Pathik Mandal - Harvard University P. Mandal et al. take this variation into account while estimating the total workload (person-hours). Further, in order to convert the person-hours

Int. J. Industrial and Systems Engineering, Vol. 20, No. 3, 2015 281

Copyright © 2015 Inderscience Enterprises Ltd.

Estimation of manpower requirement for field research: a sample survey approach

Pathik Mandal Statistical Quality Control and Operations Research Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India Email: [email protected]

Tirthankar Dasgupta* Department of Statistics, Harvard University, 1, Oxford Street, Cambridge, MA 02128,USA Email: [email protected] *Corresponding author

S.V.S.N. Murthy United Health Group Information Services, Hitech City, Madhapur, Hyderabad-500081, India Email: [email protected]

Abstract: A marketing research organisation employed a large number of field research officers (FRO) for collection of data from the field. A questionnaire-based sample survey approach was used for estimating the optimal number of FROs required for a given workload. The important design inputs for the main country-wide sample survey were obtained through a pilot survey. The data obtained from the main survey were used to obtain accurate estimates of the three components of total audit time: 1) actual audit time; 2) travel time; 3) extra time. These estimates along with the estimate of optimum workload were then used to determine the total number of FROs required. Regression models were also developed for predicting the number of FROs required for a given future workload.

Keywords: manpower modelling; audit process; questionnaire method; stratified sampling under measurement error; post stratification; regression models.

Reference to this paper should be made as follows: Mandal, P., Dasgupta, T. and Murthy, S.V.S.N. (2015) ‘Estimation of manpower requirement for field research: a sample survey approach’, Int. J. Industrial and Systems Engineering, Vol. 20, No. 3, pp.281–305.

Biographical notes: Pathik Mandal is a Technical Officer at SQC and OR Unit of Indian Statistical Institute, Kolkata. He has been engaged in consulting, teaching, training and research in the area of quality management for the last 26 years. His current research interest addresses issues related to six sigma, process control and robust design. He obtained his PhD in Metallurgical

282 P. Mandal et al.

Engineering from Indian Institute of Technology, Kharagpur. He also holds a PG Diploma in Statistical Quality Control and Operations Research from Indian Statistical Institute.

Tirthankar Dasgupta is an Associate Professor of Statistics at Harvard University. He obtained his PhD in Industrial Engineering from Georgia Institute of Technology, Atlanta. His research interests include design of experiments (DOE), causal inference, statistical and engineering process control, applications of statistics in nanotechnology, quality engineering and quality management. He also has eight years of consulting experience in Indian industries and has dual Master’s degrees in Applied Statistics and Quality, Reliability and Operations Research from the Indian Statistical Institute.

S.V.S.N. Murthy is currently working with United Health Group Information Services (UHGIS), India as a Quality Leader cum Master Black Belt. Prior to joining UHGIS, he was associated with organisations like Indian Statistical Institute (ISI), Intel Technologies, Satyam Computer Services and Computer Sciences Corporation (CSC) and has worked in various roles like Quality Consultant, Statistical Expert and Master Black Belt. He holds an MTech in Quality, Reliability and Operations Research from Indian Statistical Institute.

1 Introduction

Manpower planning may be defined as the process to ensure that the right people are at the right place at the right time in sufficient numbers to efficiently accomplish anticipated tasks (Vetter, 1967). Manpower planning, being a forward looking activity, usually involves some sort of forecasting of future requirement. Many statistical and other quantitative techniques like time series analysis, stochastic flow models (Alper et al., 1967), econometric models and expert opinion (Delphi technique) are now available in the literature for obtaining the forecasts. Bezdek (1977) classifies these methods into seven categories. However, all studies on manpower planning may not involve forecasting, although an estimate may be needed to satisfy a given future requirement. For example, Dreesch et al. (2005) propose a methodology for estimating manpower requirement to meet the Millennium Development Goals of the United Nations. See Piskor (1976) for a bibliographic survey of all types of studies on manpower planning.

In this case study, we were concerned with manpower planning at the operational level, i.e., our objective was to estimate the number of personnel required to carry out a set of well defined activities. The activities were either ongoing or might have to be performed in future in case of any modification of requirements.

A marketing research organisation (MRO) in India employed a huge field force to ensure on-time delivery of quality data required for all the tracking and customised studies that it undertook. Each of these studies, called an audit, involved gathering information on sales volume, stock levels, effectiveness of promotional efforts and other associated aspects of various brands within a product category from a selected sample of retail outlets (to be called dealers). The company classified these audits in accordance with the type of product [Fast Moving Consumer Goods (FMCG), food products, cigarettes, lighting products, drugs etc.]. We shall refer to these various types of audits as A1, A2, A3 etc. The total number of dealers audited within each audit was called the

Estimation of manpower requirement for field research 283

panel size of the audit and the persons, who conducted the audits, were called Field Research Officers (FRO). Each FRO was responsible for auditing a fixed number of dealers every month/fortnight following the process as shown in Figure 1.

Figure 1 The audit process

Filled-up schedule ready for dispatch

Return home/office

Prepare daily report

Scrutinize filled-up schedule

Audit completed?

1

Prepare day’s audit plan

Reach dealer

Exchange pleasantries

Perform audit

Monthly/fortnightly audit plan

Audit another dealer?

1

Yes

No

Yes

No

With the gradual increase in panel sizes for the existing audits, introduction of new audits and increasing demands from the subscribers to track special offers, the field workload had been continuously on the rise. This had necessitated fresh recruitment of FROs almost on a continuous basis. As a result, the management felt the need for a more scientific (data-based) approach for estimating the manpower requirement for field research. The approach, they felt, should provide with a mechanism of estimating the manpower requirement for not only the current but also for the future workload. Thus, this study was taken up with the following objectives:

1 estimating the number of FROs required for the current workload and

2 predicting the additional manpower requirement in case of either panel expansion or introduction of new audits.

An interview-based sample survey approach was used to achieve the above two goals. The rationale behind selecting such an approach is discussed in Section 2.2. However, it appears that, in general, such an approach is best suited for estimating manpower requirement for any service process having a large service network (say country-wide) and a non-standardised work environment. In such cases, it is to be expected that the time needed to carry out a given activity will vary widely (as in this study). It is important to


take this variation into account while estimating the total workload (person-hours). Further, in order to convert the person-hours to the number of persons, one should obtain an estimate of the optimum workload per person as objectively as possible. In this study, the optimal daily working hours was estimated through a satisfaction survey instead of using a management specified value.

The rest of the article is organised as follows. The next section gives the background information and a detailed description of the approach adopted for the study. This is followed by a detailed description of the basic statistical model used for manpower estimation (Section 3). The details of the pilot survey, i.e., the method of data collection, the stratification variables that were identified and determination of the sample sizes are discussed in Section 4 under three subsections. The details of the main survey are given in Section 5. The results of the two methods used for estimating the manpower requirement are presented in this section. The Section 6 is devoted to the method proposed for estimation of manpower requirement for a new audit. The article concludes with a summary of the benefits of the study and a few concluding remarks.

2 Background information and overall approach

2.1 The existing ‘norm’ and its limitations

The standard times or norms are widely used in service organisations for evaluating staffing needs. For example, a Government health and family welfare department specifies that a 100-bed hospital should have at least 21 doctors, 15 paramedical staff and 25 nurses (WBHSDP, 1997). There are many ways in which such norms may be established (see Section 2.2). Unfortunately, the MRO did not follow any systematic procedure to establish the norms, which they had been using for estimation of their manpower requirement. It used its rich experience to arrive at the norms for Ni, the number of audits of type i that can be performed by an FRO in a day. Thus, assuming 24 working days per month, the total number of FROs required is given by

( )(1/ 24) ,i iP N∑

where Pi denotes the panel size for the ith audit. However, the above method, although straightforward, had two major drawbacks.

First, the accuracy of the estimates obtained was poor. It was noted that except for the audit A3 (for which Ni = 0.7), the Ni values for all the other audits were integers (between 1 and 8). To illustrate the effect of such crude norms, suppose the true value of Ni for the audit A1 is 2.33, against the specified norm of 2. Since the panel size for this audit was 8,527, the number of FROs required for Ni = 2.33, 2.3 and 2.0 would be 152, 154 and 178 respectively. This clearly shows that the Ni values must be accurate at least to the first decimal place.

Another drawback of the standard norm was that it might, at times, lead to a wrong interpretation. The Ni values should actually be interpreted as the average time taken to audit all the dealers. However, the time taken to audit a particular dealer might be vastly different from the norm. For example, it could vary from three days (for a large dealer) to 30 minutes (for a small dealer). This also indicated that the Ni values, particularly for the


audits A1–A3, should be estimated with proper stratification to keep the sampling variance under control (see Section 4.2).

2.2 Approach

An objective determination of staffing needs usually involves some form of activity measurement using any one or a combination of the following methods.

1 Factual data-based measurement, which includes time and motion study (Niebel and Freivalds, 1999), activity sampling (BS 3138, 1992) and self monitoring using a log or a diary.

2 Opinion-based measurement, which includes expert opinion (see Ozcan and Hornby, 1999 for a case study); interviewing relevant staff using a questionnaire or the questionnaire may be filled-up by the relevant staff themselves.

It is obvious that the time and motion study is expected to yield the most accurate results. However, manpower planning should not be viewed as an isolated technical exercise. The company policies, the service needs and the employee needs should also be taken into account in any manpower planning exercise. The audit process that we wanted to measure also did not exist in isolation. It had its unique features such as the following:

1 The data collection process was very tedious. In many cases, the FROs had to do a great deal of housekeeping and physical verification of the stocks.

2 The data quality was of paramount importance since most data quality defects were likely to pass through the data scrutiny stage.

3 Timely delivery of the reports was an important business goal.

Considering the above, it was decided to involve the FROs in the measurement process and hence the interview and the mailed questionnaire methods as mentioned above were adopted for the purpose of data collection. So far as data quality is concerned, since most of the FROs were experienced and all of them had to make diary noting of each day’s work, the data sought from them were expected to be sufficiently accurate. Moreover, the questionnaire was designed carefully to collect additional information about each dealer so that the data provided by the FROs could be scrutinised for their accuracy (see Sections 4.1 and 5.3).

Broadly speaking, the approach adopted for the study was to develop a statistical model for estimation of the total time required for field activities and to estimate the parameters of the model through a country-wide sample survey. The project was conducted in two phases as follows.

1 Phase I: In this phase a pilot survey was conducted covering all the dealers located in a particular city. The objectives of the pilot study were a to fine-tune the questionnaire and the theoretical model that we had in mind (see

Section 3) b to design the sampling scheme for the main survey c to identify the factors having significant impact on various components of audit

time.


2 Phase II: This was a country-wide sample survey and the primary objective was to estimate the parameters of the statistical model. In addition, a satisfaction survey was conducted in parallel for estimating the optimum workload. The questionnaire used also had the provisions for feedbacks by the FROs regarding the problems they faced and the scope for improvement of the audit process. However, the findings from these feedbacks are not reported here.

To summarise, we adopted not only a data-based but also a process and people oriented approach for the study. Thus, the approach adopted may be called a quality approach for manpower planning.

3 The statistical model

Let Xi denote the overall time taken to conduct an audit of type i (= 1, 2,…,k). It is apparent from the flow chart of the audit process (Figure 1) that the total time Xi can be expressed as

,i i i iX U V W= + + (1)

where Ui is the time taken to carry out the regular activities, Vi is the travel time and Wi is the time required for additional activities related to the audit.

Let , ,i i iX U Vμ μ μ and iWμ denote the population means of Xi, Ui, Vi and Wi respectively. Also let , ,i i iX U Vσ σ σ and iWσ denote their respective standard deviations. Thus, the total time required in a month for conducting all the audits is given by

1

,i

k

i i Xi

T N f μ=

=∑ (2)

where Ni is the panel size for the ith audit, fi is the monthly frequency of the ith audit and .i i i iX U V Wμ μ μ μ= + +

The model parameters to be estimated are thus ,i iU Vμ μ and .iWμ If ,i iu v and iw denotes the estimators of ,i iU Vμ μ and iWμ respectively, then the total time can be estimated as

1

, .k

i i i i i i ii

t N f x x u v w=

= = + +∑ (3)

The variance of the estimator t is given by

( )2 2

1

( ) .k

ii ii

V t N f V x=

=∑ (4)

The details of the methods used for estimation of iXμ and the variance of its estimate, i.e., ( )iV x are discussed in Section 5.4.


4 The pilot survey

4.1 Data collection

It has already been mentioned that all the dealers (retail outlets) located in a particular city were considered for the pilot survey. The eight FROs, who were responsible for auditing these dealers, were interviewed by a member of the project team over a period of three days. The following information was sought from each FRO regarding every dealer he audited:

a Time taken for actual audit (minimum and maximum).

b Travel time (minimum and maximum) from the starting point (residence/office/previous dealer) to the dealer.

c Complexities involved in auditing that dealer in terms of the size of the dealer, travelling hazards, availability and organisation of stocks and other documents. The FROs were asked to rate each dealer on a 1–6 scale for each of the above four dimensions of complexity. The guidelines for rating were also prepared to achieve consistent ratings by the FROs (see Appendix 1).

In addition to the size rating as above by the FROs, the number of entries that had to be made for each dealer was also obtained separately. The main results of the pilot survey and the manner in which these results were used to develop the sampling scheme for the main survey are described in the next three sections.

Figure 2 Distribution of total audit time for audit A1

Total audit time (minutes)

Freq

uenc

y

4754253753252752251751257525

50

40

30

20

10

0


4.2 Distribution of audit time

The distribution of total audit time for the audit A1 is shown in Figure 2. The presence of multiple peaks in the distribution clearly indicated the need for stratification of the dealer universe. Similar results were obtained for the audits A2 and A3. However, for the other audits the distributions were found to be nearly normal with the exception of the audits A8 and A11, for which the distributions were smooth but positively skewed (see Table 1). Accordingly, no stratification was carried out for these audits.

4.3 The stratification variables

The dealers’ universe for the audit A1 was stratified on the basis of the number of entries, i.e. the number of fields in the data collection schedule, which the FROs were required to fill up for a given dealer. The audit time was found to be strongly dependent on this variable. The four strata were formed by classifying the number of entries as follows: ≤ 70, 71–150, 151–500 and > 500. The distributions of audit time in each of these stratums were found to be more or less smooth and normal.

The audits A2 and A3 also called for stratification. However, due to the small panel size of these audits, it was decided to adopt poststratification for these two audits. Poststratification is a technique where the sampled units are cross classified according to the levels of the stratification variables. Many researchers have suggested that poststratification has little to offer over simple random sampling so far as efficiency of the estimates is concerned [e.g., Hartley, 1962; Kish, (1965), p.91]. However, following Holt and Smith (1979), it was decided to adopt this technique with the expectation that the sampling variance of the estimates will be reduced significantly.

Apart from the number of entries, the dealers were also stratified in terms of their geographical location (east, west, north and south), since it was felt that the characteristics of the dealers could vary widely from one zone to the other.

4.4 The sampling scheme for the main survey

The sampling scheme for the phase II study was determined as follows:

4.4.1 Step 1 (determination of the total sample size for different audits)

Let ρ be the coefficient of variation of the study variable y. Further, let l denote the loss per 1% of the relative standard error (e) of the estimator of ( )Y E y= and C1 be the cost of sampling and measurement per unit. Then, for n (sample size) << N (population size) and for simple random sampling without replacement (SRSWOR), the optimal value of n is given by [Gupta and Kabe, (2011), pp.12–14]

2/3

1.

2lρnC

⎡ ⎤= ⎢ ⎥⎣ ⎦

(5)

However, in practice, it may be much easier to specify the approximate optimal relative standard error e than to specify the value of l. In such cases, the optimal sample size may be obtained from [Gupta and Kabe, (2011), pp.12–14]


2, ( / ) .1

Nnn n ρ eN n

′′= =

′+ − (6)

Of course, the sample size obtained as above must satisfy the budgetary constraint, i.e.

( )0 1,n C C C′≤ − (7)

where C’ is the total budget sanctioned for the survey and C0 is the overhead cost. So far as this study is concerned, it was not possible to specify the optimal values of e

for all the audits. Accordingly, the sample sizes were obtained as follows. The relative standard error (e%) for an assumed sample size (n) was computed from

( )% 100, ,

1ixi i

i i ii i i

sN ne ρ ρn N x

−= × × =

− (8)

where Ni is the panel size of the ith audit and ix is the average audit time defined in (3). The estimates of coefficient of variation ρi, as obtained from the pilot study were used for computing the value of ei%. Then, by varying n, an attempt was made to keep ei ≤ 5% for all i, and to allocate relatively more samples to the audits having irregular and skewed distribution of audit time. However, owing to the feasibility constraints, some accuracy had to be sacrificed for the audits A5 and A11, both of which had very high coefficient of variation (see Table 1). The sample sizes for the audits not covered in the pilot study (see Table 1) were selected purely based on practical judgement.

4.4.2 Step 2 (determination of the sample size for each stratum within an audit)

The total sample size determined as above for each audit could be distributed either equally or proportionately or optimally over the strata. In general, the equal distribution provides some practical advantages and can be used if the stratum size does not vary greatly (Stevens, 1952). In our case, the equal distribution was neither necessary nor found suitable. Further, we did not seek an optimal allocation [Cochran, (1977), pp.96–99; Rao, 1977] primarily because the estimates of within strata variances were not considered very accurate. Note that the pilot study was conducted only within a city, whereas there could be significant differences among the geographical locations. Also, the pilot study was based solely on interview, whereas both mailed questionnaire and interview methods were used in the main survey (see Section 5.2). Moreover, this was a multivariate study involving three study variables U, V, and W, where U and W were found to be correlated. There are methods available for optimal allocation in a multivariate set up (Bethel, 1989; Khan and Ahsan, 2003). However, such methods were not considered since these require much more accurate inputs than the univariate case. Accordingly, the method of proportional allocation was used for determining the sample size for each stratum.

To summarise, the sampling design obtained for the phase II study cannot be claimed as optimal. However, efforts were made to design the sampling scheme as objectively as possible. But, as is typical of any large-scale non-standard sample survey, considerable practical judgements had to be used to arrive at the final design (see Table 1).


Table 1 Sampling scheme for the country-wide sample survey

Audit code

Panel size (N)

CV* (%)

Sample size (n) RSE* (%) Stratification/remark

Total N E W S

A1 8,527 27.6 400 110 82 93 115 1.3 Yes (based on # of entries) A2 3,452 40.6 100 25 29 20 26 4.0 Post stratification A3 1,570 15.9 100 27 22 24 27 1.5 Post stratification A4 381 1.9 40 11 12 6 11 0.3 No (small universe) A5 2,498 88.0 200 55 30 59 56 6.0 No (almost normal distbn.) A6 3,422 13.6 100 34 18 23 25 1.3 No (normal distribution) A7 6,501 18.1 100 28 20 25 27 1.8 No (almost normal distbn.) A8 3,086 18.2 100 22 13 28 37 1.8 No (smooth skewed distbn.) A9 2,566 34.2 100 36 16 22 26 3.4 No (almost normal distbn.) A10 674 11.9 40 10 10 10 10 1.8 No (almost normal distbn.) A11 6,348 131.5 400 97 84 105 114 7.4 No (smooth skewed distbn.) A12 535 19.5 40 8 4 9 19 3.0 No (normal distribution) A13 311 15.1 40 10 8 10 12 2.2 No (normal distribution) A14 1,046 - 100 12 10 37 41 - Not covered in pilot study A15 906 - 60 15 5 14 26 - Not covered in pilot study A16 1,016 - 100 30 22 24 24 - Not covered in pilot study

Total - 2,020 530 385 509 596 - -

Notes: *CV = coefficient of variation, RSE = relative standard error, evaluated using equation (8).

5 The country-wide survey

5.1 Sampling, datasheet and questionnaire

A complete zone-wise listing of all the dealer codes for all the audits was provided by the MRO. The sample dealers were selected from each stratum following the method of simple random sampling. Then, for each of the sampled dealer, the zone, state, field headquarter, town and the name of the concerned FRO were identified. The datasheets were prepared FRO-wise. Each datasheet consisted of the sampled dealers which were usually audited by the FRO. The datasheet thus obtained was almost the same as that used in the pilot study. A sample datasheet is shown in Appendix 2.

Along with each datasheet, a satisfaction survey questionnaire was also prepared. The questionnaire used is shown in Appendix 3.

5.2 Data collection

The total number of dealers to be covered under the study was 2,020. These 2,020 dealers were audited by 548 FROs. Roughly, 50% of these FROs were interviewed by the project team. The team had to visit 17 field offices spread throughout the country for this purpose. The datasheets were mailed to the remaining FROs. It is seen from Table 2 that


the coverage error of the survey was low (11%). Moreover, the non-response rate was more or less uniformly distributed over various audits and over various strata within an audit. Table 2 Expected vis-à-vis achieved sample size

FRO/dealer Expected Achieved

Direct interview Mailed datasheet Total No. of FROs 548 266 227 493 (90%) No. of dealers 2,020 1002 787 1789 (89%)

5.3 Scrutiny of data

• Scrutiny of audit time (Ui): a plot of the observed audit times vs. the number of entries revealed a strong positive relationship for almost all the audits. The outliers detected from these scatter plots were scrutinised for their complexities with respect to hazards, availability and organisation (see Appendix 2). If the complexity scores could explain an outlier satisfactorily then it was retained, or else deleted from the dataset. The above methodology is schematically explained in Figure 3.

• Scrutiny of travel time (Vi) and extra time (Wi): the outliers detected from the plot of frequency distributions of these two variables were subjected to further scrutiny. The travelling time outliers which could not be explained satisfactorily by the travelling hazard ratings were removed from the dataset. Similarly, the highly unusual observations with respect to extra time were also removed if these could not be explained satisfactorily by the ratings of organisational complexity.

Figure 3 Detection of outliers with respect to actual audit time (Ui)

Number of entries

Act

ual a

udit

tim

e (U

)

260240220200180160140120100

450

400

350

300

250

200

Comple

xity

scores

?

Comple

xity

score

s?


5.4 Estimation of iXμ and the variance of the estimate

Let ,ij iju v and ijw denote respectively the sample mean of actual audit time, travel time and extra time for the ith audit in the jth stratum. Also we have i i i iX U V Wμ μ μ μ= + + (see Section 3). Thus, an unbiased estimator of iXμ is given by

,i i i ix u v w= + + (9a)

( ) ( ) ( ), , , ,i ij ij i i ij ij i i ij ij i i ijj j j j

u N u N v N v N w N w N N N= = = =∑ ∑ ∑ ∑ (9b)

where Nij denotes the panel size for the ith audit and the jth stratum. However, it may be noted that we had an incomplete sample. The data on about 18% of the dealers as planned originally could not be collected (see Table 2). Although, many methods are now available for tackling the problem of non-response bias (Groves, 2006; Blom, 2009; Armstrong and Overton, 1977), it was decided to ignore the non-response bias, if any. This is because, the non-response was low and the same was uniformly distributed over all the strata. It may also be noted here that the non-response error does not always lead to non-response bias (Groves, 2006).

The variance of ix defined in (9) is given by

( ) ( ) ( ) ( ) ( )2 , ,i i i i i iVar x Var u Var v Var w Cov u w= + + + (10)

where the covariance between U and V and between V and W are ignored since the travel time V is not expected to be correlated with either U or W. The variance of ,iu following Cochran (1977, p 92), is given by

( ) ( )2

2

1 , ,iji ij ij ij i ij

iji j j

SVar u N N n N N

N n= − =∑ ∑ (11)

where nij is the number of sampled dealers and 2ijS is the variance of actual audit time for

the jth stratum of the ith audit. However, since we have noted both the minimum and the maximum audit time for each dealer (see Appendix 2) to capture the within dealer variation, the variance of iu is given by (Chandok, 1988)

( ) ( )2

2 21 02

1 ,ij iji ij ij ij ij

ij iji j

NNVar u N n S S

N n n⎧ ⎫⎪ ⎪= − +⎨ ⎬⎪ ⎪⎩ ⎭

∑ (12)

where 20ijS and 2

1ijS are respectively the within and between dealer variation for the jth stratum of the ith audit. The estimates of the within and between dealer variances were obtained as follows. Let

( )min max 2ijk ijk ijku u u′ = +

and max min .ijk ijk ijkR u u= −


Now, assuming that uijk follows normal distribution with standard deviation σ, then from the standard literature on process control charts [Montgomery, (2001), p.183], we have E(R/σ) = d2, where R is the range of n observations on uijk and the values of d2 may be obtained from standard tables [e.g., Montgomery (2001, Appendix VI)]. Thus, we have

( )222 20 , , 3.931 25,ij ij ijk ijij

k

s R d R R n d for n= = = =∑ (13a)

( ) ( ) ( ) ( )22 21 0var 2, var 1 .ijk ijk ijk ij ijij ij

k

s u s u u u n′ ′ ′= − = − −∑ (13b)

It was felt that even though the FROs were highly experienced, it will be difficult for them to recall events which were too old (about two years or more), since the events were of routine nature. Accordingly, the value of n in (13a) above was taken as 25.

The variances of iv and iw were estimated in a similar fashion. However, note that the within dealer variance 2

0ijs does not exist for .iw It may also be noted here that although the audits A2 and A3 were subjected to poststratification (see Table 1), the variances of ,i iu v and iw were estimated using (11). This means, we used the conditional variance ( | ),i ijV u n as advocated by Holt and Smith (1979) instead of the unconditional variance ( ),iV u as is usually recommended in standard text books for poststratified data [e.g., Cochran, (1977), p.135].

So far as the estimation of the covariance term is concerned, an unbiased estimate of Cov(ui, wi) may be obtained by estimating the within and between strata covariance separately (see Ghosh and Vogt, 2004). However, since the correlation between u and w within a stratum was found to be insignificant in most cases, it was decided to use

( , )ij ijr u w as an estimate of ( , ).i ir u w Thus, the covariance between iu and iw was estimated as

( ) ( ) ( ) ( ), , .i i i i i is u w r u w s u s w=

The estimates , , ,i i i iu v w x and their estimated variances obtained as above are summarised in Appendix 4.

5.5 Determination of optimum workload

The data gathered through the satisfaction questionnaire (Appendix 3) were used for estimating the optimum workload, i.e., the workload corresponding to the maximum satisfaction. The scatter plot of satisfaction vs. workload was obtained by first grouping the hypothetical workload into seven mutually exclusive classes and then plotting the average satisfaction score (S) of each class against the average workload (T) of that class (Figure 4).

It is seen from Figure 4 that the satisfaction function is quadratic, which (using the ordinary least square method) was estimated as

23.08 1.24 0.093 .S T T= + − (14)


Figure 4 Scatter plot of satisfaction vs. working time

Average working hours

Ave

rage

sat

isfa

ctio

n sc

ore

111098765432

8.0

7.2

6.4

5.6

4.8

Figure 5 Distribution of workload among the FROs

Working hours

Freq

uenc

y

141312111098765432

120

100

80

60

40

20

0

The optimum workload, by equating dS/dT of (14) to zero was found to be Topt = 6.5 hours. The maximum satisfaction score of 7.2 corresponding to Topt = 6.5 hours was not very encouraging. However, the most critical issue that needed immediate attention of the management was the high variation in satisfaction scores resulting from the uneven distribution of workload. It may be seen from Figure 5 that the distribution of working hours among the FROs was far from uniform. In fact, 12% of the FROs reported to have


been working for less than 5 hours, whereas 18% reported to be working for more than 8 hours. It was expected that a more uniform distribution of workload would lead to higher average satisfaction. Accordingly, it was suggested that the regression models listed in Table 4 may be used for a more uniform allocation of workload among the FROs.

5.6 Estimation of the number of FROs required (direct method)

The procedure adopted for estimation of ix and its variance has been described in detail in Section 5.4. The estimates obtained are listed in Appendix 4. Substituting these estimates in equations (3) and (4) of Section 3, the estimate of total man-minutes required for all the audits was calculated as t = 5,328,087.90 (see Table 3). The standard error of this estimate is 33,232.98 minutes (see the 7th column of Table 3). The last column of Table 3 also gives the estimates of the number of audits that can be performed daily by a FRO. Comparing these values with the existing norms, it was found that the existing norms, in general, were conservative and hence would lead to a gross overestimation of the total manpower requirement. Table 3 Estimation of total man-minutes required for performing all the audits and the

variance of the estimate

Audit code Ni fi ix ( )iVar x i i iN f x ( )2 2

i i iN f Var x # Audits/FRO/day

A1 8,527 1 166.0 5.6556 1,415,482.0 411,217,143.33 2.35 A2 3,452 1 165.2 5.8366 570,270.4 69,550,699.93 2.36 A3 1,570 1 463.2 108.2155 727,224.0 266,740,385.95 0.84 A4 381 1 245.9 87.0622 93,687.9 12,638,036.01 1.59 A5 2,498 1 71.1 1.0392 177,607.8 6,484,612.16 5.49 A6 3,422 1 90.3 7.1122 309,006.6 83,284,459.42 4.32 A7 6,501 2 43.8 0.7046 569,487.6 119,114,042.02 8.90 A8 3,086 2 63.1 0.3046 389,453.2 11,603,305.69 6.18 A9 2,566 1 78.9 6.2256 202,457.4 40,991,566.71 4.94 A10 674 1 48.9 3.6262 32,958.6 1,647,295.63 7.98 A11 6,348 1 47.2 1.2342 299,625.6 49,734,685.76 8.26 A12 535 1 46.0 3.6795 24,610.0 1,053,164.89 8.48 A13 311 1 64.8 13.2551 20,152.8 1,282,046.53 6.02 A14 1,046 1 103.6 4.2071 108,365.6 4,603,055.42 3.76 A15 906 1 44.4 1.3340 40,226.4 1,094,995.22 8.78 A16 1,016 1 342.0 22.6607 347,472.0 23,391,643.54 1.14 Total 5,328,087.9 1,104,431,138.21 -

Now, we have already noted that the optimal workload is 6.5 hours/day (see Section 5.5). The management of the company felt this to be slightly on the lower side. However, considering the tedious nature of the audit work, it was decided to use the above estimate as the basis for manpower planning. Thus, assuming the above estimate (6.5 hours) as a known value, the total man-days required was estimated as (t in minutes) / (60 × 6.5) = 13,661.76 man-days. Further, assuming 24 working days per month, the number of FROs required was obtained as 13,661.76/24 = 569. It was also decided that


10% relievers shall be provided for smooth functioning of the audit process. Thus, finally the number of FROs required was estimated as 569 + 57 = 626.

The standard error of the above estimate is (1.1 × 33232.98) / (60 × 6.5 × 24) = 3.91. Thus, assuming that the estimate follows Normal distribution, the 99% confidence interval for the total number of FROs required is 626 ± 10.

5.7 Estimation of the number of FROs required (regression method)

It has already been noted in Section 4.3 that the actual audit time was strongly dependent on the number of entries. Specifically, the linear model

,i iU E= +α β

where Ui and Ei denote respectively the audit time and number of entries of the ith audit, was found to be adequate for all the audits. Thus, by substituting iE (the average number of entries for the ith audit) in the estimated linear model, the average audit time was estimated as

.i iu E= +α β

The estimates thus obtained are summarised in Table 4 along with the estimates obtained by the direct method. Using these estimates and the previously obtained values of iv and

,iw the total number of FROs required was found to be 646, which is about 3% higher than the estimate obtained by the direct method. Table 4 Estimates of average audit time (in minutes per audit) by two methods

Audit code

Regression equation Avg. no. of entries ( )iE

Avg. audit time ( )iu estimated by

Avg. travel time ( )iv

Avg. extra time ( )iw

Avg. total audit time ( )ix

α β R2% Reg. Direct Reg. Direct

A1 11.0 0.712 52.7 206 157.7 124.09 25.62 16.32 199.60 166.03 A2 27.1 0.614 84.0 77 74.38 66.95 89.12 9.11 172.61 165.17 A3 26.1 0.758 83.5 459 374.02 407.85 27.04 28.31 429.37 463.20 A4 31.6 0.486 64.0 160 109.36 122.89 107.18 15.83 232.37 245.90 A5 - - - - - 35.41 24.71 10.98 71.10 71.10 A6 21.6 1.40 72.0 13 39.80 53.76 27.95 8.60 76.35 90.31 A7 14.3 0.444 28.1 14 20.52 22.04 15.75 5.96 42.23 43.75 A8 19.8 0.680 75.0 67 65.36 66.05 25.66 11.93 102.95 103.63 A9 26.3 0.945 16.0 10 35.75 38.42 16.84 7.83 60.42 63.09 A10 24.6 0.801 63.7 19 39.82 45.58 21.91 11.40 73.13 78.90 A11 18.7 0.755 49.8 10 26.25 26.34 15.21 7.35 48.81 48.90 A12 - - - - - 22.08 15.50 6.79 44.37 44.37 A13 - - - - - 185.70 135.42 20.88 342.00 342.00 A14 12.0 0.997 81.9 12 23.96 23.15 16.96 7.05 47.97 47.16 A15 16.6 1.89 47.6 7 29.83 14.34 26.73 4.98 61.54 46.05 A16 20.1 1.220 34.1 17 40.84 35.97 18.05 10.76 69.65 64.79


6 Prediction of manpower requirement for a new audit

Let ,new newu v and neww be the estimates of mean actual audit time, travel time and extra time respectively for a new audit. Thus, using the same model and the notations as before [see equation (3)], the estimate of total time required for conducting a new audit is given by

,new new new newt N f x=

where

.new new new newx u v w= + +

As before, it is thus necessary to estimate the three components ,new newu v and .neww The regression method similar to that used in Section 5.7 may be used for this purpose. The details of the regression models developed are discussed below. It is obvious that the proposed approach could be used only for those audits for which the average number of entries was known.

6.1 Prediction of newu and neww

The scatter plot of average audit time Ui against the average number of entries Ei for the 14 out of the 16 audits (A1–A16) is shown in Figure 6. The concept of number of entries was meaningless for the audits A5 and A16. It is evident from Figure 6 that there was a strong linear relationship between Ui and Ei. The best fit line for the data is given by

( ) ( ) ( )2log 0.631 0.688log , 90.0%, 0.1269 .i iU E R s= + = = (15)

Figure 6 Effect of number of entries on audit time

Average number of entries

Ave

rag

e au

dit

tim

e (M

inu

tes)

5004003002001000

400

300

200

100

0

A3

A1A4


Similarly, the average extra time Wi and Ei is also seen to be linearly related (Figure 7) and the relationship may be expressed as

( ) ( ) ( )2log 0.455 0.347 log , 84.7%, 0.8197 .i iW E R s= + = = (16)

The equations (15) and (16) may be used for predicting the audit time and extra time separately. However, predicting Ui and Wi separately and then adding these two predictions will lead to a large prediction error. It will be better to predict the sum of Ui and Wi using the following model

( ) ( ) ( )2log 0.793 0.638log , 90.2%, 0.1163 .i i iU W E R s+ = + = = (17)

Figure 7 Effect of number of entries on extra time

Average number of entries

Ave

rag

e ex

tra

tim

e (M

inu

tes)

5004003002001000

30

25

20

15

10

5

A3

A1

A4

6.2 Prediction of newV

It was observed that the average travel time ( )newv for a rural audit was much higher than that of an urban audit. However, within the rural and urban strata, the travel time did not vary significantly from one audit to the other. The average travel times for the urban and rural audits were found to be 21.4 minutes and 110.6 minutes respectively. Thus the predictions of travel time for a new audit were

( ) 21.4 .newV Urban mts=

and

( ) 110.6 .newV Rural mts=


6.3 Prediction of :newX an example

To illustrate the use of the above models, let the average number of entries (Ei) for a new audit as estimated from the census data is 100. Thus, using equation (17), the logarithm of the sum of average audit and extra time is obtained as (0.793 + 2 x 0.638) = 2.069. The predicted value of average audit and extra time is then given by 22.069 0.1163 /210 119.06+ = minutes. This is a slightly biased estimate. A better estimate of the sum (Ui + Wi) may be obtained as 2 2(0.09794 0.06054 )/2119.06*10 117.2558− + = minutes, where 0.09794 and 0.06054 are the standard error of the coefficients of (17). Thus, if the audit is to be conducted in urban areas only, then 117.3 21.4 138.7newX = + = minutes.

Figure 8 Zone-wise requirement of FROs

Num

ber

of F

RO

SouthWestEastNorthRMDMRMDMRMDMRMDM

200

150

100

50

0

174162

121

169177

165

122

172DM : Direct methodRM : Regression method

7 Benefits of the study and concluding remarks

This study provided

1 an objective and data-based estimate of the current field staff requirement

2 a scientific methodology for prediction of the manpower required for a new audit.

Specifically, the main conclusions and recommendations of the study were as follows:

1 The zone-wise requirement of the number of FROs was as shown in Figure 8. The metro/non-metro stratification had also been made. However, such strata-wise estimates are not reported due to the high sampling variance associated with these estimates.


2 The MRO could use the regression models and the estimates of the average travel and extra time given in Table 4 for estimating the zone-wise, town-class wise and town-wise FRO requirements with a high degree of precision after preparing a town/zone-wise list of the dealers along with the corresponding number of entries.

3 The manpower requirement for a new or an expanded audit could be determined using the methodology described in Section 6. However, such a method was applicable only for those audits for which the average number of entries could be determined at least approximately. The estimates of the number of audits/man-day provided in the last column of Table 3 might be used as guidelines in such cases.

4 The present distribution of workload among the FROs was found to be highly non-uniform (see Figure 5). The situation required urgent improvement. The regression models listed in Table 4 could serve as very useful tools for predicting the workload of the FROs and thereby achieving a more uniform distribution of workload.

5 The visits of the project team members to the field offices generated a tremendous amount of enthusiasm among the FROs. The perception of the FROs was that the management had tried to establish a communication with them through this study.

References Alper, P., Armitage, P.H. and Smith, C.S. (1967) ‘Educational models, manpower, planning and

control’, Operational Research Quarterly, Vol. 18, No. 2, pp.93–103. Armstrong, J.S. and Overton, T.S. (1977) ‘Estimating non-response bias in mail surveys’, Journal

of Marketing Research, Vol. 14, No. 3, pp.396–402. Bethel, J. (1989) ‘Sampling allocation in multivariate surveys’, Survey Methodology, Vol. 15,

No. 1, pp.47–57. Bezdek, R.H. (1977) ‘Some critical issues in manpower modelling and forecasting’, Modelling and

Simulation of Engineering Manpower Studies: Proceedings of a Conference, Assembly of Engineering, National Research Council, Washington.

Blom, A.G. (2009) Non-Response Bias Adjustment: What Can Process Data Contribute?, Report no. 2009_21, Institute for social and economic research, University of Essex, Essex [online] http://www.iser.essex.ac.uk (accessed 7 October 2011).

BS 3138 (1992) Glossary of Terms used in Management Services, British Standards Institution, London.

Chandok, P.K. (1988) ‘Stratified random sampling under measurement error’, Proceedings of the Survey Research Methods Section, pp.508–510, American Statistical Association.

Cochran, W.G. (1977) Sampling Techniques, 3rd ed., Wiley Eastern Limited, New Delhi. Dreesch, N. et al. (2005) ‘An approach to estimating human resource requirements to achieve

millennium development goals’, Health Policy and Planning, Vol. 20, No. 5, pp.267–276. Ghosh, D. and Vogt, A. (2004) ‘Covariance estimates in stratified and multistage clustered

sampling’, Proceedings of the Survey Research Methods Section, pp.3577–3580, American Statistical Association.

Groves, R.M. (2006) ‘Non-response rates and non-response bias in household surveys’, Public Opinion Quarterly, Vol. 70, No. 5, pp.646–675.

Gupta, A.K. and Kabe, D.G. (2011) Theory of Sample Surveys, World Scientific Publishing Co., Singapore.


Hartley, H.O. (1962) ‘Multiple frame surveys’, JSM Proceedings, Social Statistics Section, pp.203–206, American Statistical Association.

Holt, P. and Smith, T.M.F. (1979) ‘Post stratification’, Journal of Royal Statistical Society, Series A (General), Vol. 42, Part 1, pp.33–46.

Khan, M.G.M. and Ahsan, M.G. (2003) ‘A note on optimum allocation in multivariate stratified sampling’, S. Pac. J. Nat. Sci., Vol. 21, No. 1, pp.91–95.

Kish, L. (1965) Survey Sampling, Wiley, New York. Montgomery, D.C. (2001) Introduction to Statistical Quality Control, John Wiley & Sons, Inc.,

New York. Niebel, B.W. and Freivalds, A. (1999) Methods, Standards and Work Design, 11th ed.,

WCB/McGraw Hill, Boston. Ozcan, S. and Hornby, P. (1999) ‘Determining hospital workforce requirements: a case

study’, Human Resources Development Journal, Vol. 3, No. 3, pp.210–220 [online] http//www.who.int/entity/hrh/en/HRDG_3_3_05.pdf (accessed 27 September 2011).

Piskor, W.G. (1976) Bibliographic Survey of Quantitative Approaches to Manpower Planning, WP 833-76, Massachusetts Institute of Technology, A.P. Sloan School of Management, Cambridge [online] http://www.archive.org/details/bibliographicsur00pisk (accessed 14 October 2011).

Rao, T.J. (1977) ‘Optimal allocation of sample size and prior distributions: a review’, International Statistical Review, Vol. 45, No. 2, pp.173–179.

Stevens, W.L. (1952) ‘Samples with the same number in each stratum’, Biometrica, Vol. 39, No. 314, pp.414–417.

Vetter, E.W. (1967) Manpower Planning for High Talent Personnel, Bureau of Industrial Relations, University of Michigan, Ann Arbor.

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Appendix 1

Table A1 Criteria for rating dealers against complexities

1 SIZE OF THE AUDIT Very large number of products/large quantity 6 Large number of products/medium quantity 5 Medium number of products/large quantity 4 Medium number of products/medium or low quantity 3 Low number of products/medium or large quantity 2 Low number of products/low quantity 1 2 TRAVEL TO REACH THE DEALER Inaccessible location 6 Most difficult to reach 5 Difficult to reach 4 Somewhat difficult to reach 3 Reachable with little effort 2 Easy to reach 1 3 DEALER AVAILABLE FOR AUDIT Getting an appointment itself is very difficult 6 Wait for his convenience even after fixing the time of visit 5 Appointment is a must 4 No need for appointment but have to wait 3 Particular day/particular time 2 Any day/any time 1 4 PRODUCTS/DOCUMENTS ORGANISED FOR AUDIT Absolute chaos 6 You have to put efforts to organise 5 Dealer takes effort to organise 4 Dealer and you both put efforts to organise 3 Partly well organised 2 Extremely well organised 1


Appendix 2

Table A2 Datasheet

Fiel

d H

Q:

Tow

n:

Num

ber o

f FRO

s:

Tim

e ta

ken

for a

udit

Trav

el ti

me

Com

plex

ity sc

ores

* FR

O n

ame

Dea

ler c

ode

Min

M

ax

Star

ting

poin

t M

in

Max

Si

ze o

f au

dit

Trav

el to

reac

h th

e de

aler

D

eale

r av

aila

bilit

y Pr

oduc

ts/d

ocum

ents

or

gani

sed

for a

udit

Tim

e ta

ken

for o

ther

ac

tiviti

es

Mr.

X

4430

4160

02


Appendix 3

Table A3 Satisfaction questionnaire

1 How many hours, on an average, do you work daily (your own rough estimate)? i Less than 2 hours □ ii 2–3 hours □ iii 3–4 hours □ iv 4–5 hours □ v 5–6 hours □ vi 6–7 hours □ vii More than 7 hours □ 2 How satisfied are you with your existing workload? [1 = Extremely dissatisfied, 10 = Extremely satisfied] 1 □ 2 □ 3 □ 4 □ 5 □ 6 □ 7 □ 8 □ 9 □ 10 □ 3 Assuming that your salary and other working conditions remain unchanged, how satisfied

will you be if your present workload is increased by 25%? [1 = Extremely dissatisfied, 10 = Extremely satisfied] 1 □ 2 □ 3 □ 4 □ 5 □ 6 □ 7 □ 8 □ 9 □ 10 □ 4 Assuming that your salary and other working conditions remain unchanged, how satisfied

will you be if your present workload is increased by 50%? [1 = Extremely dissatisfied, 10 = Extremely satisfied] 1 □ 2 □ 3 □ 4 □ 5 □ 6 □ 7 □ 8 □ 9 □ 10 □ 5 Assuming that your salary and other working conditions remain unchanged, how satisfied

will you be if your present workload is reduced by 25%? [1 = Extremely dissatisfied, 10 = Extremely satisfied] 1 □ 2 □ 3 □ 4 □ 5 □ 6 □ 7 □ 8 □ 9 □ 10 □ 6 Assuming that your salary and other working conditions remain unchanged, how satisfied

will you be if your present workload is reduced by 50%? [1 = Extremely dissatisfied, 10 = Extremely satisfied] 1 □ 2 □ 3 □ 4 □ 5 □ 6 □ 7 □ 8 □ 9 □ 10 □ 7 Do you have any suggestions for improvement of work allocation and enhancement of

satisfaction?


Appendix 4

Table A4 Estimates of average times and their sampling variances and covariances

Mea

n

Vari

ance

Cov

aria

nce

Audi

t co

de

iu

iv

iw

ix

(

)2

is

u

()

2i

sv

(

)2

is

w

()

2i

sx

()

ˆ, i

ir

uw

(

)co

v, i

iu

w

A1

124.

0916

25

.623

0 16

.315

9 16

6.03

04

3.

2574

0.

1578

0.

3704

5.

6556

0.85

13

0.93

51

A2

66.9

463

89.1

175

9.11

11

165.

1749

2.06

55

2.41

98

0.62

36

5.83

66

0.

3206

0.

3639

A

3 40

7.85

32

27.0

428

28.3

060

463.

2020

95.5

664

0.52

20

10.4

928

108.

2155

0.11

57

0.36

64

A4

122.

8898

10

7.17

90

15.8

314

245.

9002

39.3

819

27.4

394

7.32

91

87.0

622

0.

3800

6.

4559

A

5 35

.411

9 24

.713

2 10

.984

2 71

.109

3

0.17

20

0.13

21

0.73

51

1.03

92

-

- A

6 53

.761

7 27

.948

8 8.

5967

90

.307

1

2.78

10

1.51

17

1.20

83

7.11

22

0.

4395

0.

8057

A

7 22

.042

5 15

.752

4 5.

9562

43

.751

1

0.07

30

0.15

52

0.40

24

0.70

46

0.

2160

0.

0370

A

8 38

.416

2 16

.843

7 7.

8339

63

.093

8

0.03

72

0.01

91

0.12

13

0.30

46

0.

9451

0.

0635

A

9 45

.582

5 21

.910

7 11

.403

0 78

.896

2

0.84

69

2.80

26

1.20

12

6.22

56

0.

6816

0.

6875

A

10

26.3

364

15.2

056

7.35

35

48.8

995

0.

8795

0.

6950

1.

4922

3.

6262

0.24

42

0.27

98

A11

23

.152

4 16

.962

2 7.

0496

47

.164

2

0.07

71

0.08

62

0.63

63

1.23

42

0.

9813

0.

2174

A

12

14.3

421

26.7

254

4.98

48

46.0

523

0.

3770

2.

1505

0.

7050

3.

6795

0.43

36

0.22

35

A13

35

.967

3 18

.054

8 10

.764

6 64

.786

7

5.71

66

1.42

10

2.29

33

13.2

551

0.

5281

1.

9121

A

14

66.0

459

25.6

627

11.9

251

103.

6337

1.94

52

0.21

33

0.83

89

4.20

71

0.

4735

0.

6049

A

15

22.0

793

15.5

019

6.79

15

44.3

726

0.

0034

0.

6251

0.

6238

1.

3340

0.88

48

0.04

07

A16

18

5.70

38

135.

4227

20

.883

6 34

2.01

01

8.

5118

4.

5621

9.

5868

22

.660

7

- -

Documents

Pathik Mandal - Harvard University P. Mandal et al. take this variation into account while estimating the total workload (person-hours). Further, in order to convert the person-hours