Exploring the Dynamics of Production Functions.pdf
IJEBEA14-419
1. International Association of Scientific Innovation and Research (IASIR)
(An Association Unifying the Sciences, Engineering, and Applied Research)
International Journal of Engineering, Business and Enterprise
Applications (IJEBEA)
www.iasir.net
ISSN (Print): 2279-0020
ISSN (Online): 2279-0039
Performance Evaluation for Productivity Management
1
Ajin T Thomas, 2
Anup Nair
1
M.Tech. Scholar, Industrial Engg. & Management
2
Assistant Professor, Dept. of Mechanical Engg.
1, 2
Mangalam College of Engineering,
Kottayam, Kerala, INDIA
__________________________________________________________________________________________
Abstract: Productivity management is one of the major problems faced by many firms all over the world.
Without identifying productivity influence factor it is difficult to manage the production cycle. The paper
concentrates on the evaluation of management controls over the production. The day to day productivity must
be measure and compare for to take corrective actions and to increase the productivity. This paper presents a
project work done in a small scale footwear industry in south India. Few research efforts have specifically
evaluated productivity in the context of the productivity management cycle. Consequently, there is still a lack of
useful indicators for determining which items should be prioritized and improved upon in order to yield the
highest benefits from productivity management. In an effort to address this issue, this study proposes a method
for calculating productivity. Tool used for the project is Productivity Achievement Ratio (PAR), Regression
analysis, Relative Importance Index (RII) etc.
Keywords: PAR, OP, AP, RII, Variable Ranking, Reduction Factors etc.
_______________________________________________________________________________________
I. INTRODUCTION
Productivity-one of the major factors used in measuring industry outcomes- is defined as the relation between a
production system output and the input set in that system. The importance of managing productivity has long
been emphasized in the manufacturing industry, and a considerable amount of research has been conducted on
the issue. Both managers and employees should pay close attention to productivity management and that the
productivity management cycle has four phases: measurement, evaluation, planning, and improvement. There
have been many research efforts to examine productivity measurement and consequently contribute to the better
productivity management However, despite yielding decent estimations of productivity, these studies have
rarely identified which items require the most attention for optimal productivity management. Indeed,
productivity has commonly been estimated by the ratio between system output and input without consideration
of the particulars of each work item. Considering each work item when measuring productivity is a complex
process. For instance, it must be taken into account that work items associated with low productivity do not
always have high potential for improvement. As well, a minimal change in productivity does not necessarily
signify the presence of a work item linked with a poor management performance. To deal with these
complexities, an advanced productivity indicator, which can account for the unique characteristics of each item,
is needed. This work is done for the enhancement of productivity and reduces the productivity fluctuations in a
small scale footwear industry in Kerala, India (Footmate polymer Footwears India Pvt. Ltd- a LUNAR Group of
company).
For example, Table 1 shows the labor productivity calculated using the data collected from FOOTMATE for the
months of April and March in packing unit. As seen in Table 1, the productivity of the month March is 103.02,
while that of the month April is 132.96. However, this fact does not directly indicate that the productivity
management of the month April is better than that of the month March. It would also be inappropriate to
conclude that the month April has higher potential for improvement than the month March. Instead, it must be
determined which of the Month should be focused on during the planning and improvement phases of the
productivity management cycle. These items should not be chosen merely by estimating productivity without
considering the potential effects of management activity. Although conversion factors can be used to account for
different labor resources and conditions required for the outputs, they still do not provide clear information
regarding the potential effects of management activity. Thus, this research aims at developing a productivity
evaluation indicator that takes management aspects into account so that the most appropriate items for
management activity are selected, and so that the benefits of productivity are maximized.
Table 1: Labor Productivity of PACKING UNIT in FOOTMATE.
WORKERS(A) TOTAL UNITS(B) PRODUCTIVITY (B/A)
MARCH 227 23385 103.02
APRIL 239 31778 132.96
4. Ajin T Thomas et al., International Journal of Engineering, Business and Enterprise Applications, 10(1), September-November, 2014, pp.
41-51
OP = IP – an amount of productivity loss caused by UC_RF (3)
AP = OP – an amount of productivity loss caused by C_RF (4)
Figure 2 visualizes the relationship between RFs and productivity
While some RFs, such as “worker faithfulness,” change from day to day, other RFs, such as “Plant Lay out,”
remain unchanged over the course of production. The former RF type is called a Variable-RF (V_RF), while the
latter is called an Invariable-RF (IV_RF). Previous researcher says that the Invariable reduction factors do not
have an impact on the productivity. But, Invariable reduction factors have serious impact on the productivity
and the invariable reduction factors effects are vary over time. KIM Tae Wan [1] classifies the variables into
Invariable and Variable Reduction factors and excludes the invariable RF. In this study not classifies the
reduction factors into the variable or invariable. In this study classify the variables into Controllable and
Uncontrollable and then grouped the variables according to their characteristics. The Uncontrollable variables
are classified separately.
IV. METHODOLOGY
A. Research Process
The research process consists of 7 steps illustrate in Figure 3. In step 1 define the research problem and conduct
a detailed literature review. In next step determine a data collection method and develop a plan for data analysis.
Through Literature review and pilot survey identify the variables affect productivity and short list it. In step 3
conducts a pilot survey to short list the variables affect the productivity and classify according to the
characteristics of the variables. Next stage is to design the observation data sheet and collect the data through
field observation. The scaling of the data is done with this step. In data analysis stage Conduct reliability
analysis to find the data is significant or not. And a correlation analysis need to conduct because to identify any
mutually exclusive relation between the variables. Through forming a regression equation calculates the value
of obtainable productivity and then calculates the productivity achievement ratio. As part of that rank the
variables with relative importance index, it help to prioritized problem solving.
Figure 3: Research Process.
Figure 4: Variable ranking Procedure
7. Ajin T Thomas et al., International Journal of Engineering, Business and Enterprise Applications, 10(1), September-November, 2014, pp.
41-51
Table 7: Person Correlation – Molding Unit. Table 8: Person Correlation – Packing Unit.
D. Regression Analysis
The main task of statistic analysis is applied in the Multiple Linear Regression in order to study the correlation
and measure the prediction level of independent factors (Productivity Reduction Factors) on dependent factor
(Actual Productivity). Because IP cannot be attained through efforts at the project level, the OP and AP should
be calculated for the purpose of a practical productivity evaluation. Based on the labor productivity calculation,
AP is measured as follows:
(5)
Actual Productivity of the four units will be calculated and shown Table 15.
A multiple linear regression analysis yields an OP value. In each case, RFs are explanatory variables and APs
are dependent variables. The stepwise multiple linear regression coefficients summaries are collected from
regression output of the SPSS statistical software and shown in Table 9.
Some variables are excluded because of insignificant P value or higher partial correlation. The table for p value
and partial correlation for all variables are shown in the Table 10. The excluded variables P values and partial
correlations are highlighted with red color. The excluded variables effects on the dependent variables are
explained by the other independent variables.
Table 11: R square and Adjusted R square
Table 9: Regression Summaries
Table 10: P value and Partial correlation.
Table 12: ANNOVA
RF1 RF2 RF3 RF4 RF5 RF6 RF7
RF1 1 0.292 0.166 0.497 0.345 0.221 0.514
Sig.(1-tailed . 0.034 0.154 0.001 0.015 0.085 0
RF2 0.292 1 0.467 0.384 0.308 0.305 0.579
Sig.(1-tailed 0.034 . 0.001 0.007 0.026 0.028 0
RF3 0.166 0.467 1 0.467 0.244 0.579 0.269
Sig.(1-tailed 0.154 0.001 . 0.001 0.065 0 0.047
RF4 0.497 0.384 0.467 1 0.292 0.444 0.514
Sig.(1-tailed 0.001 0.007 0.001 . 0.034 0.002 0
RF5 0.345 0.308 0.244 0.292 1 0.264 0.313
Sig.(1-tailed 0.015 0.026 0.065 0.034 . 0.05 0.025
RF6 0.221 0.305 0.579 0.444 0.264 1 0.191
Sig.(1-tailed 0.085 0.028 0 0.002 0.05 . 0.118
RF7 0.514 0.579 0.269 0.514 0.313 0.191 1
Sig.(1-tailed 0 0 0.047 0 0.025 0.118 .
Pearson Correlation-MOLDINGUNIT
RF1 RF2 RF3 RF4 RF5 RF6 RF7
RF1 1 0.282 0.271 0.344 0.197 0.466 0.083
Sig.(1-tailed . 0.039 0.045 0.015 0.111 0.001 0.305
RF2 0.282 1 0.118 0.422 0.063 0.451 0.046
Sig.(1-tailed 0.039 . 0.234 0.003 0.349 0.002 0.389
RF3 0.271 0.118 1 0.563 0.43 0.316 0.382
Sig.(1-tailed 0.045 0.234 . 0 0.003 0.023 0.008
RF4 0.344 0.422 0.563 1 0.274 0.434 0.608
Sig.(1-tailed 0.015 0.003 0 . 0.044 0.003 0
RF5 0.197 0.063 0.43 0.274 1 0.058 0.205
Sig.(1-tailed 0.111 0.349 0.003 0.044 . 0.362 0.103
RF6 0.466 0.451 0.316 0.434 0.058 1 ‐0.042
Sig.(1-tailed 0.001 0.002 0.023 0.003 0.362 . 0.399
RF7 0.083 0.046 0.382 0.608 0.205 ‐0.042 1
Sig.(1-tailed 0.305 0.389 0.008 0 0.103 0.399 .
Pearson Correlation-PACKINGUNIT
CONSTANT RF1 RF2 RF3 RF4 RF5 RF6 RF7
CUTTING UNIT 56.153 ‐3.249 ‐1.742 ‐2.127 ‐2.624
STITCHING UNIT 12.943 ‐0.483 ‐0.39 ‐0.528 ‐0.458
MOLDING UNIT 14.705 ‐0.328 ‐0.481 ‐0.36 ‐0.601 ‐0.468
PACKING UNIT 23.333 ‐1.043 ‐0.888 ‐1.54 ‐0.937
REGRESSION SUMMARY
RF1 RF2 RF3 RF4 RF5 RF6 RF7
CUTTING UNIT 0 0.042 0.446 0.105 0.008 0.009 0.585
STITCHING UNIT 0.02 0.589 0.797 0.085 0.233 0.025 0.052
MOLDING UNIT 0.023 0.007 0.069 0.333 0.023 0 0.008
PACKING UNIT 0.063 0.941 0.001 0.007 0 0.004 0.83
CUTTING UNIT ‐0.32 ‐0.171 ‐0.131 0.275 ‐0.227 ‐0.226 0.094
STITCHING UNIT ‐0.381 ‐0.093 ‐0.044 ‐0.287 ‐0.204 ‐0.369 ‐0.322
MOLDING UNIT ‐0.377 ‐0.443 ‐0.311 ‐0.168 ‐0.377 ‐0.664 ‐0.433
PACKING UNIT ‐0.313 0.013 ‐0.519 ‐0.439 ‐0.545 ‐0.465 0.037
P VALUE
PARTIAL CORRELATION
CUTTING UNIT 0.877 0.77 0.743
STITCHING UNIT 0.839 0.704 0.67
MOLDING UNIT 0.909 0.826 0.8
PACKING UNIT 0.891 0.794 0.771
R R Square
Adjusted
R Square
Sumof
Squares
df Mean
Square
F Sig.
Regression 1349.469 4 337.37 29.223 0
Residual 404.06 35 11.545
Total 1753.529 39
Regression 56.025 4 14.006 20.802 0
Residual 23.566 35 0.673
Total 79.592 39
Regression 71.429 5 14.286 32.247 0
Residual 15.062 34 0.443
Total 86.491 39
Regression 271.089 4 67.772 33.753 0
Residual 70.276 35 2.008
Total 341.366 39
CUTTING
UNIT
STITCHING
UNIT
MOLDING
UNIT
PACKING
UNIT
( )
k e r *
O u t p u t q u a n t i t i e s
A P
W o r s W o r k t i m e
8. Ajin T Thomas et al., International Journal of Engineering, Business and Enterprise Applications, 10(1), September-November, 2014, pp. x
The Table 12 shows the f value and significance level of test. The p value is less than less than .001, so the
relationships are significant. The R2
values for the four units are shown in Table 11. The R2
value is 0.77, and
the adjusted R2
is 0.743 in cutting unit. R2
value is called the coefficient of determination and is the percentage
of the total variation in y, which is explained by regression. In this case study, this means that 77%of the total
variation in AP is explained by the regression model. Similarly 70.4%, 82.6% & 79.4% of variations in AP were
explained using the Regression Model. The regression equation is as follows:
(6)
Where,
A is the y-intercept;
B1,n is the regression coefficient for C_RFn;
B2,l is the regression coefficient for UC_RFl.
Table 13 shows the equations formed using the regression coefficients and the above AP equations. OP during a
certain period t is calculated in the equation below:
(7)
Where,
UC_RFl,t is the value of UC _RFl at the period t.
That is, OP is the productivity value when the C_ RFs have not yet occurred. Mathematically, the value of the
C_RF is 0. Table 5.9 shows OP equation after excluding the controllable reduction factors. We first grouped the
RF6 as uncontrollable because it only enters in the OP equation. Using the above equations the op values are
calculated and shown in Table 15.
Table 13: AP Equation. Table 14: OP Equation.
E. PAR Calculation
The Productivity Achievement Ratio (PAR) can be represented as the quotient of AP and OP. This value
considers the potential effect of improvement and therefore can be used as a productivity evaluation indicator to
determine the main items that should be focused on during production. The PAR is formulated as follows:
(8)
The PAR value calculated also shown in Table 15. The first five observation PAR value comparison chart is
shown in Figure7. The chart shows that the comparison of PAR between units easily. It is the better way to
compare productivity than the previous methods. The process for determining the OP value becomes
increasingly accurate as more data are collected. If the variables considered are explain fewer amount of total
variations in AP. That leads to OP less than AP. This will reason for the PAR higher than 100%. So consider
maximum variables affect the productivity in the site.
Figure 7: Productivity Achievement Ratio for first five
observations. Figure 8: Productivity Management Model using PAR.
CUTTINGUNIT AP=56.153-3.249*RF1-1.742*RF2-2.127*RF5-2.624*RF6
STITCHINGUNIT AP=12.943-0.483*RF1-0.39*RF4-0.528*RF6-0.458*RF7
MOLDINGUNIT AP=14.705-0.328*RF1-0.481*RF2-0.36*RF5-0.601*RF6-0.468*RF7
PACKINGUNIT AP=23.333-1.043*RF3-0.888*RF4-1.54*RF5-0.937*RF6
CUTTINGUNIT OP=56.153-2.624*RF6
STITCHINGUNIT OP=12.943-0.528*RF6
MOLDINGUNIT OP=14.705-0.601*RF6
PACKINGUNIT OP=23.333-0.937*RF6
1, 2 ,* _ * _n n l l
n l
A P A B C R F B U C R F
2 , * _l l t
l
O P A B U C R F
*100(% )(where, 0 PAR 100)
AP
PAR
OP