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AN APPLICATION OF PERT TO R & D SCHEDULING
N. K. KWAK
St. Louis University, 3674 Lindell Blvd., St. Louis, MO 63108. U.S.A.
and
LAWRENCE JONES
National Center for Drug Analysis, U.S. Food and Drug Administration, 1114 Market St., St. Louis, MO 63101, U.S.A.
(Received 19 November 1976)
Abstract-This paper deals with an application of PERT to R & D scheduling for the National Center for Drug Analysis, U. S. Food and Drug Administration. The Center is a phar- maceutical-chemistry laboratory having specialized functional responsibilities for research and development of analytical chemical procedures. The model was constructed based on the empirical data obtained at the Center for a five-year period. The model has been statistically tested and interpreted. It assists the management of the Center in developing a complete work-planning process and in controlling the project tasks, thus achieving the effective utilization of human and physical resources.
INTRODUCTION
The National Center for Drug Analysist is a division of Pharmaceutical Research and Testing, Bureau of Drugs, U.S. Food & Drug Administration (FDA). It is an analytical laboratory specializing in the analysis of unit dosage forms of various pharmaceutical products. One of the primary functions of the Center is to develop and test automated methods to be used in the analytical programs conducted by the Center. The operations of the Center require intricate inter-organizational plans which must be well coordinated with the specific research being conducted at the Center.
This paper deals with the application and implementation of Program Evaluation and Review Technique (PERT) to the research scheduling of the Center. PERT helps in developing a more complete work-planning process for both planning and controlling projects, and thereby enhancing effective utilization of human and physical resources. PERT is also being evaluated for monitoring samples through the analytical operations of the Center.
BACKGROUND
The FDA has 21 district offices that include within their boundaries the entire United States.
Geographically, the different drug manufacturers’ plants are located within these districts. FDA investigators from these districts visit the firms to make inspections and collect samples for analysis. The investigators collect samples that are of interest to the FDA at that time.
The decision to investigate a category of drugs rests with the Associate Director for Compliance, Bureau of Drugs. The category of drugs and the different types within the category are specified in a compliance program called a Study. The proposed Study is drafted by Compliance and copies are distributed within for review. The Study is sent to the Director of Regional Operations (EDRO), and to the Associate Director for Pharmaceutical Research and Testing (PRT), Bureau of Drugs. The Center is a division of PRT and is the analyzing laboratory for the drug products collected under the Study. As the analyzing laboratory, the Center receives a copy of the proposed program and is one of the principal reviewers.
The drugs included in the Study are reviewed for their therapeutic significance and the extent that the drugs are prescribed by physicians to the total population. For example, “birth control
tHereinafter referred to as the “Center”.
121
122 N. K. KWAK and I_. JONES
pills” are highly potent. they are administered to alter or change the vital functions of the female reproductive system, and they are widely prescribed by physicians, thereby making them drugs of high significance.
ERDO receives a copy of the study for informational purposes. This office controls the operations in the district offices where the samples are eventually to be collected. When the study is activated, EDRO issues the authorization for the samples to be collected.
The director of PRT reviews the study for its suitability, supplies comments as to whether there exist analytical methods appropriate for any proposed analyses, and determines the status of the methods relative to the posture of FDA to undertake legal action should it become necessary.
The Center has the responsibility for estimating the feasibility of developing methods and setting a target date for having the methods available to do the analysis. The target date supplied by the Center is generally the date set for beginning the Study. When the Study is begun, the inspectors in the districts go to the firms and collect the specified drugs and send them to the Center for analysis.
R & D PLANNING AND SCHEDULING
After the decision has been made to investigate a particular category of drugs, the research director begins the planning and scheduling process by reviewing the schedule of drugs, and noting the dosage levels, different product forms, the specific chemical and physical properties, and very importantly, the similarities to products previously analyzed. From these facts it is possible to estimate the degree of difficulty and the probability of developing a suitable automated approach. Preliminary planning considers tentative personnel assignments. the status of current projects, and the need for specialized equipment or supplies.
The Methods Research Branch has the primary responsibility for testing and developing automated methods and the Drug Monitoring Branch performs the analyses using the developed methods. The chemists assigned to the development of methods work sometimes individually and sometimes in teams. As a result, a Study conceivably can include several people working simultaneously or possibly sequentially in developing the methods, thus making planning and controlling difficult.
A research procedure checklist (Exhibit I) has been developed that details guidelines to be used by the research chemists. It serves as a feedback and control mechanism to the research director in monitoring the progress of research on methods for the Study. The checklist is in a sequential order, and in most instances the preceding step must be completed before the succeeding step can be started. However, many of the steps can be carried out simultaneously: this is very often the case. All of the steps, up to and including the Preparation of Reports: Methodology, must be completed before the research can be considered complete.
If the research cannot be completed by the scheduled date, there are several possible alternatives. One alternative would be to proceed with the Study using manual methods of analysis. Under most circumstances, this is not desirable because of the large amount of valuable chemist time and energies that would be consumed in accomplishment of the work. The other alternative would require postponing the starting date, which would require considerable adjustment of planning at all levels within the Bureau of Drugs and to a lesser extent in the district offices. The Center’s work plans would be most seriously affected. The failure to start the analytical phase of a Study within some reasonably close time to the target date can cause a serious depletion of available work, resulting in a less than effective utilization of the Center’s resources. Experience has shown that for peak output, the number of samples awaiting analysis must be sufficiently large to have a steady flow of sample input.
The research director’s checklist is a part of the Center’s internal Quality Assurance Program, which establishes standards and requirements comparable to those expected of quality control laboratories in the pharmaceutical industry. Every effort is made to assure that the methods developed and used at the Center are as accurate and precise as scientifically possible.
The chemist assigned to the development work for a Study, is expected on a weekly basis, to review his own progress, complete the checklist and give a verbal report to the research director. The research director reviews the progress of the work. Problems are encountered in
An application of PERT to R & D scheduling 123
Exhibit I
Drug
Study
Projected activation date
Date
Team Leader
Action
Standards: Supply adequate
Purity known
Responsible
person Assigned Target Completed
Commercial samples: Requested
Received
Quality control samples prepared
Literature search
NCDA method: Selected
Linearity and carryover tests
RSD (Research Standard Deviation)
WSD (Working Standard Deviation)
Trials on commercial spls
Validation on authentic
Prepare quality control charts
Determine standard stability
Prepare standard control chart
Official method:
RSD (Research Standard Deviation)
WSD (Working Standard Deviation)
Trials on commercial spls
Validation on authentic
Preparation of reports: Methodology
Publication
Research report
124 N. K. KWAK and L. JONES
the various phases of the method development process, and occasionally the entire method development must be modi~ed or restarted.
From the standpoint of planning, the checklist aids the chemist in viewing the logical
sequence of the total project, and enabling him to develop an overall research schedule with tentative time estimates for completing each component.
F{)R~ULATlON OF THE PERT NETWORK
By its nature, development of chemical analysis procedures cannot be set down into rigid time sequences. Much of the work is highly theoretical, and the chemical processes that must be automated often lead into seemingly insurmountable problems. The example presented in this paper uses time estimates representing the ~omposited opinions of the director of research and a senior research chemist. The time estimates are based on the following assumptions:
(1) The time estimates given are representative of a Study of average complexity. (2) The time estimates are for a Study consisting of four or six drug products. (This is the
normal number). (3) All of the drug products are similar in chemical nature. This would make the analytical
method. with minor modifications, amenable to all of the products covered under a Study. (4) The time estimates are in days and they represent (expected) elapsed time. Before the construction of the PERT network. the logic of the research guideline was
charted to determine if there was a detectable fault. Figure 1 represents the logic flow of the checklist in its present form as shown in Exhibit I. An analysis of Exhibit i and Fig. I shows that steps 13 and 14 of the logic chart do not have a listed preceding activity showing the assembly of the automated chemical system to carry out the carryover and linearity tests.
Discussion with the research director revealed that construction of the automated chemical system, preparation of reagents, checking of the system for proper flow characteristics. and check for spectrophotometric accuracy should precede the tests for linearity and carryover. The failure of a system to meet these tests would most likely be due to problems dealing with the liquid flow characteristics of the system. Further analysis of the logic chart shows that a similar problem exists in steps 16 and 17. Again. the failure of an automated system to meet the requirements for Research Standard Deviation (RSD) or Working Standard Deviation (WSD) is related to the construction of the automated system.
Step 20 of the logic chart shows that validation work was to be done on authentic samples but at no time in the operation had their preparation been designated. Authentic samples are mixtures of the drug material and a common material like lactose sugar, blended very finely to make a uniform mixture. Often the step becomes time consuming and is therefore added to the
list of activities. Table 1 is a revised checklist of Exhibit 1 and Fig. 2 is the revised logic chart showing the
items that were previously omitted from the activity list. They include the two additional activities that were not previously shown. The three time estimates for each activity are the standard designation used for PERT: optimistic time (a), most likely time (m). and pessimistic time lb). The formula used to compute 1, (expected elapsed time) is based on the beta
distribution. It is given as
11 i” 4trl + h t, = __--
6 .
Because there is the degree of uncertainty associated with the expected time for each activity. the variance is calculated by
(T’ = ((h - u)/6)‘.
The PERT network shown in Fig. 3 was constructed on the basis of information presented in Table 1. The analysis is further elaborated upon in Table 2.
The preceding computation shows that the longest path requires a total of 69.6 days of elapsed time, The final calculation, and the one that has the most significance from the standpoint of control. is the determination of the probability of meeting the project completion
An application of PERT to R & D scheduling 125
I
r
PREP
ARE
AUTH
ENTI
C
(I>
SAM
PLES
M
REVI
EW
REm
AT
TEST
PR
OCE
DURE
MET
HOO
S PL
AN
DETE
RMIN
E O
FFIC
IAL o--
M
ETHO
D RS
D
25
Fig.
1.
R
e\lte
d lo
gic
flow
An application of PERT to R & D scheduling 127
128 N. K. KWAK and L. JONES
Table I. Time estimates and variances of activities
Events Time estimates in days
I.
2. 3.
4.
5 _.
6.
I.
8.
9.
IO.
II.
I?.
13.
14.
15.
16.
17.
Review & assignment
Standards: supply
Purity known
Commercial samples: requested
received
Quality control samples prepared
Authentics samples prepared
Literature search
NCDA method: selected
Automated system assembled &
checked
Linearity and carryover tests
Research standard deviation
Working standard deviation
Trials on commercial samples
Validation samples
Prepare quality control charts
Determine standard stability
Prepare standard control chart
18. Official method: research standard
deviation
19. Official method: working standard
deviation
20. Trials on commercial samples
21. Validation samples
22. Preparation of reports: methodology
23. Publication
24. Research report
(1
-
IO
I -
5
0.25
0.5
I
0.5
I
2
0.5
10.0
2
I
0.2
10.0
0.2
0.5
5
2
I
3
300
20
tt1 tJ f‘, o- - 21
4
-
90 IO
30.7
4.5
-
177.X
2.3 -
IO
0.5
I
4
I.0
2
-
20
3.0
3
I5
5.0
4
-
10.8
0.9
I.?
5.3
I.6 31 _._
-
6.3
0.2
0.2
5.4
0.6
0.3
5 20 7.0 9.0
I .o 7.0 I.0 0.06
I? I5 12.2 0.7
4 6 4.0 0.4
2 3 2.0 0. I
0.5 I.0 0.5 0.02
I4 21 14.5 3.4
0.5 I.0 0.5 0.02
1.0 2 I.1 0.06
I? IS I I.!
4 6 4.0
2 3 2.0
5 IO 5.5
360 420 360
30 40 30
‘8
0.4
0.1
I.4
400
II.1
in the number of days indicated. Since it focuses on the completion of the project as a whole. the probability is calculated for the final event in the PERT network.
Since the value of t, is based on the beta distribution, the computation of the probability of completion of projects on a specified date requires the Z score:
Ts - TE ’ = V/c%* for c.p.)
where (Ts - TE) is the final event in the network and Cm2 is the sum of all the variances in the critical path (c.p.) of the PERT network. The required probability is found by making reference to the Z table (normal distribution).
It is of value to mention at this point why PERT instead of CPM was chosen, since the network had already been established and future R & D would follow essentially the same development path. The primary difference between the techniques is that CPM requires fewer computations and is suited for projects consisting of activities of well known duration. Whereas PERT is applicable to activities with time duration that are random variables, such as the R & D areas, where activities are often being done for the first time. Understandably, PERT is best for predicting before a project is begun.
IMPLEMENTATION
Prior to the preceding analysis, PERT had not been utilized by the Center as a tool. In January 196, the Center decided to implement PERT as a part of an overall management system. The decision was based in part on the analysis and model presented above. It was felt
An application of PERT to R & D scheduling
Table 2. Method development sequence PERT computation
129
Events Earliest Latest
z expected allowable
2 8
8 date date
d z t, u2 TE T,. TL - TE E :: p. 2
2
2
4
7
9
10
II
12
13
14
3
16
3
18
19
20
I5
21
4
5
6
8
9
IO
II
I2
13
14
I5
16
I7
I8
19
20
21
22
I5
Req. Standards
Purity Determination
Rec. Comm. Samples
Prep. Qual. Control
Auth. Samples Prep.
Liter. Search
NCDA Method Selected
Automated System Prep.
Linearity & Carryover
NCDA Method: RSD
NCDA Method: WSD
Trial on Comm. Sample
Valid on Auth. Sample
Prepare Qual. Charts
Determine Std. Stab.
Prep. Std. Control Ch.
Off. Method: RSD
Off. Method: WSD
Off. Method: Comm.
Sample
Valid. on Auth.
Sample
Reports: Methodology
Prepare Qual. Charts
30.7 177.8
4.5 2.3
10.8 6.3
0.9 0.2
1.3 0.2
5.3 3.4
I.6 0.6
2.2 0.3
7.0 9.0
I.0 0.06
12.2 0.7
4.0 0.4
2.0 0.1
0.5 0.2
14.5 3.4
0.5 0.02
I.1 0.06
II.3 2.8
4.0 0.4
2.0
5.5
0.5
0.1
I.4
0.2
30.7 30.7
35.2 35.2
10.8 60.7
II.7 61.6
36.5 63.6
5.3 29. I
6.9 30.7
37.4 37.4
44.4 44.4
45.4 45.4
57.6 57.6
61.6 61.6
63.6 63.6
64.1 64.1
49.7 69. I
50.2 69.6
36.3 64.3
47.6 57.6
51.6 61.6
53.6 63.6
69.6 69.6
64.1 64.1
0
0
49.9
49.9
27.1
23.8
23.8
0
0
0
0
0
0
0
19.4
19.4
10.0
10.0
10.0
10.0
0
0
Critical Path: l-2-3-9-lO-ll-l2-13-1615-22
that in order for the PERT system to be effectively implemented, it would require the support of all levels of management. The director of the Center accepted the idea and immediately saw the potential for broader-ranging application to other ideas.
The implementation went through the following stages: (I) Development of a data-input form, a computer program and format for the information.
Although a computer was utilized by the Center, it is certainly not a necessary requirement for utilizing PERT for small, short-term projects.
(2) Training of personnel at all levels on the purpose and objectives of a PERT system. Particular emphasis was placed on the need for developing more accurate work plans to avoid the chronic problems associated with improper work loading.
(3) A small scale-pilot application involving a trial and evaluation of one project over a period of six weeks to work out implementation snags.
(4) A full scale-pilot application involving a number of studies. The information from this phase was used to assist in the work planning process and assignment of personnel.
The implementation was begun on a pilot basis by monitoring the activities of a soon to be scheduled Study. The director, the immediate supervisor, and the chemist in charge of the project were briefed on the objectives of PERT and the advantages of the tool in the planning and managing process. The orientation was a needed first-step so that all who were involved would be cognizant of the pilot project. The mechanisms of planning using PERT were explained initially using very simple projects and the analogies of planning very simple projects were extended to the larger, more complicated R & D for a Study.
The activities in the project were listed individually and interdependence of each discussed. The network (Fig. 3) was used to show the geometric representation of the entire project and smaller interrelated sub-projects comprising the full model.
130 N. K. KWAK and 1,. JONES
The small scale-pilot was evaluated as being very successful and many of the suggestions and feedback obtained from the “pilot” chemist were incorporated into the data-input form and the overall control procedures for keypunching of the time estimates and computer processing of the data.
The next phase involved an orientation seminar for the entire Center staff. The funda- mentsls of PERT were explained, and again the emphasis was placed on its potential as a planning and control tool to better meet the needs of the Center’s modern. high-production laboratory operations. The full scale pilot was equally as successful as the small scale pilot and the decision was made to proceed with full implementation.
c’ONCLUSIONS
The implementation of PERT as a planning and control procedure has shown to date to have many tangible benefits. For examples:
(1) From the standpoint of the chemist, the source of the input, the PERT approach to work planning provides the professional with a more comprehensive procedure for planning and organizing work. Concomitantly providing a more accurate and realistic input into the total organization’s scheduling and planning. The analytical chemist, accustomed to analyzing problems and developing solutions to them, readily absorbed the procedures of PERT.
(2) From the standpoint of the supervisor. it provides better estimates of the weekly progress of the ongoing projects. The output data from the computer program utilized by the Center lists: (i) the critical path. the second most critical path, a listing of all activities and in their required order; (ii) the scheduled and expected completion time for the entire project, for each path, and a listing of all completed activities: (iii) the variance, the earliest and latest expected dates, and the slack time for each activity. With slight changes in the input format. the supervisor is able at a glance review personnel assignments and take advantage of resource- saving intra- and inter-project personnel assignments. For example, utilizing a technician instead of a chemist to conduct certain phases of the project.
(3) From the standpoint of management. it provides a more realistic estimate of the amount of required time and the expected probability of completing a project in the scheduled time. The information of all R & D progress is easily collated for review and evaluation. From this information, appropriate decisions on work planning and personnel assignments can be made.
The overall evaluation of PERT has been very favorable and future applications are being envisioned for its use. For example. PERT is being evaluated for planning and scheduling of samples for analysis in the Drug Monitoring Branch (analytical operations) of the Center for increased efficiency of analyzing samples after they are received.
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An application of PERT to R & D scheduling 131
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