuous technology these processes are interconnected and run
112
at a constant rate, e.g., 25 kg/h. Figure 2 also displays supporting processes such as testing,
113
disposal, cleaning, maintenance of PAT and heat, ventilation, and air conditioning (HVAC). As
114
to testing, in-process control is performed during manufacturing, which is normally done by a
115
classical sampling approach in batch technology, and, if applicable, by PAT. In continuous
116
technology, the dependence on real-time monitoring is so high that PAT is inevitable for the in-
117
process control. After manufacturing, the products undergo release testing to become the final
118
products by performing various laboratory tests such as content uniformity test, dissolution test,
119
and microbial limit test. Losses generated during manufacturing are collected and disposed
ACS Paragon Plus Environment
6
Page 7 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
120
according to the company protocol after the production. Cleaning is another critical
121
postproduction process, where the machine, in particular the product contacting surface, is
122
cleaned by solvents including purified water. In case of campaign manufacturing, where multiple
123
lots are produced in sequence, the cleaning process is performed after the end of the campaign.
124
Maintenance of PAT is required to calibrate the PAT model on a regular basis; HVAC is
125
installed to keep temperature, humidity and cleanliness of the manufacturing space. All the
126
above mentioned processes and technologies need to be validated,38 i.e., the compliance to the
127
Good Manufacturing Practice (GMP) is proven, before the commercial production can start.
128
Because of the vast efforts required for changes, the conditions that are once validated will
129
remain the same for the product lifetime unless required. The validation applies to batch size as
130
well as the maximum continuous run time. But for the continuous technology, the run time can
131
be changed within the validated maximum run time according to the ongoing GMP-related
132
discussions.39,40,41
133
The difference between continuous and batch technologies can be summarized in the following
134
five points that may affect the evaluation of operating cost. First, in batch technology there is a
135
fixed batch size, whereas under the current regulation, continuous technology can easily deal
136
with demand change by tuning the continuous run time. Second, the number of operators in
137
continuous technology is smaller than that in batch technology because the machine in the
138
former is so compact that manual transfer of materials is not needed. This size advantage leads to
139
a third characteristic: namely, that the manufacturing space for continuous technology is smaller
140
than that for batch technology. Fourth, the continuous technology requires PAT maintenance that
141
costs man-hours.42 Finally, continuous technology needs some time (which can be several tens of
ACS Paragon Plus Environment
7
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 48
142
minutes) until the machine operation is sufficiently stable. During this start-up operation, the
143
precious materials are disposed.
144
2.3. Step I: Modeling of operating costs
145
In step I, models are created so that the abovementioned characteristics of the two
146
technologies, such as product yield, numbers of operators, or required space for manufacturing,
147
can be reflected in the evaluation. We developed a set of standard models to calculate the
148
operating cost of the processes using the two technologies. The models were created on the
149
assumption that the products obtained by both technologies are pharmacologically equivalent for
150
the patient needs. The annual operating cost of the ith year after the launch of the product, C(i)
151
[$/yr], is defined in Eq. (1).
= Material cost + Disposal cost + Labor cost + Utility cost + Capacity cost
= !,# $%&'()*+,# + %!'+++,# , #
+ !,+'!-. %+'!-. / + ( +&'+! %!'+++,#
(1)
#
+ !0' $1.)2*) .3 + 1*!. .3 + 1+ .3
+ 1456 , + 7859 : ;7859 + *&* <
152 153
The parameters Cmaterial, j [$/kg], Cmaterial, solvent [$/kg], Mproducts, j(i) [kg/yr], Mlosses, j(i) [kg/yr],
154
and Msolvent(i) [kg/yr] represent cost of raw material j, raw material cost of solvent, the annual
155
amount of material j used to make the product, amount of annual losses of material j, and amount
156
of solvent used annually, respectively. The suffix j is an element of the API, binder, coating
ACS Paragon Plus Environment
8
Page 9 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
157
agent, disintegrant, excipient, or lubricant. Solvent, which is typically water, is used to dissolve
158
binders or coating agents to make the solutions to add to the granulation or coating processes,
159
respectively. The parameter Cdisposal [$/kg] represents the cost to dispose a unit amount of loss,
160
which was assumed to be independent of the type of materials. The parameter Clabor [$/man/h] is
161
the labor rate, and the parameters Wmanufacturing(i) [man-hour/yr], Wcleaning(i) [man-hour/yr],
162
Wtesting(i) [man-hour/yr], and WPAT(i) [man-hour/yr] represent annual man-hours for
163
manufacturing, cleaning, testing, and PAT maintenance, respectively. The latter is assumed to be
164
conducted once a year, and the man-hours of the PAT maintenance are not affected by the
165
quantities produced. The parameters CHVAC [$/m2/h], A [m2], THVAC(i) [h/yr] represent HVAC
166
cost, manufacturing space, which is covered by HVAC, and HVAC running time, respectively.
167
As HVAC is known as a dominant utility for maintaining a clean manufacturing environment,43
168
other utilities such as water or electricity were not included in this equation. The parameter
169
Ccapacity(i) [$/yr] represents capacity cost, i.e., the loss of profits from capacity displaced by the
170
new product as an additional operating cost. If the production amount of the new product is so
171
large that the existing products have to be produced by a third party, and if a commission
172
expense needs to be paid, this additional cost will be covered by Ccapacity(i).
173
Eqs. (2)–(8) determine the dependency of Mproducts, j(i), Mlosses, j(i), Msolvent(i) Wmanufacturing(i),
174
Wcleaning(i), Wtesting(i), and THVAC(i) on the annual production amount, Nprod(i) [tablet/yr]. All
175
subequations of Eqs. (2)–(8) are presented in Eqs. (S1)–(S11) in Supporting Information.
176
%&'()*+,# = =# >?&'( %!'+++,# =
1 >>!'+++,# ?&'( >!'
%+'!-. = =+'!-. >?&'(
(2) (3) (4)
ACS Paragon Plus Environment
9
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
1.)2*) .3 = 1*!. .3 = 1+ .3 = ;7859 = 177
1 >A.)2*) .3 ?&'( >!'
1 >A*!. .3 ?&'( >!' ?*& 3.
1 >A+ .3 ?&'( >!'
1 >B*& 3. ?&'( >!' ?*& 3.
Page 10 of 48
(5) (6) (7) (8)
178
The parameters αj [–], m [kg/tablet], mlot [kg/lot], mlosses, j [kg/lot], and αsolvent [–] represent the
179
mass fraction of material j in the product, weight of one tablet, lot size, total amount of losses of
180
material j in one manufacturing lot, and the mass ratio of the solvent to the product used in the
181
granulation and coating processes, respectively. The parameters wmanufacturing [man-hour/lot],
182
Ncampaign [lot/campaign], wcleaning [man-hour/campaign], wtesting [man-hour/lot], and tcampaign
183
[h/campaign] stand for man-hours of one-lot manufacturing, number of lots in one campaign
184
manufacturing, man-hours of one cleaning, man-hours of testing in one manufacturing lot, and
185
total time needed for one campaign manufacturing, respectively. In this paper, mlot for batch
186
technology is defined as the production amount in one lot, hereafter termed as batch size V
187
0*C [kg/lot]. The parameter V is equivalent to >!' . The parameter mlot for continuous technology,
188
*'. .)')+ *'. .)')+ >!' , is calculated by using the validated run time ;-! [h] in continuous
189
technology. It was assumed that all the lots in year i would be manufactured for the time of
190
*'. .)')+ *'. .)')+ ;-! except for the last lot. The run time for the last lot in year i, ;+ [h/lot], is ()
191
adjusted using Eq. (S25) in Supporting Information, in order to produce Nprod(i). For the
192
parameter mlosses, j, five types of causes are considered: material sticking to the inner surface, and
193
sampling for in-process control in batch technology; tablets produced until the machine runs in a
ACS Paragon Plus Environment
10
Page 11 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
194
stable manner, and remaining raw material in the feeder after production in continuous
195
technology; and tablets produced in compression testing for both technologies. The parameter
196
wmanufacturing(i) depends on the number of operators and manufacturing time; wcleaning(i) depends
197
on the number of operators and cleaning time. The parameter Wcleaning(i) considers the frequency
198
of cleaning, which is expressed as
199
process control in batch technology, and release testing in both technologies. The parameter
200
tcampaign is an all-inclusive time for one manufacturing campaign covering not only the actual
201
manufacturing time, but also cleaning, weekends, and buffer time. HVAC systems are
202
considered to run continuously during tcampaign.
DEFGHI J
DKHL EMNOFNPQR
in Eq. (6). The test for wtesting consists of in-
203
As can be seen in Eqs. (2)–(8), Nprod(i) is a key parameter for calculating C(i). To determine
204
Nprod(i), we regard the following three industry-specific practices as worth incorporating in the
205
model. First, a specific number of lots, which is typically three in the industry, are produced at
206
the launch of the process for process validation. Second, the production amount is decided to
207
secure sufficient inventory and avoid drug shortages. Third, there is the shipping deadline, which
208
should be earlier than the expiration date. Under these common conditions to both technologies,
209
the determined value of Nprod(i) would be different because of the flexibility of each technology.
210
In batch technology, the production quantity responds to the demand amount stepwise, whereas
211
in continuous technology, the production quantity can change continuously. For example, if the
212
demand has an amount that corresponds to a quantity of 1.1 lots, batch technology has to produce
213
2 lots, whereas continuous technology can produce the exact quantity by adjusting the
214
continuous run time. Because the demand changes over the lifetime of a drug product, Nprod(i)
215
will be different between the two technologies, even when the demand profile is the same.
ACS Paragon Plus Environment
11
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 48
216
In the model as well as in the case study, one year was set as the unit interval of time. This is
217
because pharmaceutical companies typically use annually estimated data for a long-range
218
planning like 30 years, which is the assumed situation in the case study. If a shorter unit interval,
219
such as quarter or month, is more appropriate, the model can be used by defining i as the
220
corresponding time unit.
221
2.4. Step II: Evaluation
222
In step II, an economic evaluation is conducted. In this study, the net present cost (NPC) [$],
223
was chosen as the standard objective function to evaluate the economic performance after the
224
launch. The NPC of technology, NPC [$] can be calculated using Eq. (9):
225
?S = ∑ZJ[\ VWXY , UJ
(9)
226
where τ [yr] and r [–] represent the selling period from launch and interest rate, respectively.
227
Similar to net present value (NPV), the indicator NPC considers the time value of money, but
228
excludes capital cost and revenue, which is different from NPV. This modification is suitable for
229
design situations as introduced in the case study, where the facility was supposed to have the two
230
technologies installed.
231
The technology selection can be expressed as the optimization problem shown in Eq. (10): *'. .)')+ min ?S_B`aℎ, ;-! c
s.t.
B`aℎ ∈ ebatch, continuoush
(10)
*'. .)')+ ; . ≤ ;-! ≤ ;j ,
kl2 , l* = 0,
232
ACS Paragon Plus Environment
12
Page 13 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
233
where tech, xf, xc, and g(x) represent batch or continuous, vectors of the input constraint
234
parameters that are fixed (f) or changeable (c) at the stage of the decision-making, and a vector
235
of constraint functions, respectively. The parameters Tmin [h/lot] and Tmax [h/lot] represent the
236
minimum and maximum values of the validated continuous run time, respectively. The
237
*'. .)')+ *'. .)')+ parameter ;-! is to be optimized because ;-! determines the production amount
238
of the three validation lots, overproduction of which could lead to unnecessary discard. Too
239
*'. .)')+ small ;-! could lead to frequent changeover, and thus increase of the cost. We specified
240
*'. .)')+ tech and ;-! as the optimization parameters because (a) the remaining parameters are
241
related with the process given and/or the product quality and thus cannot be freely optimized,
242
and (b) this could be a typical setup of the decision-making in the future pharmaceutical industry.
243
In the next step, sensitivity analysis is offered in order to investigate how the solution is affected
244
if the elements of xc were given differently.
245 246
The overall comparison indicator y [$] was defined to compare the economic performance of the two technologies as in Eq. (11): *'. .)')+ n = min ?S_continuous, ;-! c − ?Sbatch,
(11)
247
By analyzing whether the obtained y is positive or negative, a tentative conclusion is drawn on
248
which technology to choose.
249
2.5. Step III: Sensitivity analysis
250
The sensitivity analysis is conducted to quantify the effects of the values in the input constraint
251
parameters on the evaluation. The elements of xc are subject to the analysis here. One example is
252
manufacturing rate of continuous technology that could be changed/given differently if the target
253
product quality cannot be achieved with the intended rate. Eq. (12) is a general description of the
ACS Paragon Plus Environment
13
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 14 of 48
254
relation between xk, an input parameter k that is an element of xc, and the output function y, e.g.,
255
the overall comparison indicator given in Eq. (11):
n = pqr .
(12)
256 257
In this step, two kinds of indices were introduced. The first index was δyk [$], the response to
258
the perturbation of the input parameter k, δxk, given in Eq. (13); the second was ∆yk [$], the
259
response to a possible change in the input parameter k, ∆xk, given in Eq. (14):
snr =
max
u∈evwx ,yvwx h
∆nr = maxw OPR w x
260
z{p_qr. ! + |c − p_qr. ! c{}
ON x wx
pqr − minw OPR w x
ON x wx
(13)
pqr ,
(14)
where qr. ! , sqr , qrj and qr . represent initial value, perturbation, maximum, and minimum
261
values of the input parameter k, respectively. The parameter | is a placeholder for δxk. If the
262
value of the output function increases or decreases monotonously according to the increase in the
263
value of k, ∆yk [$] can also be expressed as given in Eq. (15):
264
∆nr = {pqrj − p_qr . c {.
(15)
265
To simplify the calculation effort, Eq. (15) can be used as long as there is no significant
266
difference between the results of Eqs. (14) and (15). After the calculation of δyk and ∆yk, the
267
parameters are classified according to the effect on the result. If both δyk and ∆yk are large, the
268
parameter xk is classified as a high-impact parameter. Additionally, if either δyk or ∆yk is large, it
269
could be worth investigating the cause in detail.
270
2.6. Step IV: Interpretation
271
In the last step, all the results obtained in the previous steps are interpreted to produce decision
272
support information as the final output of the method. The main task here is to examine the
ACS Paragon Plus Environment
14
Page 15 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
273
necessity of iterating the previous steps based on all the obtained results. First, the evaluation
274
results in step II are interpreted, and if necessary, step I is conducted again to adjust the model.
275
Next, the result of the sensitivity analysis in step III is interpreted, in particular on the high-
276
impact parameters. One interesting analysis would be to change the input parameter values and
277
investigate the influence on the temporary conclusion obtained in step II. The step of iteration is
278
performed until the results can be judged sufficiently solid to suggest which technology is
279
economically preferable in the given design situation.
280
3.
281
3.1. Design situation
Case Study
282
The objective of this case study was to demonstrate the proposed method under certain design
283
situation that is likely to exist in the future. The following items were assumed as the design
284
situation: (i) a new tablet product is assumed, which is in the later development stage; (ii) the
285
selling period is assumed to be 30 years; (iii) there is a facility that is equipped with both batch
286
and continuous technologies where the capacity is so sufficient that Ccapacity(i) can be assumed as
287
zero; and (iv) the technology needs to be chosen based on the estimates of the peak demand
288
j amount of the API during , ?(.( , and the price of the API, !,54 . For the batch
289
technology, V is fixed at 300 kg; and for the continuous technology, Tmin and Tmax are set as 7
290
and 20 h, respectively. We regarded the values of Tmin and Tmax, which correspond to one to three
291
shift operation, as realistic for the actual continuous manufacturing, and thus adopted as the input
292
values. In general, the demand amount and the price of APIs on the market have a wide range,
293
e.g., 106 to 109 tablets/yr and $10 to 104/kg, respectively. In our calculation, this entire range was
294
applied; to demonstrate the execution of the method, we used the predetermined estimates of
ACS Paragon Plus Environment
15
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
295
Page 16 of 48
j and !,54 , respectively. Hereafter, the 5.0 × 107 tablets/yr and $1,000/kg for ?(.(
296
j vector of _?(.( , !,54 c = 5.0 × 10 , 1.0 × 10 was denoted as point P.
297
3.2. Step I: Modeling of operating costs
298
For the process shown in Figure 2, the models for evaluating annual operating cost were
299
defined as Eqs. (1)–(8). The values of the parameters used in the calculations were shown in
300
Table S1 and Table S2 in Supporting Information. The entire dataset was provided and reviewed
301
by the industrial coauthors, which included typical manufacturing data for batch technology, and
302
estimated values for continuous technology. For the demonstration purpose of the model, the
303
data quality was judged sufficient. The parameters A, ∑# >!'+++,# , tcampaign, wcleaning, wmanufacturing,
304
wtesting, WPAT were defined differently in the two technologies. As to the in-process control,
305
sampling was set as the method in the batch technology whereas in the continuous technology
306
PAT was employed. With these models and parameter settings, the following characteristics of
307
the two technologies could be reflected in the calculation of C(i). For the same value of Nprod(i),
308
the material and disposal costs of the continuous technology were larger than for batch
309
technology because of the input values of mlosses. The labor cost, except for the term Clabor WPAT,
310
and utility cost for continuous technology was smaller than for batch technology because of the
311
input values of wcleaning, wmanufacturing, wtesting, and A. The cost Clabor WPAT for continuous
312
technology was higher than for batch technology because of the number of PAT, nPAT (see Table
313
S2 in Supporting Information).
314
To determine Nprod(i) as a key parameter in the calculation of C(i), a demand profile of 30
315
years was assumed (Figure 3). This is a typical profile of pharmaceutical tablets according to
316
.' [–], which is the normalized industrial expert knowledge. The vertical axis shows ?(.(
317
demand amount in year i after the launch, as given by Eq. (16):
ACS Paragon Plus Environment
16
Page 17 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
.' = ?(.(
EIONRI J ON EIONRI
,
(16)
318
where ?(.( [tablet/yr] represents the demand amount in year i. The reason for the peak in
319
Figure 3, which is found in year i = 10, is the expiration of the patent. By specifying the value of
320
j ?(.( , the value of ?(.( can be defined, and then the value of ?&'( is calculated.
321
Here, the industry-specific practices mentioned earlier were concretized as follows. (i) Three lots
322
are produced at the launch, i.e., year i = 0, for process validation; (ii) at least a half year of
323
inventory is maintained; and (iii) the shipping deadline is one year before the expiration date,
324
which is three years after the production, and the expired tablets are disposed of. Under these
325
conditions, the models for calculating ?&'( were defined as per Eqs. (17) and (18):
0*C ?&'(
0*C 0*C ? 0*C .-_.( − ? .-_!+ − ? .-_!' 0*C >!'
*'. .)')+ .)')+ *'. .)')+ .)')+ = ? *'. − ? *'. , ?&'( .-_!'++V,# in Supporting Information). This
352
product loss was the key contributor to the result in the area where the material cost was
353
dominant.
354
*'. .)')+ The optimal ;-! that yielded the minimum NPC for continuous technology was also
355
obtained for the entire area of Figure 4. The result is shown in Figure S1 in Supporting
356
*'. .)')+ Information. In most of the area, the optimal ;-! was Tmax, i.e., 20 h, however, a
357
monotonic decrease was observed to the upper-left area. This decreasing trend is because too
ACS Paragon Plus Environment
18
Page 19 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
358
*'. .)')+ leads to overproduction in the first three lots for process validation, and the long ;-!
359
unnecessary discard of expensive products.
360
The preferable technology can be suggested in Figure 4 by applying the predictions of the peak
361
demand amount and the price of API. At point P, continuous technology is found to be
362
advantageous, which is the tentative conclusion of the step.
363
3.4. Step III: Sensitivity analysis
364
Sensitivity analysis was performed for the elements of xc using the result of y at point P. The
365
response to perturbation, δyk [$], was calculated using Eq. (13) with setting δxk as 1% of the
366
initial value; the response to possible change, ∆yk [$], was calculated using Eq. (15) with setting
367
qr . and qrj based on industrial expert knowledge.
368
Figure 5 shows the obtained results. Two parameters, namely, v, the manufacturing rate in
369
continuous technology (initial value: 25 kg/h) and Ncampaign (initial value: 5 lots), were classified
370
*'. .)')+ as high-impact parameters. The parameter v affects the >!' (see Eq. (S11) in Supporting
371
Information), and then Mlosses, j(i), Wmanufacturing(i), Wcleaning(i), Wtesting(i), and THVAC(i) (see Eqs. (3)
372
and (5)–(8)); the parameter Ncampaign affects D
373
DEFGHI J
KHL EMNOFNPQR
, and then Wcleaning, and THVAC (see Eqs.
0*C (6) and (8)). There were two parameters that showed a large ∆yk, i.e., ∑# >!'++,# , and
374
*'. .)')+ ∑# >!'++V,# . These two parameters that are associated with product losses were identified
375
because of the large ranges of ∆x set for these parameters (see Table S2).
376
3.5. Step IV: Interpretation
377
The sensitivity analysis in step III extracted v and Ncampaign as the high-impact parameters. We
378
repeated step II to investigate whether and how far the temporary conclusion could be affected
379
by changing the input values of these parameters. Figure 6 shows the results of changing v from
ACS Paragon Plus Environment
19
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 20 of 48
380
25 kg/h to 10 kg/h (Figure 6 (a)) and 19 kg/h (Figure 6 (b)). As these graphs suggest, the
381
continuous-preferred area becomes larger along with the increase in v. This change leads to the
382
*'. .)')+ (see Eq. (S11)), the decrease in %!'+++,# , %+'!-. , increase in >!'
383
1.)2*) .3 , 1*!. .3 , 1+ .3 , and ;7859 (see Eqs. (3) and (5)–(8)), and finally
384
the decrease in C(i) of continuous technology (see Eq. (1)). At point P, the preferability of the
385
technology changes from continuous to batch at around v = 19 kg/h. This result indicates the
386
importance of v, determination of which requires consideration of various factors such as
387
properties of the raw materials. For example, if the raw materials have high wettability, there is a
388
risk that its flowability would decrease, and that the maintenance of v becomes difficult. In the
389
case of selecting continuous technology at point P, the actual value of v should be larger than 19
390
kg/h, which needs to be consolidated, e.g., through thorough experimental investigations.
391
The result of changing Ncampaign is shown in Figure 7 (from 5 lots/campaign to 2 is shown in
392
Figure 7 (a) and to 8 lots/campaign in Figure 7 (b)). The batch-preferred area is extended when
393
the value of Ncampaign in batch technology becomes larger. This change leads to the decrease in
394
Nprod(i)/Ncampaign, Wcleaning(i), and THVAC(i) (see Eqs. (6) and (8)), and the decrease in C(i) of batch
395
technology (see Eq. (1)). At point P, the continuous technology is always better, i.e., the decision
396
can be made without determining the actual value of Ncampaign in batch technology. As can be
397
seen in this case, some parameters may not affect the choice even if they were classified as high-
398
impact parameters in the sensitivity analysis.
399
After executing all the steps, the decision support information was obtained as follows. “At the
400
predetermined estimates, continuous technology is economically preferable as long as the actual
401
value of v is larger than 19 kg/h.”
402
4.
Discussion
ACS Paragon Plus Environment
20
Page 21 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
403
Industrial & Engineering Chemistry Research
4.1. Role of the method in drug development and manufacturing
404
The most important role of the presented method is to support decision-making on the
405
technology choice considering economic performance. The standard model introduced in the
406
paper can incorporate major differences in the evaluation between the two technologies, such as
407
flexibility in lot size. As soon as the estimation of peak demand and API price is available, an
408
economically preferable technology can be suggested at any stage of the drug development and
409
manufacturing. As the prerequisite for executing the evaluation, industrial expert knowledge is
410
required to set a large number of parameter values, which was 83 in the case study. The method
411
defines the sensitivity analysis to help identify the high-impact parameters that, among large
412
numbers of input parameters, require certainty for producing reliable decision support
413
information. By integrating other critical aspects such as quality, safety, or occupational health,
414
the actual decision-making would become more rationalized.
415
4.2. Improvement opportunities for continuous technology
416
In the case study, several opportunities were observed for improving continuous technology
417
*'. .)')+ , resulted toward the future. From Figure 4, the loss during the start-up operation, ∑# >!'++V,#
418
in the steep increase in y in the upper-right area where blockbusters would find their place. To be
419
competitive in this lucrative area, quick stabilization in the start-up operation will be the key
420
opportunity. From Figures 4 and 5, the landscape changed drastically depending on the value of
421
v. This indicates that continuous technology should have the capability to maintain a high
422
manufacturing rate from granulation to tableting while dealing with various properties of inlet
423
materials such as wettability.
424
4.3. Application of the method in other design situations
ACS Paragon Plus Environment
21
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 22 of 48
425
An additional analysis was performed for different values of V, which was fixed at 300 kg/lot
426
in the case study. Figure 8 (a) and (b) shows the evaluation results of y at V = 100 and 500 kg/lot,
427
respectively, where the parameters for continuous technology were kept the same. Comparing
428
Figures 4 and 8 (a), an extension of the continuous-preferred area is observed, which was caused
429
by the increase in Nprod(i)/V and the resulting increase in C(i) in batch technology (see Eqs. (3)
430
and (5)–(8)). Additionally, the continuous-preferred area in the upper-left part of Figure 4
431
disappeared in Figure 8 (a). This result was caused by the fact that increment of batch size
432
change according to demand becomes smaller, which makes the batch technology more flexible
433
at V = 100 kg/lot. For the case of V = 500 kg/lot, the opposite tendencies can be observed
434
because of the decrease in Nprod(i)/V, and the increase in the increment in batch size change. At
435
the point of P, the maximum y is given by the batch technology at V = 500 kg/lot (Figure 8 (b)).
436
Figures 4 and 8 (a, b) correspond to the result at step II when V was open in the given design
437
situation. This is possible when the development stage is earlier than the stage investigated in the
438
case study where V was fixed. The temporary conclusion at point P would be to suggest batch
439
technology with V = 500 kg/lot; i.e., the method can be applied to other design situations.
440
5.
Conclusions and Outlook
441
In this article, we presented a decision support method for the choice between batch and
442
continuous technologies in solid drug product manufacturing based on economic evaluation. The
443
method comprises four steps of modeling of operating costs, evaluation, sensitivity analysis, and
444
interpretation, to produce decision support information under the given design situation. As a
445
basis for executing the method, we developed a set of standard models to calculate annual
446
operating cost, and defined the points to incorporate in the calculation model of the annual
447
production amount. This generic model considered costs of materials, disposal, labor, and utility
ACS Paragon Plus Environment
22
Page 23 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
448
where the two technologies showed different characteristics, and enabled calculation of NPC and
449
the overall comparison indicator. The sensitivity analysis was defined to identify important
450
parameters that need to be set appropriately with analyzing the responses to perturbation and
451
possible changes in the input parameters. The step of interpretation had the role of investigating
452
the necessity to iterate the previous steps before producing solid decision support information as
453
the final output.
454
We demonstrated the method in the case study with assuming a design situation where either
455
technology needs to be chosen considering the peak demand and the price of API. Using the data
456
that were provided and reviewed by the industrial coauthors, the four steps of the method could
457
be completed, and the following quote was obtained as the decision support information. “At the
458
predetermined estimates, i.e., 5.0 × 107 tablets/yr and $1,000/kg for peak demand amount and
459
API price, respectively, the continuous technology is economically preferable as long as the
460
actual manufacturing rate is larger than 19 kg/h.” In the contour line graph obtained in step II,
461
continuous technology was economically preferable for the products that have high demand and
462
low price, e.g., generics, or low demand and high price, e.g., orphan drugs. The obtained results
463
and suggestions are dependent on the input parameter values, however, we could explain the
464
result with the characteristics of the two technologies. In the case study result, quick stabilization
465
in the start-up operation and a high manufacturing rate throughout the entire process were found
466
as the key improvement opportunities for continuous manufacturing.
467
The actual decision-making in solid drug product development/manufacturing needs to cover
468
various aspects. Regarding economic evaluation, costs for investment as well as clinical
469
development are relevant; the revenue may differ because the time duration of the regulatory
470
process would be different for batch and continuous technologies. Another critical aspect would
ACS Paragon Plus Environment
23
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 24 of 48
471
be product quality. Depending on the choice of technology, the quality, such as particle size
472
distribution of granules or dissolution profile of the tablet, would be different. In addition, the
473
aspect of safety and occupational health would be critical, because the process might well
474
involve a highly potent powder API. The available information would differ depending on the
475
stage of the drug development and manufacturing, which is another complexity to be considered.
476
Lastly, there is an expansion possibility towards advanced sensitivity analysis such as
477
multivariate and distribution-based sensitivity analysis. Actually we proceeded with the
478
incorporation of parameter uncertainty in the result using Monte Carlo simulation, and will
479
present the first result in a six-page conference proceedings paper.44 Uncertainty-conscious
480
modeling and evaluation will enable expansion to the earlier design phases where degrees of
481
freedom is higher whereas the available information is more limited.
482 483
ASSOCIATED CONTENT
484
Supporting Information. Details of equations and the values of parameters are given in
485
Supporting Information. This information is available free of charge via the Internet at
486
http://pubs.acs.org/.
487 488
AUTHOR INFORMATION
489
Corresponding Author
490
*Tel.: +81 3 5841 7227. Fax: +81 3 5841 7227. E-mail:
[email protected].
491
Funding Sources
ACS Paragon Plus Environment
24
Page 25 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
492
Industrial & Engineering Chemistry Research
493 494
Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (A) No. 17H04964 and Grant-in-Aid for Young Scientists (B) No. 26820343
495
Ministry of Education, Culture, Sports, Science and Technology, Global Leader Program for Social Design and Manage
496
497
Notes
498
The authors declare no competing financial interest.
Nagai Foundation Tokyo, Research Grant 2017
499 500
ACKNOWLEDGMENT
501
Financial support by Grant-in-Aid for Young Scientists (B) No. 26820343 and (A) No.
502
17H04964 from the Japan Society for the Promotion of Science, and by Research Grant 2017
503
from the Nagai Foundation Tokyo, as well as discussions with Mr. Yasuhiro Suzuki from Daiichi
504
Sankyo Co., Ltd. and Mr. Hiroaki Inoue from Daiichi Sankyo Propharma Co., Ltd. are gratefully
505
acknowledged. This research was supported through the Leading Graduates Schools Program,
506
“Global Leader Program for Social Design and Management,” by the Ministry of Education,
507
Culture, Sports, Science and Technology.
508
ACS Paragon Plus Environment
25
Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
509
Page 26 of 48
Nomenclature Variables
:
Manufacturing space covered by HVAC [m2]
Annual operating cost [$/yr]
|
*&* <
Placeholder of sqr
Capacity cost [$/yr]
( +&'+!
Cost to dispose unit amount of loss [$/kg]
!0'
Labor rate [$/man/h]
!,+'!-.
Material cost of solvent [$/kg]
7859
!,# i
>
%!'+++,# >!'+++,# 0*C >!'++V,# 0*C >!'++,# 0*C >!'++,# 0*C >!'++,# 0*C >!'++,# 0*C >!'++,# 0*C >!'++,#
HVAC cost [$/m2/h]
Raw material cost of material j [$/kg]
Production time after the launch [yr] Weight of one tablet [kg/tablet] Amount of material j that ends up in losses annually [kg/yr] Total amount of losses of material j from one-lot manufacturing [kg/lot] Amount of loss of material j caused by sampling in granulation in batch technology [kg/lot] Amount of loss of material j caused by sticking in granulation in batch technology [kg/campaign] Amount of loss of material j caused by sampling in blending in batch technology [kg/lot] Amount of loss of material j caused by sticking in blending in batch technology [kg/campaign] Amount of loss of material j caused by sampling in compression in batch technology [kg/lot] Amount of loss of material j caused by compression testing in compression in batch technology [kg/lot] Amount of loss of material j caused by sampling in coating in batch technology [kg/lot]
ACS Paragon Plus Environment
26
Page 27 of 48 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Industrial & Engineering Chemistry Research
0*C >!'++,#
*'. .)')+ >!'++V,# *'. .)')+ >!'++,# *'. .)')+ >!'++,# >!'
%&'()*+,#
%+'!-. ?*& 3.
Amount of loss of material j caused by other reasons in coating in batch technology [kg/campaign] Amount of loss of material j generated during the start-up operation in continuous technology [kg/lot] Amount of loss of material j remaining in the feeder in continuous technology [kg/campaign] Amount of loss of material j caused by compression testing in compression in continuous technology [kg/lot] Lot size [kg/lot] Amount of material j used to make the product annually [kg/yr] Amount of solvent used annually [kg/yr] Number of lots in one campaign manufacturing [lot/campaign]
.' ?(.(
Normalized demand amount [‒]
j ?(.(
Peak demand amount during [tablet/yr]
? .-_!+
Amount of inventory that was produced one year before the ith year [tablet/yr]
?(.( ?( +&'+! ? .-_.( ? .-_