Group-5-Business Analysis and Management docx

15BSP039 - Business Analysis & Planning
Leicester Cases (Group 5) Coursework
Produced By
Group 5
Jin Yan B516815
Vikram Vaghela B119158
Shan Liang B514634
Jiawei Wu B529214
Number of Pages: 50
Submission date: 7th
September 2016
Loughborough University
Leicester Cases (LC)

1
ABSTRACT
This report is designed to deliver explanations for Leicester Cases (LC) Company in the
range of sales forecasting and production scheduling planning. LC runs a prosperous trade of
business in manufacturing superior quality soft fabric cases. To prosper in the forthcoming
years, LC considers making changes in the management of its five product lines: Wallet,
Digi-Bag, SLR Bag and Camcorder Bag. Upon the request of LC, a methodical approach is
presented to increase the precision level of sales of forecasting and to advance the efficiency
of production arrangement. The first fragment of the report includes five dependable ARIMA
models which are identified for the five product lines. On analysing the historical sales data
in SPSS software this would produce future demand. The second fragment of the report
shows the current production capacities that are estimated through running a simulation
model constructed through Microsoft Excel Solver. Once information is captured from the
first two parts, a cost-effective production schedule is created by solving a linear
programming model. This draws to a conclusion that, LC’s current production capacity still
cannot meet the forecasted demand. Therefore, nine production plans are projected at the end
of this report to discover the opportunity for LC to encounter the forecasted demand. It is
suggested that LC would be highly advised to adopt Scenario 2, as it would resolve their
financial difficulty in offering lowest total cost in fulfilling the forecasted demand.
Nevertheless, except for the doubts in the data used in this report for investigation resolution,
there are also assumptions and limitations exist along with the three models.

2
Content
1. Introduction.........................................................................................................................................1
2. Demand Forecasting ...........................................................................................................................1
2.1. Examine The Data....................................................................................................................2
2.2. Regression Model Building With Dummy Variables ..............................................................4
2.2.1. Linear trend model................................................................................................................5
2.2.2 Quadratic trend model............................................................................................................8
2.2.3. Cubic trend model.................................................................................................................9
2.2.4. Regression model evaluation ..............................................................................................10
2.3. Decomposition of the testing data..........................................................................................10
2.4.1. SAS data analysis........................................................................................................11
2.4.2. ARIMA model for first difference of SAS .................................................................12
2.4.3. Model over-fitting.......................................................................................................13
2.4.4. Diagnostic Checking...................................................................................................15
2.5. Brief Data Analysis and Final Model for SLR Production Line............................................16
2.6. Brief Data Analysis and Final Model For Wallet Production Line........................................18
2.7. Brief Data Analysis And Final Model For Digibag Production Line ....................................20
2.8. Brief Data Analysis And Final Model For Camcorder Product Line ....................................21
2.9. Results of Demand Forecasting And Assumptions For Model Building...............................23
3. Simulation.........................................................................................................................................24
3.1. Entities, Activities, And Excel Plots......................................................................................26
3.1.1. Wallet Product Line:...................................................................................................26
3.1.2. Digibag Product Line:.................................................................................................26
3.1.3. SLR Bag Product Line:...............................................................................................26
3.1.4. Camcorder Bag Product Line:.....................................................................................27
3.1.5. Accessory Bag Product Line:......................................................................................27

3
4. Linear Program Modelling................................................................................................................29
4.1. Conceptual Modeling.............................................................................................................30
4.2. Mathematical Modelling........................................................................................................31
4.2.1. Define Decision Variables ..........................................................................................31
4.2.2. Objective Function Formulating .................................................................................31
4.2.3. Constraints Formulating..............................................................................................31
4.3. Results Of Linear Programming ............................................................................................33
5. Link Between LP, Simulation And Forecasting ...............................................................................36
6. Scenarios Analysis............................................................................................................................37
7. Limitation Of Using The Models......................................................................................................45
7.1. Limitations Of Forecasting ....................................................................................................45
7.2. Limitations Of Simulation .....................................................................................................45
7.3. Limitation Of Linear programming .......................................................................................46
8. Recommendations.............................................................................................................................48
9. Conclusion ........................................................................................................................................50
10. References.......................................................................................................................................51
11. Appendix.........................................................................................................................................53
Appendix 1: SLR ..........................................................................................................................53
Appendix 1-1: Examine Time Series Of SLR.......................................................................53
Appendix 1.2- SPSS Output For Regression with dummy variable (SLR) ..........................54
Appendix 1.3: Classical decomposition................................................................................62
Appendix 1.4: Summary Of SLR Forecasting Result From Different ARIMA Models ......63
Appendix 1.5: ARIMA Model Overfitting Result................................................................64
Appendix 1.6: Summary Of Final Model Comparison And Error Checking Result ............65
Appendix 2: Wallet.......................................................................................................................66
Appendix 2.1: Examine Time Series Of Wallet....................................................................66
Appendix 2.2: SPSS Output For Regression with dummy variable (Wallet).......................67

4
Appendix 2.3: Classical decomposition (Wallet)..................................................................75
Appendix 2.4: Summary Of Wallet Forecasting Result From Different ARIMA Models...76
Appendix 2.5: ARIMA Model overfitting Results ...............................................................77
Appendix 2.6: Summary Of Final Model Comparison And Error Checking .......................78
Appendix 3: Digibag.....................................................................................................................78
Appendix 3.1: Examine Time Series Of Digibag .................................................................78
Appendix 3.2: SPSS Output For Regression with dummy variables (Digibag) ...................80
Appendix 3.3 - Classical Decomposition..............................................................................83
Appendix 3.4: Summary Of Wallet Forecasting Result From Different ARIMA Models...83
Appendix 3.5: ARIMA Model Overfitting Result (Digibag)................................................85
Appendix 4 Camcorder.................................................................................................................86
Appendix 4.1: Examine Time Series Of Camcorder ............................................................86
Appendix 4.2 - SPSS Output For Regression with dummy variable (Camcorder)...............87
Appendix 4.3 - Classical Decomposition..............................................................................93
Appendix 4.4: Summary Of Camcorder Forecasting Result From Different Models ..........93
Appendix 4.5: ARIMA Model Overfitting Result (Camcorder)...........................................96
Appendix 4.5: Summary Of Final Model Comparison And Error Checking .......................97
Appendix 5: Linear Programming Results....................................................................................98
Appendix 6: Diary of Meeting....................................................................................................107

5
Acknowledgement
Deepest appreciations thank Professor Victor Podinovski and Professor Gilberto Montibeller
for great encouragement and patience throughout the construction of Business Analysis and
Planning project. We are indebted to them for their continual guidance, constructive
suggestions and encouragement that undoubtedly made this whole journey an infinitely
smoother experience.
We would like to thank all parents of group members who played an important part in
supporting us throughout this challenging journey also thank the selfless individuals who
gave up time from their own work to also give advice and guidance. Thank you.

1
1. Introduction
This report is constructed on Leicester Cases (LC), Founded in 1987 and located in the
United Kingdom. LC is a company which specialises in manufacturing a range of soft fabric
cases (Wallet, Digibag, SLR Bag, Camcorder Bag, and Accessory Bag). LC over the years
has created premium quality products. Without any strategic vision, the management now
appreciates moving forward they need to implement a more strategic approach intending to
improve control of their operational procedures.
The knock on effect with no strategic vision has had financial implications in having
significant overtime expenditure of meeting orders and an overestimation of demand, has
made LC experience difficulties of amplified inventory costs. A large section of this report
will evaluate and analyse each soft fabric case's operation with descriptions of what
specifically to focus. The purpose of this report will give a cost-effective production schedule
to the LC company by 1) Aiming to generate a projection model, 2) Constructing a
simulation model to produce sensible production capabilities,3) Develop a linear
programming model to analysis a working production schedule, 4) Deliver the production
advise to the LC company based on the different scenarios analysis. The report would create
several proposals and scenarios to LC, in offering different ways to currently work with its
benefits such as more employment to reduce some cost factors. The report would pay
attention to processes that cut costs and schedules that satisfy LC concern of their financial
position.
This reports structure will firstly start from the aspects of forecasting modelling, then
simulation modelling which would be directed towards the Linear Programming modelling.
Once these three models are completed, the report would indicate the linkage between the
three models and how they relate to each other. Following the model, there are nine
scenarios which would suggest possible outcomes with different approaches. To have a non-
bias approach, this report it will also produce a limitation section indicating potential
problems using the models. Finally, a recommendation of what would be the best possible
solution for LC.
2. Demand Forecasting
Business forecasting’s concept is a scheduling instrument that aids management in businesses
to cope with the improbability of the future. This mainly relies on the historical and current
data sets with an analysis of its trends. There are 4 main types of forecasting methods: 1)
model building, 2) forecast combination, 3) judgement decomposition and 4) judgement
adjustment (Webby and O’Conner, 1996). The judgement decomposition link of evaluation
and analyse the effect of past contextual information in time series before building
mathematical models. When the mathematical forecasts are reached, factors of future
businesses will be considered and forecasting data are judged by human possibly (Granger,

2
2014). The last judgement adjustment process is based on experts’ knowledge and
experiences.
A business forecast is more than an informed guess, but would be an important suppose it
would supply important decisions (Ord and Fildes 2012). A forecasting has several steps.
First of all, the data point is selected. Analysts, theoretical, choose raw data sets for
prediction among their experience, and it is very subjective. For instance, data merely
selected from November 2008 to date rather from the start of the production. Secondly, an
assumption line to cut down the time and data to produce the forecast. A model is picked
which fits the data set, and analyst generates the forecasting model for the purpose of
verifying if any change needed in the process to identify problems in advance (Carver and
Nash, 2009). Therefore, LC’s management team is confident to use the result of the
forecasting if forecasting model produces small error value during the model checking
process.
Business forecasting begins with assured assumptions constructed from management
understandings, awareness and findings. The management estimates are predicted from the
coming days, weeks, months and years using several techniques. Some of which are;
Regression Analysis with dummy variables, Decomposition methods and Box Jenkins
approach. Any assumption would enlarge the error in forecasting result; sensitivity is used to
bring into line the range of values for these indeterminate factors.
This section consists of seasonal effects, trend-cycles of the data. Taking Accessory
production line as an example explains a Regression with Dummy variable methods in line
with linear and non-linear models with trend-cycle and seasonal components. Leading on to a
combination of a decomposition method and box ARIMA style against the modelling data
and hold back data. Finally, a discussion of forecasting results from the methods described
above with a choice of a final model. This report concludes forecasting results of each four
production line in section 2.5 (SLR), 2.6 (Wallet|), 2.7 (Digibag), 2.8 (Camcorder). Finally, it
provides the forecasting result to Leicester Cases management team as a reference of demand
in next 18 months.
2.1. Examine The Data
Firstly, an essential step is to split the data to evaluate the model further and data for model
checking. About the Accessory product line, it can be seen as 96 sets of raw data which
recorded from November 2008 to October 2016. There are two reasons for choosing 96 sets
of data instead of using the whole data. 1) The historical data can become obsolete;
companies rely on data from company leader’s industry experts and marketing surveys but
the option of one person and should not justify a forecast of a whole company because this
can create pessimistic and optimistic forecasts (Ascher and Overholt, 1983). 2) Considering

3
the noise effect in the model, thus, the model building tries to omit unpredictable time such as
financial crisis.
Data from November 2008 to October 2015 (84 sets) would be the modelling data used for
model building and the rest of 12 sets of raw data from November 2015 to October 2016
would be classified as the holdback data for a model to be evaluated.
Figure 1: Plot of Accessory
Figure 1 is the time series plot for the accessory sales which evidently shows an upward
trend holistically. According to the plot, there might have a trend-cycle and seasonal effects.
Also, the seasonal pattern reveals in the ACF plot which is seen lag1, lag5, lag6 and lag12 are
significant to sales data.
For the purpose of understanding the pattern repeat, the correlation analysis (Table 1)
indicates a 12 pattern repeat because lag12 reveals a number of correlations (0.984) closest to
1. The scatter plots of the lagged data are used. They are monthly data, creating scatter plot
for sales in lag1, lag5, lag6 and lag12 (Figure 2). In understanding the scatter plots of sales
against the lag12 this produces dot most like a straight line, thus, it provides further evidence
to a 12 point pattern repeat within the data and justified as a stable seasonal pattern.

4
Table 1: Correlation analysis
Figure 2: lagged data for Accessory
2.2. Regression Model Building With Dummy Variables
The statistical model for regression can be linear and non-linear models. The popular
criterion for model determination is to find out the best- fitting line to the sales holdback data.
The forecasting analyses primarily based upon the adjusted R2
, and also consider T-test
result; Durbin-Watson test result and the significant of these independent decision variables
in the equation. Model for forecasting assumes these irregular components contents white
noises. According to the data examination above, regression with dummy variable will be
used for model building. Table2 indicates dummy variables generated by SPSS. Where
Dummy variable “months” are good for capturing seasonal effects, and these “time” Dummy
Variables are able to capture trend-cycle for prediction.

5
Table 2: Dummy Variables
From analysis of data examination (Figure 1), forecasting model for Accessory should
produces trend with a slight curvature inside and also effect from seasonal changes. Relating
to trend of accessory would be used to produce a regression models that include linear,
quadratic and cubic models, with the formulation of:
Linear: Sales = b0+ b1*time+b2*M1+b3*M2+b4*M3+b5*M4…. +error
Quadratic: Sales = b0+ b1*time+b2*M1+b3*M2+b4*M3+b5*M4…. +bn*time2
+error
Cubic: Sales = b0+ b1*time+b2*M1+b3*M2+b4*M3+b5*M4… +bn*time2
+bn+1*time3
+error
2.2.1. Linear trend model
Table 3 indicates a linear trend model that holds a respectable adjusted R2 of 0.985 and the
F- value of 513.562. This result still shows that month 11 is still not applicable and should
remove from the model because the P-Value indicates that M-11 is 0.024 which results in the
variables is not significant within this model.

6
Table 3 Model summary for linear
Table 4 indicates a linear trend model that's goods a respectable R2 of 0.984 and the F- value
of 532.616; these still shows that after lag11 is removed all variables are significant. The P-
Value indicates that all variables are smaller than 0.05 which results in all variables are
important within this model, shown in the formulation:
Forecasting_1=225.917+0.858*Time-104.162*M_1-111.271*M_2-61.254*M_3-
65.612*M_4-38.720*M_5-44.954*M_6-38.312*M_7-106.295*M_8-115.653*M_9-
62.137*M_10
Table 4:Model Summary for Linear
Model Summaryb
Mod
el R
R
Square
Adjusted R
Square
Std. Error of
the Estimate
Durbin-
Watson
1 .993a
.986 .984 5.70223 1.398

7
a. Predictors: (Constant), MONTH_=10.0, Time, MONTH_=4.0,
MONTH_=5.0, MONTH_=3.0, MONTH_=6.0, MONTH_=2.0,
MONTH_=1.0, MONTH_=7.0, MONTH_=8.0, MONTH_=9.0
b. Dependent Variable: Accessory
ANOVAa
Model
Sum of
Squares df Mean Square F Sig.
1 Regression 190500.692 11 17318.245 532.616 .000b
Residual 2731.298 84 32.515
Total 193231.990 95
a. Dependent Variable: Accessory
b. Predictors: (Constant), MONTH_=10.0, Time, MONTH_=4.0, MONTH_=5.0,
MONTH_=3.0, MONTH_=6.0, MONTH_=2.0, MONTH_=1.0, MONTH_=7.0,
MONTH_=8.0, MONTH_=9.0
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t
Sig.
B Std. Error Beta
1 (Constant) 225.917 1.697 133.124 .000
Time .858 .021 .530 40.548 .000
MONTH_=1.0 -104.162 2.469 -.642 -42.182 .000
MONTH_=2.0 -111.271 2.470 -.685 -45.054 .000
MONTH_=3.0 -61.254 2.470 -.377 -24.797 .000
MONTH_=4.0 -65.612 2.471 -.404 -26.553 .000
MONTH_=5.0 -38.720 2.472 -.239 -15.664 .000
MONTH_=6.0 -44.954 2.473 -.277 -18.178 .000
MONTH_=7.0 -38.312 2.474 -.236 -15.484 .000
MONTH_=8.0 -106.295 2.476 -.655 -42.936 .000
MONTH_=9.0 -115.653 2.477 -.712 -46.685 .000
MONTH_=10.
0
-62.137 2.479 -.383 -25.064 .000
a. Dependent Variable: Accessory

8
2.2.2 Quadratic trend model
Table 5 shows a Quadratic trend model that holds a respectable R2 of 0.985 and an F-Value
larger than 4 (485.423). Apart from this, all variables have a smaller P-Value of 0.05 which
indicates all variables are significant within this model produced. The Durbin-Watson result
is 1.378 which indicates a confident, positive relation with the real data. Concerning the F-
Test the figure of 485.423 showing the regression is significant, despite the coefficient
analysis does not produce a satisfying time2 (0.090) and M_11 (0.022) results and should be
removed from the result obtained. However, if time2 is removed from the model, the
forecasting model is as same as linear trend model.
Table 5: Quadratic summary

9
2.2.3. Cubic trend model
Table 6 indicates a Cubic trend model, that hold an adjusted R2 of 0.985 and the F-Value of
447.286, despite this all variables in the P-Value is smaller than 0.05 which shows all
variables are significant in this model presented. The Durbin-Watson result is 1.381 which
indicates a confident, positive relation with the real data. With the F-Test the figure of
485.423 showing the regression is significant, despite this, the coefficient analysis does not
produce a satisfying time2 and time3 results and should be removed from the result obtained.
Table 6: Cubic Summary

10
2.2.4. Regression model evaluation
According to Table 7 the adjusted R2
figures are all the same (0.985), and all Durbin-Watson
results reveal a positive correlation regression because the result is from two towards nil. The
linear model is the idea candidate because the smaller amount of independent variables might
provide a more accurate forecasting result.
Table 7 Regression Model Summary for Accessory
Model Linear Quadratic Cubic
Adjusted R2 0.985 0.985 0.985
DW 1.398 1.378 1.381
The graph below (Figure 3) shows the forecasting result with the product Accessory, and this
shows, a close line between the forecast and the accessory raw data, which indicates the error
result is small. Figure 4 shows a fluctuation at a constant mean, showing it does not have any
trend-cycle seasonal effect leading to the error which containing white noise.
Figure 3: Regression model forecasting Figure 4: Error analysis
2.3. Decomposition of the testing data
To divide the measurement data into motion components (Trend-Cycle, Seasonal
Components and Irregular component) can be done through the decomposition of a time
series which is seen as the most applicable method. About the time series described earlier in
Figure 1, it indicates the size of trend-cycle and seasonal components are increasing and
directly related to the scale of the data values. Thus, the Multiplicative model is a sensible
way to make the decomposition. Once the decomposition process is finished, the SPSS data
presents result in Table 8, seasonally adjusted series (SAS), and figure 5, seasonally adjusted
factors (SAF), which produce a trend-cycle pattern and seasonal pattern respectively.

11
Table 8: Classical Decomposition Figure 5: Seasonal Factor
2.4. The Box-Jenkins (ARIMA) Method
2.4.1. SAS data analysis
Figure 6 reveals the SAS plot for Accessory which still has an upper trend and up and down
cycle. This phenomenal indicates that it needs first difference to remove the trend-cycle.
Figure 7 and Figure8 are ACF and PACF of SAS data which provide further evidence of the
trend-cycle.
Figure 6: SAS Plot
Figure 7: ACF for SAS Figure 8: PACF for SAS

12
2.4.2. ARIMA model for first difference of SAS
The Box-Jenkins forecasting approach considers procedures to identify, fitting and checking
ARIMA models against time series (Hanke & Wichern, 2014, pp.401). Analyst follows the
parsimony principle while choosing between models. The ARIMA forecasting model
formulas as:
ARIMA model: pth-order autoregressive model
Yt = a0 + a1 * Yt-1 + a2*Yt-2 + …..ap*Yt-p + E
ARIMA model: qth-order moving average model
Yt = u + et – w1* et-1 – w2*et-2 -…… - wq*et-q
For the purpose of using Auto-regression Moving Average ARIMA model, the data should be
stationary. However, SAS data is not accurately stationary, and therefore, applying the first
difference to SAS to modify the data. The data is indeed stationary because there is no trend
and cycle left. According to Figure 9, the first difference produced as seen. Figure 10
produce the ACF to show spikes at Lag2 and Lag6, which result in significantly lagged data
with the remaining which exceed the two certain levels to be justified as significant by
chance. Comparative to PACF, the spikes at Lag2, Lag5 and Lag10 are again significant-
lagged data and again result in significantly lagged data. This results in a justified model of
ARIMA (10, 1, 0), ARIMA (5, 1, 0) and ARIMA (0, 1, 6).
Figure 9: SAS Diff
Figure 10: ACF and PACF of SAS Diff

13
SPSS generate the model result of ARIMA (5, 1, 0). From the summary below Figure 11, the
normalised BIC gives a result of 4.506. Secondly, from the Ljung-Box test result, it is 0.223
indicates not significant of the result and it means the model is reliable. From the Model
parameters analysis, AR lag1, lag2, lag3, and lag 5 are significant, which means these lags
are good expansionary to the forecasting model.
Figure 11: Summary of ARIMA (5, 1, 0)
Refer to Table 9, a summary of ARIMA (10, 1, 0), ARIMA (5, 1, 0) and ARIMA (0, 1, 6) is
shown. With the aim of finding the most reliable forecasting model, the model provides the
smallest normalised BIC is considered as the appropriate model for prediction by the analyst.
Therefore, ARIMA (5, 1, 0) is the most reliable choose because 4.008 is smaller over 4.257
and 4.029. Moreover, from the table summarise, the Ljung-Box Q test is not significant.
Ljung-box test is used widely in autoregressive integrated moving average (ARIMA)
modelling, but it is only applied to the residuals of ARIMA model which fits, not the initial
series. Despite this, in such applications the hypothesis actually, in the process of testing,
indicates the residual of the ARIMA model has no autocorrelation. In testing, ARIMA model
residual shows degrees of freedom and needs to be adjusted to produce parameter estimation.
An example of this is an ARIMA (p,d,q) model should be set to (degree of freedom).
Table 9: Summary of ARIMA models
ARIMA model MAE Normalised BIC Ljung-Box Q
ARIMA (10, 1, 0) 4.47 4.257 0.234
ARIMA (5, 1, 0) 4.506 4.008 0.223
ARIMA (0, 1, 6) 4.38 4.029 0.369
2.4.3. Model over-fitting
Table 10 indicates ARIMA (5, 1, 0) model that produces the smallest BIC of 4.008, which
means that the ARIMA (5, 1, 0) model, ARIMA (6, 1, 0) and ARIMA (5, 1, 1,) need to test

14
further. When applying the test, it indicates that the MA lag1 in ARIMA (5, 1, 1) model and
AR lag6 in ARIMA (6, 1, 0) show that these are not significant. Despite this, both are
overfitting models, and the BIC is larger the ARIMA (5, 1, 0) shown in the table below under
Normalized BIC (4.073). This result evidently indicates that ARIMA Model (5, 1, 0) within
the ARIMA candidate models.
Table 10: BIC Summary for overfitting model and Parameters
ARIMA model Normalised BIC
ARIMA (5, 1, 0) 4.008
ARIMA (6, 1, 0) 4.073
ARIMA (5, 1, 1) 4.073
According to error checking below, the ACF and PACF (Figure 12 and 13) of residual
indicate that majority of the lags are at the 5% confidence level indicating a containment of
white noise. One or two spikes can be defined as significant by chance and ignored. The
error2 graph below shows is disputed at a constant mean, which indicates, it does not contain
any trend cycle or seasonal pattern making this model reliable.

15
Figure 12: Plot for Error
Figure 13: Forecasting using ARIMA (5, 1, 0)
2.4.4. Diagnostic Checking
ARIMA (5, 1, 0) and Linear trend model
The Table 11 below indicates a diagnostic check, which produces MSE and MAD results for
ARIMA (5, 1, 0) and Linear trend model. The results figures show that the linear model is
much better than ARIMA (5, 1, 0) result because of the smaller MSE of 9.4 than 44.22. The
MAD results follow this by the figures for Linear trend of 2.555 and ARIMA (5, 1, 0) 6.007
which the smallest produced shows less error.
Table 11: MSE and MAD comparison

16
These graphs in figure 14 indicate forecast 1 which is linear trend model and Forecast 2
which is ARIMA (5, 1, 0). The linear trend model has a perfect fit to the holdback data than
the ARIMA (5, 1, 0), which is not as close to the holdback data.
Figure 14: Forecasting Plot of linear and ARIMA(5, 1, 0)
2.5. Brief Data Analysis and Final Model for SLR Production Line
The sales of the SLR Bag data are selected from November 2008 to October 2016 which
contains 96 datasets. Concerning the plot of the SLR sales and first difference data
(Appendix 1.1) the patterns of cyclical and seasonal can be explicitly acknowledged. In
addition to this, the magnitude of the irregular components is directly related to the size of the
data values. From a holistic view of the time series plots, the data is not very stationary.
Selecting data from November 2008 to October 2015 is defined as testing data of 84 sets and
the data from November 2016 to October 2016 is shown as having 12 sets of data for model
checking.
The summary of regression with dummy variable (Table 12), the Cubic model without month
one variable gives adjusted r2
value of 0.905 which is the highest comparing with the linear
and quadratic model. The adjusted r2
value indicates the cubic model capture 90.5% of total
real data. The DW test result indicates a positive correlation of this model. Detail of SPSS
output of all model summaries is shown in Appendix 1.2.
Table 12: Summary of SLR regression model
SLR Column1 Column2 Column3
Model
Adjusted
R2 F-test Durbin-Watson
Linear (4) 0.878 55.305 0.653
Quadratic 0.875 45.567 0.650
Cubic (2) 0.905 61.907 0.841
About the ACF and PACF outputs of SAS in Appendix 1.3, the SAS data is non-stationary
which needs programming first difference. The first difference of the SAS is used to remove

17
the trend cycle pattern (within SAS) and identify the ARIMA models. The result of this has
produced a plausible model understood by ARIMA (1, 1, 0), ARIMA (0, 1, 5). The outcome
of the figures in Appendix 1.4 presented for the normalised BIC is 5.551 and 5.785
respectively, and Ljung-Box test display non-significant results which are shown in Table 13.
Table 13: ARIMA model Summary for SLR
SLR Column1 Column2 Column3
ARIMA
Model
MAE
Normalised
BIC
Ljung-Box
Q
(1, 1, 0) 11.024 5.551 0.449
(0, 1, 5) 10.881 5.785 0.602
In Table 14, ARIMA (1, 1, 0) model produced a smaller normalised BIC of 5.551 than
another model. Therefore with ARIMA (1, 1, 0) model, the ARIMA (1, 1, 1) model and
ARIMA (2, 1, 0) model are needed for testing the overfitting results. The test shows that the
overfitting models do not have a more admirable normalised BIC than the ARIMA (1, 1, 0)
model whereas the ARIMA (1, 1, 1) model and the ARIMA (0, 1, 2) model show the AR
log1 and MA log2 are not significant (Appendix 1.5). This overall results in over-fitting
models and need to reduce back to the original ARIMA (0, 1, 1) which is now evidently
proven to be the best model with the ARIMA models described.
Table 14: SLR Model overfitting
ARIMA Model Normalised BIC
(1, 1, 0) 5.551
(2, 1, 0) 5.616
(1, 1, 1) 5.615
In relation to the residual time-series plot and the ACF/PACF plots of cubic trend model and
ARIMA (1, 1, 0) model produces a pattern with a remainder of error in the cubic trend model
(Appendix 1.6). The error or ARIMA (1, 1, 0) seems acceptable and can be well-defined as
white noise which is to be ignored.
In addition to MAD, The ARIMA (0, 1, 1) model is chosen as a dependable model to make
demand forecasting in relation to the SLR Bag product line. This decision made because from
the error checking result the MAD of ARIMA is 18.175 which smaller than the Cubic result
(126.274).The large value of MAD indicates that there is some valuable information which
cannot capture by the model. For instance, management can consider if there are any external
reasons leads to the irregular fluctuation during 2010. To summarise, the final model is used
to forecasting is ARIMA (1, 1, 0).

18
MSE and MAD results
2.6. Brief Data Analysis and Final Model For Wallet Production Line
Choosing sales data of the Wallet from November 2008 to October 2016 build and check the
forecasting models. Same as Accessory firstly split the 96 sets of data into prediction data and
holdback data. From Appendix 2.1, the raw data plot involving trend-cycle and seasonal
effects. Thus, the forecasting model should consider trend-cycle and seasonal effects.
Table 15 illustrates the summary of the regression models with dummy variables. This chart
including adjusted r2
, F-test results and Durbin-Watson results (Appendix 2.2). The cubic
model can be used for forecasting because it captures 81.1% of total data examined. The
outcome of DW test indicates a positive relationship between data and independent variables.
Therefore, the forecasting_1 equation is:
Forecasting_1 = 649.253+0.076*Time2-0.001*Time3-127.460*M_1-98.108*M_2-
155.026*M_3-21.779*M_4-61.222*M_5-53.493*M_6-59.588*M_7-66.217*M_8-
56.089*M_9-15.987*M_11
Table 15: Summary of Regression Models
Model Adjusted R2 F-test Durbin-Watson
Linear 0.792 32.64 0.706
Quadratic 0.804 31.922 0.804
Cubic 0.811 28.372 0.795
In relation to the plot of the Wallet sales data (Appendix 2.3), the pattern of trend-cyclical
and seasonal can acknowledge explicitly. In addition to this, the magnitude of the seasonal
and irregular components is directly related to the size of the data values and the model which
should be considered is the multiplicative model in the classical decomposition process.
Therefore, about the ACF and PACF of SAS data, SAS need to be the difference once. In
reference to the Appendix 2.3.2, from the differenced SAS ACF and PACF results have
produced a plausible model understood by ARIMA (2, 1, 0), ARIMA (0, 1, 2).
SLR Cubic trend model ARIMA (1, 1, 0)
actual fore error error2 absolute |et|/|yt| actual fore error error2 absolute |et|/|yt|
410 487 -76.68 5879.8224 76.68 0.187 410 430 -20.39 415.75 20.39 0.050
431 515 -83.85 7030.8225 83.85 0.195 431 452 -20.53 421.48 20.53 0.048
430 522 -92.32 8522.9824 92.32 0.215 430 457 -26.96 726.84 26.96 0.063
283 399 -115.97 13449.0409 115.97 0.410 283 295 -12.28 150.80 12.28 0.043
258 380 -121.98 14879.1204 121.98 0.473 258 265 -6.91 47.75 6.91 0.027
303 441 -137.58 18928.2564 137.58 0.454 303 329 -26.20 686.44 26.20 0.086
370 494 -124.21 15428.1241 124.21 0.336 370 388 -18.22 331.97 18.22 0.049
395 536 -141.16 19926.1456 141.16 0.357 395 431 -35.77 1279.49 35.77 0.091
386 531 -144.56 20897.5936 144.56 0.375 386 411 -24.73 611.57 24.73 0.064
292 450 -157.57 24828.3049 157.57 0.540 292 302 -10.23 104.65 10.23 0.035
284 441 -157.32 24749.5824 157.32 0.554 284 279 4.58 20.98 4.58 0.016
370 532 -162.09 26273.1681 162.09 0.438 370 381 -11.30 127.69 11.30 0.031
Sum up 200792.964 1515.29 4925.41 218.10
MSE 16732.747 MAD 126.274 MSE 410.451217 MAD 18.175

19
According to the below Table 16, the ARIMA (0, 1, 2) model produces smaller normalised
BIC than ARIMA (2, 1, 0). Moreover, the Ljung-Box Q test is 0.773 which is not significant.
With regards of MA lag1 and lag2, both of them are significant to the models (Appendix
2.4), therefore, no need to remove any of them.
Table 16: Summary of ARIMA Models
ARIMA Model Normalised BIC Ljung-Box Q
(2, 1, 0) 6.431 0.578
(0, 1, 2) 6.414 0.773
Model overfitting test summary shows in Appendix 2.5. Table 17 indicates that the ARIMA
(0, 1, 2) indications a more admirable normalised BIC of 6.141whereas the ARIMA (1, 1, 2)
model and the ARIMA (0, 1, 3) show the AR lag1 and MA lag2 are not significant, which
means they are not a good expansionary to this model. Thus, these overall results in over-
fitting models need to reduce back to ARIMA (0, 1, 2) which is now evidently proven to be
the best model with the ARIMA models described.
Table 17: Summary of Overfitting models
(0, 1, 2) 6.414
(1, 1, 2) 6.465
(0, 1, 3) 6.459
Appendix 2.6 reveals the forecasting plots for model checking, and the ARIMA (0, 1, 2)
shows a higher degree of intersection level. By comparing Linear and ARIMA (0, 1, 2) MSE
and MAD result, the latter is the ideal model for forecasting the demand of Wallet because it
displays a smaller MAD result of 15.814 comparing with 267.333. To conclude, the Wallet
forecasting demand should be generated by this ARIMA model.
Wallet Cubic trend model ARIMA (0, 1, 2)
758 568 189.76 36008.8576 189.76 0.250 758 774 -16.38 268.30 16.38 0.022
748 575 172.71 29828.7441 172.71 0.231 748 801 -53.30 2840.89 53.30 0.071
660 439 221.47 49048.9609 221.47 0.336 660 663 -3.16 9.99 3.16 0.005
710 458 251.78 63393.1684 251.78 0.355 710 694 16.44 270.27 16.44 0.023
692 391 300.75 90450.5625 300.75 0.435 692 673 18.85 355.32 18.85 0.027
803 514 288.93 83480.5449 288.93 0.360 803 785 17.99 323.64 17.99 0.022
717 464 253.18 64100.1124 253.18 0.353 717 735 -17.95 322.20 17.95 0.025
734 460 273.66 74889.7956 273.66 0.373 734 747 -12.50 156.25 12.50 0.017
741 443 298.37 89024.6569 298.37 0.403 741 739 2.34 5.48 2.34 0.003
725 424 301.01 90607.0201 301.01 0.415 725 740 -14.63 214.04 14.63 0.020
736 422 314.31 98790.7761 314.31 0.427 736 751 -14.55 211.70 14.55 0.020
807 465 342.07 117011.885 342.07 0.424 807 809 -1.68 2.82 1.68 0.002
Sumup 886635.084 3208 4980.91 189.77
MSE 73886.257 MAD 267.333 MSE 415.075508 MAD 15.814

20
2.7. Brief Data Analysis And Final Model For Digibag Production Line
The Appendix 3.1 shows there is a slow upper wards trend of Digibag sales data, and the
first difference can remove this trend-cycle. From the summary of regression with dummy
variable (Table 18), the Cubic model contributes the highest adjusted r2
result (0.936), but
the time3
is not a good expansionary of this model (Appendix 3.2), thus is should be removed
and the linear model becomes the best model over the three. All regression model details can
be found in Appendix 3.2.
Linear 0.935 100.57 0.697
Quadratic 0.934 91.988 0.701
Cubic 0.936 87.456 0.737
The Forcasting_1 equation for Wallet is as below:
Forecasting_1 = 393.013+1.176 * Time-38.605 * M_1-76.496 * M_2-105.243 * M_3-
163.705 * M_4-187.167 * M_5-161.629*M_6-96.949M_7-89.268 * M_8 -100.301 * M_9-
93.763 * M_10-55.538*M_11
About the ACF and PACF of SAS in Appendix 3.3, the SAS data might content trend-cycle,
and it is not stationary for ARIMA model building. Hence, the first difference of the SAS is
used to remove the trend-cycle, and it assists in identifying the ARIMA models. The outcome
of the Table 19 produced for the normalised BIC shows that the ARIMA (0, 1, 3) produce
smaller BIC value of 5.044. The detail of ARIMA models output can be found at Appendix
3.4.
ARIMA
Model
MAE Normalised BIC Ljung-Box Q
(3, 1, 0) 8.733 5.141 0.479
(0, 1, 3) 8.125 5.044 0.767
The Table 20 below compared the overfitting results of ARIMA (0, 1, 3). This chart
concludes the normalised BIC result from Appendix 3.5. The test shows that the overfitting
models do not provide a better BIC value than the original ARIMA (0, 1, 3). Hence, the
forecasting_2 result generates by ARIMA (0, 1, 3).

21
(0, 1, 3) 5.044
(1, 1, 3) 5.109
(0, 1, 4) 5.109
By comparing MSE and MAD results of linear trend model and the ARIMA (0, 1, 3). The
linear trend model is better than the ARIMA because it generates a smaller value than
ARIMA.
2.8. Brief Data Analysis And Final Model For Camcorder Product Line
Appendix 4 reveals SPSS result for Camcorder forecasting. The data examines the trend-
cycle, seasonal patterns as well as the irregular components in this plot (Appendix 4.1). The
upwards trend and up down up cycle are found. In addition to this the magnitude of the
seasonal and irregular components are directly related to the size of the data values. The
dummy variable time and months are created for regression model building.
Table 21 concludes the regression result of adjusted r2
from Appendix 4.2 SPSS output. In
reference to the summarised results, the quadratic and cubic capture the same amount of data
(97.7%). However, the Appendix 4.2.3 reveals that time3 has a significant result of 0.386
which is far more beyond the 5% confident level. Therefore, the quadratic model generates
forecasting_1 results.
Linear 0.976 392.579 1.427
Quadratic 0.977 312.862 1.500
Cubic 0.977 289.72 1.513
Digibag Linear trend model ARIMA (0, 1, 3)
438 437 0.57 0.3249 0.57 0.001 438 441 -2.82 7.95 2.82 0.006
490 494 -4.15 17.2225 4.15 0.008 490 508 -18.19 330.88 18.19 0.037
463 457 6.28 39.4384 6.28 0.014 463 471 -8.10 65.61 8.10 0.017
427 420 6.99 48.8601 6.99 0.016 427 423 3.74 13.99 3.74 0.009
382 392 -10.43 108.7849 10.43 0.027 382 391 -8.83 77.97 8.83 0.023
334 335 -1.15 1.3225 1.15 0.003 334 325 8.61 74.13 8.61 0.026
304 313 -8.86 78.4996 8.86 0.029 304 299 4.61 21.25 4.61 0.015
333 340 -6.58 43.2964 6.58 0.020 333 328 4.57 20.88 4.57 0.014
381 405 -24.43 596.8249 24.43 0.064 381 410 -28.63 819.68 28.63 0.075
409 414 -5.29 27.9841 5.29 0.013 409 413 -3.74 13.99 3.74 0.009
400 404 -4.43 19.6249 4.43 0.011 400 406 -6.08 36.97 6.08 0.015
410 412 -2.15 4.6225 2.15 0.005 410 412 -2.12 4.49 2.12 0.005
Sumup 986.8057 81.31 1487.79 100.04
MSE 82.2338083 MAD 6.776 MSE 123.98245 MAD 8.337

22
The equation of Camcorder forecasting_1 is:
Forecasting_1 = 267.963+1.233*time-0.003*Time2-46.622*M_2-124.102*M_3-
122.827*M_4-177.421*M_5-14.384*M_6-39.545*M_8-47.118*M_9-20.310*M_10-
22.149*M_11
With the aim of building ARIMA model for forecasting, multiplicative classical
decomposition (Table 22) removes the seasonal effect to smooth out raw data. Consequently,
the ARIMA (10, 1, 0), ARIMA (2, 1, 0) and ARIMA (0, 1, 2) are candidates models
(Appendix 4.4). By concluding these models, ARIMA (0, 1, 2) arrange for the smallest BIC
value at 4.540. ARIMA (0, 1, 2) is the idea model for forecasting_2.
ARIMA Model MAE Normalised BIC Ljung-Box Q
(10, 1, 0) 6.273 4.999 0.192
(2, 1, 0) 7.111 4.654 0.083
(0, 1, 2) 6.348 4.540 0.317
Table 23 below summarised overfitting result of ARIMA models. The normalised BIC
results from Appendix 4.5. The test reveals that the overfitting medals do not have a smaller
BIC value than the original model. Therefore, the forecasting_2 result generated by ARIMA
(0, 1, 2).
(0, 1, 2) 4.540
(1, 1, 2) 4.601
(0, 1, 3) 4.602
According to the MAD analysis, the Linear trend model creätes a smaller MAD (9.165 <
9.602) results than ARIMA (0, 1, 2). However, the MSE provides an opposite result with
MAD, which the ARIMA gives a much smaller value amount (121.081583 < 351.0955).
With the aim of parsimony principle, the ARIMA (0, 1, 2) is choosing for Camcorder demand
forecasting.

23
2.9. Results of Demand Forecasting And Assumptions For Model Building.
While selects the final models, the SPSS package presents reliable prediction results for
eighteen months from November 2016 to April 2018 for every product line. Regarding
designing cost-effective production processes, for each line, the monthly demand is provided
as Table 24.
Table 24: 18 months demand forecasting
Year Month Accessory SLR Wallet Digibag Camcorder
2016 11 309 367 794 452 343
12 310 396 826 508 362
2017 1 207 396 682 471 370
2 200 248 712 434 317
3 251 219 692 407 225
4 248 279 808 349 228
5 276 316 756 327 235
6 270 370 768 354 357
7 278 347 760 420 381
8 211 250 761 428 330
9 202 220 772 419 318
10 256 315 832 426 359
11 319 375 814 466 356
12 320 404 847 522 375
2018 1 217 405 699 485 384
2 211 254 730 448 329
3 262 224 710 421 234
4 258 285 828 363 236
Camcorder Quadratic trend model ARIMA (0, 1, 2)
336 329 7.06 49.8436 7.06 0.021 336 326 9.51 90.44 9.51 0.028
352 352 0.19 0.0361 0.19 0.001 352 353 -0.96 0.92 0.96 0.003
346 353 -6.53 42.6409 6.53 0.019 346 357 -10.93 119.46 10.93 0.032
311 307 4.39 19.2721 4.39 0.014 311 304 6.61 43.69 6.61 0.021
237 230 7.16 51.2656 7.16 0.030 237 218 19.50 380.25 19.50 0.082
232 232 0.19 0.0361 0.19 0.001 232 220 12.42 154.26 12.42 0.054
240 178 62.1 3856.41 62.1 0.259 240 227 13.30 176.89 13.30 0.055
348 342 6.38 40.7044 6.38 0.018 348 344 3.73 13.91 3.73 0.011
357 357 0.31 0.0961 0.31 0.001 357 367 -10.28 105.68 10.28 0.029
320 318 2.19 4.7961 2.19 0.007 320 318 2.29 5.24 2.29 0.007
323 311 12.09 146.1681 12.09 0.037 323 306 16.86 284.26 16.86 0.052
337 338 -1.37 1.8769 1.37 0.004 337 346 -8.83 77.97 8.83 0.026
Sum up 4213.146 109.96 1452.98 115.22
MSE 351.0955 MAD 9.163 MSE 121.081583 MAD 9.602

24
With the aim of producing reliable models for forecasting, there are some assumptions need
to make. For instance, while building the forecasting models, it assumes that the irregular
components are stuffing white noise which means there is no useful information. However, in
reality, models tried above cannot capture all the information for forecasting. For instance,
the occasional change of sales during 1998 and 2008 might occur due to the financial crisis.
Moreover, model building assumes the prediction is consistent over time. Seasonal factors
eventually accurately correspond year by year, but these factors are changed from time.
Business forecasting is a formal science and principle meteorology with pragmatism rather
than only refer to informal intuition, which would lead to more accurate predictions and more
efficient analyzing and planning (Ord and Fildes, 2013). However, forecasting is usually a
weak relation of more theoretical statistical data in regression and time series (Gilliland,
2002). Therefore, assuming that sale and stock have partial knowledge of the LC case, they
can identify potential future value by forecasters and salesmen. Sanders and Ritzman (1995)
state that despite this way support good results for time series with a low variation
coefficient.
Nevertheless, business forecasting is not a single methodology to consider information in the
downstream or upward part of the forecasting processes (Fildes et al., 2008). In other words,
where disclosed different combinations of forecasting and other methods are needed. For
instance, decision makers in LC management team can consider expected value for
probability distribution analysis. Moreover, Harvey (2007) argues that this practice is
criticised as its informal nature is increasing accuracy information. Due to the uncertainty of
future sales data, management refers to forecasting demand with the management experience
to allocate capacity
3. Simulation
Simulation is an assumption, which is usually taken account into as a system of mathematical
or logical relationships with the computer (Law et al., 1991). In the LC case, simulation
designing is aimed to analysing manufacturing, business processes, stock and transportation
systems. However, there are some impediments in the simulations.
First, a large size system is so complex and writing computer programs could cause an
arduous task. The second issues are that some complex systems need to spend the amount of
computer time. Third, to simulate a thorough understanding is required awareness of all the
factors and assumptions involved. Therefore, an efficient measurement, it needs to consider
all around unknown conditions (Gosenpud and Washbush, 2014).
On the other hand, the simulation has several advantages exist in below areas. Robinson
(2014) argue that the primary strength is that simulation can support practical feedback when
implement a system. For example, variability, stochastic nature of parameters. In addition,
these simulations need a high level component with the system and counteract complexity of

25
the whole system. This complexity includes too many variables and scenarios and all of them
need to assume whether data correct or not.
Additionally, Kinghorn (2013) suggested that the simulation methods have the
interconnectedness which provides inferences between earlier stages and later stages. If
assume the simulation is the best way to proceed, the next step is to choose simulation
approaches. Usually, such as system dynamics (Repenning, 2002; Rudolph & Repenning,
2002) and NK fitness,landscapes (Levinthal, 1997; Rivkin & Siggelkow, 2003). Others are
less frequently used, such as genetic algorithms (Bruderer & Singh, 1996) and cellular
automata (Lomi & Larsen, 1996). Each of these is a designed approach that obliges the
theoretical logic, assumptions, and research questions that can be explored.
Simulation modelling is the artificial practice of an operation in the real world process in time,
the management of company could make the best decision helping a company running more
efficiency. When completed the operation of the model results can be studied, which any
properties concerning the behaviour of the actual process can be pointed out. In short, it is the
process of experimenting with a computerised mathematical model. Based on analysis results,
it will be applied before the system runs in reality, and in this way, the chances of failure to
meet specifications, the elimination of unforeseen bottlenecks, the over-utilization of
resources, and the optimal system performance can be achieved. Within this report, it will use
the Excel to simulate LC Company of 100 batches in operating circumstances to estimate the
production time and inspection time of each batch.
In relation to the case study, it is clearly identified that LC have five production lines, which
consists of; Wallet, Digi-Bag, SLR Bag, Camcorder Bag, Accessory Bag. Each production
line has two dedicated operators and two quality inspectors all five lines, which are available
65% of their possible time. Table 25, 26, 27, 28, 29 show activities of how the bags are
produced. To provide sensible estimations close to a real life scenario function. For
production lines the data obtained from the task brief data will be used to generate an excel
spreadsheet to assess how much operator's and inspectors time it takes to produce one batch
and evaluate how many batches LC can produce per month. In addition to this, the data
captured would be used in the linear programming function (Supply constraint).

26
3.1. Entities, Activities, And Excel Plots
3.1.1. Wallet Product Line:
Table 25: Wallet Product Line
Entities Activities
Operators Cut single piece of material, folding and sewing, first quality inspection,
rework after the first inspection, sew velcro fastenings, attach hooks, second
quality inspection, rework after the second review, attach logo and card
hanger
Inspectors First inspection, second inspection
3.1.2. Digibag Product Line:
Table 26: Digibag Product Line
Entities Activities
Operators Cut back piece of material, Sew on belt loop, Cut the first piece of material,
Attach small velcro pocket, Cut longer piece of material, Attach zip to side
piece, Rework after the first inspection, Sew three pieces together, Add hook,
Rework after the second inspection, Attach logo and card hanger
Inspectors First inspection, Second Inspection
3.1.3. SLR Bag Product Line:
Table 27: SLR bag Product Line
Entities Activities
Operators Cut back piece of material, Sew on belt loop, Cut the first piece of material,
Attach small velcro pocket, Cut longer piece of material, Attach zip to side
piece, Rework after the first inspection, Sew three pieces together, Add hook,
Rework after the second inspection, Attach logo and card hanger

27
3.1.4. Camcorder Bag Product Line:
Table 28: Camcorder bag Product Line
Entities Activities
Operators Cut side pieces, attach pockets to both side pieces, cut front piece of material,
attach zipped pockets, cut back piece, sew on belt hook, attach zip to back
piece, first quality inspection, rework after first quality inspection, sew three
pieces together, attach hooks, second quality inspection, rework after second
inspection, attach logo and card hanger
3.1.5. Accessory Bag Product Line:
Table 29: Accessory Bag Product Line
Entities Activities
Operators Cut side pieces, attach pockets to both side pieces, cut front piece of material,
attach zipped pockets, cut back piece, sew on belt hook, attach zip to back
piece, first quality inspection, rework after first quality inspection, sew three
pieces together, add partition, attach hooks, second quality inspection, rework
after second inspection, attach logo and card hanger
The simulation model is established by the suitable data in each activity. The Table 30 below
shows the simulation results for each product line's production capacity. It is essential that,
the LC has two dedicated operators for each product line and the standard production time of
the LC is 150 hours per employee and overtime of 30 hours per employee. Therefore, the
standard production capacities and the overtime capacities need to be simulated by this model
with 150 hours and 30 hours of limitation and 65% of available time.
Table 30: Current Production Capacity Summary
Production line Normal
time capacity
(65% 300hrs)
Overtime
capacity
(65% 60hrs)
Total capacity
Wallet 641 130 771
Digibag 437 85 522
SLR 398 80 478
Camcorder 297 59 356
Accessory 244 49 293
Total capacities 2017 403 2420
The Table 31 below shows (next page) the process of how simulation is worked out. This is
showing the product of the accessory bag.

28

4. Linear Program Modelling
Linear programming (LP) is a best result（highest profit or lowest cost）in a mathematical
model which is based on a linear relationship. Generally, the LP is involved numerous of the
central concepts of optimization theory, for example, duality, decomposition, and the
importance of convexity (Wong and Beasley, 1990). For duality, it is possibly show two
perspectives, the primal and dual problem. A good dual problem would achieve a lower
bound in the results of the primal problem (Boyd et al., 2004). However, in practice, the
optimal value of the primal dual problems is not equal.
Therefore, it is required to build mathematical models for LP. First, according to influence
coefficient make decision variables and then combine different decision variables to make an
objective function. The last step, the constraint conditions should fit decision variables’
constraint (Minoux, 1986). While LP exists a weak about time, which no algorithms have yet
been found that allow strongly polynomial-time performance in the number of constraints and
the number of variables (Smale, 2012).
Hence, this LP model needs use together with other models in order to acquire data of
constraints and variables. In this LC Cases, it is built 90 decision variables in five different
products. So the problem is characterised by the 18 possible activities of each product from
various decision variables.
A problem is that the possible activities are manufacturing different products and stock
levels. The future level of supply and demand constraints need to find other combinations. In
addition to that, Dantzig (1998) state that the LP problem is scheduling activities through
time, which discuss about workers and output of each product between teaching and
production, and between over- and under – production in order to minimise cost.
The decision variables in linear programming are the set of quantities that need to be
determined in command to solve a problem; solving problems once the best values have been
identified. A decision variable decides what value each variable should take. In the case of
the LC Company which produces five product lines, the decision variables are 1) Regular
production; 2) Overtime Production and 3) Storage cost.
The Objective Function specifies how much each variable contributes to the value in the
optimised problem. The Objective Function is the minimising cost for five production line
and storage of finished goods.
Constraints can be equalities and inequalities of supply and demand, in the case of the supply
are normal output and overtime production. Demand is also a constraint of what the market
need.

30
Overall, this section will solve problems under supply and demand constraints (Table 31). It
helps Leicester Cases make decisions under different limitations and solving staffing
problems can calculate the number of staff needed in LC for production.
Product
Cost (£/batch)
Normal production
cost
Overtime
production cost
Storage cost
Wallet 60 90 6
Digibag 110 165 11
SLR 120 180 12
Camcorder bag 130 195 13
Accessory bag 160 240 16
Table 31: The Production and storage cost of five product lines
4.1. Conceptual Modeling
Decision to be made: Volume of standard production and sum of overtime
production of five products need to be produced in next 6
months
Objective: Minimise total cost
Constraints: 1. Normal production capacity limit,
2. Overtime production capacity limit,
3. Storage size limit,
4. Encounter the demand in each month,
5. Non-negativity restrictions.

31
4.2. Mathematical Modelling
4.2.1. Define Decision Variables
Xij = Regular production of product line i in month j,
i=W, D, S, C, A; j=1, 2, 3, 4, 5, 6.
Yij = Overtime production of product line i in month j,
i= W, D, S, C, A; j=1, 2, 3, 4, 5, 6.
Zij = Extra production of product line i left as inventory at the end of month j,
i= W, D, S, C, A; j=1, 2, 3, 4, 5, 6.
4.2.2. Objective Function Formulating
Minimize Cost = Normal production cost+ Overtime production cost+ Storage cost
Normal production cost: 60 * (XW1 + XW2 + XW3 + XW4 + XW5 + XW6)+
110 * (XD1 + XD2+ XD3 + XD4 + XD5 + XD6)+
120 * (XS1 + XS2 + XS3 + XS4 + XS5 + XS6) +
130 * (XC1 + XC2 + XC3 + XC4 + XC5 + XC6) +
160 * (XA1 + XA2 + XA3 + XA4 + XA5 + XA6)
Overtime production cost: 90 * (YW1 + YW2 + YW3 + YW4 + YW5 + YW6) +
165 * (YD1 + YD2 + YD3 + YD4 + YD5 + YD6) +
180 * (YS1 + YS2 + YS3 + YS4 + YS5 + YS6) +
195 * (YC1 + YC2 + YC3 + YC4 + YC5 + YC6) +
240 * (YA1 + YA2 + YA3 + YA4 + YA5 + YA6)
Storage cost: 6* (ZW1 + ZW2 + ZW3 + ZW4 + ZW5 + ZW6) +
11 *(ZD1 + ZD2 + ZD3 + ZD4 + ZD5 + ZD6) +
12* (ZS1 + ZS2 + ZS3 + ZS4 + ZS5 + ZS6) +
13 *(ZC1 + ZC2 + ZC3 + ZC4 + ZC5 + ZC6) +
16 *(ZA1 + ZA2 + ZA3 + ZA4 + ZA5 + ZA6)
4.2.3. Constraints Formulating
Production Capacity:
Due to the current production situation of LC, the batches of production for each month for
each product line need within the monthly production capacity (Table 32).
Normal Production Limit Overtime Production Limit
XW1 ≤ 641 YW2 ≤ 130 Month:1.2.3.4.5.6
XD1 ≤ 437 YD1 ≤ 85 Month:1.2.3.4.5.6
XS1 ≤ 398 YS1 ≤ 80 Month:1.2.3.4.5.6
XC1 ≤ 297 YC1 ≤ 59 Month:1.2.3.4.5.6
XA1 ≤ 244 YA1 ≤ 49 Month:1.2.3.4.5.6

32
Table 32: Five products capacity in first 6 months
Month Normal Production Overtime Production
WALLET DIGIBAG SLR CAMCORDER ACCESSORY WALLET DIGIBAG SLR CAMCORDER ACCESSORY
Oct-16 641 437 398 297 244 130 85 80 59 49
Nov-16 647 431 397 297 247 129 86 80 59 49
Dec-16 650 431 398 293 244 131 85 81 60 48
Jan-17 644 427 397 297 244 131 85 80 59 49
Feb-17 651 434 398 295 243 131 86 80 59 48
Mar-17 637 437 398 297 244 130 85 80 59 49
Storage Capacity:
The LC’s optimum level of storage is 300 batches. Thus, the monthly figure of inventory is 5
product lines cannot be excess 300 batches.
ZW1+ZD1+ZS1+ZC1+ZA1 ≤ 300
Products Demanding:
Within each month the total figure of production amount (from both normal and overtime
period) plus opening inventory and minus closing inventory need to satisfy the next month
demand.
1) Wallet forecasted demand
XW1 + YW1 – ZW1 + 50 = 794 (November 2016)
XW2 + YW2 – ZW2 + ZW1 = 826 (December 2016)
XW3 + YW3 – ZW3 + ZW2 = 682 (January 2017)
XW4 + YW4 – ZW4 + ZW3 = 712 (February 2017)
XW5 + YW5 – ZW5 + ZW4 = 692 (March 2017)
XW6 + YW6 – ZW6 + ZW5 = 808 (April 2017)
2) Forecasted demand for Digibag
XD1 + YD1 – ZD1 + 50 = 452 (November 2016)
XD2 + YD2 – ZD2 + ZD1 = 508 (December 2016)
XD3 + YD3 – ZD3 + ZD2 = 471 (January 2017)
XD4 + YD4 – ZD4 + ZD3 = 434 (February 2017)
XD5 + YD5 – ZD5 + ZD4 = 407 (March 2017)
XD6 + YD6 – ZD6 + ZD5 = 349 (April 2017)

33
3) Forecasted demand for SLR bag
XS1 + YS1 – ZS1 + 50 = 367 (November 2016)
XS2 + YS2 – ZS2 + ZS1 = 396 (December 2016)
XS3 + YS3 – ZS3 + ZS2 = 399 (January 2017)
XS4 + YS4 – ZS4 + ZS3 = 248 (February 2017)
XS5 + YS5 – ZS5 + ZS4 = 219 (March 2017)
XS6 + YS6 – ZS6 + ZS5 = 279 (April 2017)
4) Forecasted demand for Camcorder bag
XC1 + YC1 – ZC1 + 50 = 343 (November 2016)
XC2 + YC2 – ZC2 + ZC1 = 362 (December 2016)
XC3 + YC3 – ZC3 + ZC2 = 370 (January 2017)
XC4 + YC4 – ZC4 + ZC3 = 317 (February 217)
XC5 + YC5 – ZC5 + ZC4 = 225 (March 2017)
XC6 + YC6 – ZC6 + ZC5 = 228 (April 2017)
5) Forecasted demand for Accessory bag
XA1 + YA1 – ZA1 + 50 = 309 (November 2016)
XA2 + YA2 – ZA2 + ZA1 = 310 (December 2016)
XA3 + YA3 – ZA3+ ZA2 = 270 (January 2017)
XA4 + YA4 – ZA4 + ZA3 = 200 (February 2017)
XA5 + YA5 – ZA5 + ZA4 = 251 (March 2017)
XA6 + YA6 – ZA6 + ZA5 = 248 (April 2017)
Non-Negativity Constraints:
The production and storage figure shall not be under zero, thus, as there are non-negativity
limitations.
Xij ≥ 0 ; i=W, D, S, C, A; j=1, 2, 3, 4, 5, 6 ;
Yij ≥ 0 ; i=W, D, S, C, A; j=1, 2, 3, 4, 5, 6 ;
Zij ≥ 0 ; i=W, D, S, C, A; j=1, 2, 3, 4, 5, 6.
4.3. Results Of Linear Programming
The model produced identifies the linear programming optimum results which would be
attained by using Excel Solver (Appendix 5.1). Regarding the future demands (forecasting
results) and the current capacity (simulation results), the recommended production schedule
is shown as below (Table 33).

34
Table 33: Linear Programming Results
Month Stock
WALLET DIGIBAG SLR CAMCORDER ACCESSORY
Oct-16 27 0 0 9 14
Nov-16 0 9 81 3 0
Dec-16 77 54 83 0 85
Jan-17 82 79 139 0 0
Feb-17 41 0 0 0 0
Mar-17 0 0 0 0 0
Table 34: Current supply compare with demands
In this case (Table 34), LC can maximise its profit through production cost is minimal of
£1,330,161, which is at the lowest level. Nevertheless, it finds in this production plan is not
the optimal solution for LC. As can be seen from Table 29, LC used lots of overtime to meet
the current demand. Production in overtime costs is 50% more than normal production time.
Meanwhile, the supply of camcorder and accessory cannot fully meet the demand. As the
results, LC need consider change current production capacity to decrease the cost and
improve the space for profit.
Supply vs Demand Supply vs Demand Supply vs Demand Supply vsDemand Supplyvs Demand Supply vs Demand
Wallet 794 = 794 803 < 826 682 = 682 712 = 712 692 = 692 808 = 808
Digibag 452 = 452 508 = 508 471 = 471 434 = 434 407 = 407 349 = 349
SLR 367 = 367 396 = 396 396 = 396 248 = 248 219 = 219 279 = 279
Camcorder 343 = 343 362 = 362 356 < 370 317 = 317 225 = 225 228 = 228
Accessory 309 = 309 310 = 310 207 = 207 200 = 200 251 = 251 248 = 248
Product
Nov-16 Dec-16 Jan-17 Feb-17 Mar-17 Apr-17
Oct-16 641 402 317 297 244 130 0 0 5 29
Nov-16 647 431 397 297 247 129 86 80 59 49
Dec-16 650 431 398 293 244 109 85 0 60 48
Jan-17 644 427 304 297 155 73 32 0 20 0
Feb-17 651 328 0 166 203 0 0 80 59 48
Mar-17 637 264 199 169 199 130 85 80 59 49

35
4.4. Current Production And Stock Level Of LC
According to LP solver solution, Table 35 shows the LC current supply, demand and stock
level. From looking at the chart below the opening stock for October 2016 start with 50
batches of each type of case. An example of the Wallet Bag in November 2016 the closing
stock is 803 and the demand for next month (forecasted) is 826 this leaves a difference of 23,
indicating a loss of batches that could have been sold, in theory, the supply cannot meet the
demand. In relation to November 2016, the Digibag, SLR and Camcorder has over
production of a batch which indicates more batches would be produced than needed,
indicating high inventory costs and risk of obsolescent. And so on, the rest of data refers to
the same methodology for production situation.
Table 35: Current production schedule
Date Items Wallet Digibag SLR Camcorder Accessory
Oct-16 Opening stock 50 50 50 50 50
Normal production 641 402 317 297 244
Overtime production 130 0 0 5 29
Closing stock 821 452 367 352 323
Next month demand 794 452 367 343 309
Over stock 27 0 0 9 14
Under stock 0 0 0 0 0
Nov-16 Opening stock 27 0 0 9 14
Closing stock 803 517 477 365 310
Dec-16 Opening stock 0 9 81 3 0
Closing stock 759 525 479 356 292
Over stock 77 54 83 0 85
Jan-17 Opening stock 77 54 83 0 85
Closing stock 794 513 387 317 200
Over stock 82 79 139 0 0
Feb-17 Opening stock 82 79 139 0 0

36
Closing stock 733 407 219 225 251
Mar-17 Opening stock 41 0 0 0 0
Closing stock 808 349 279 228 248
5. Link Between LP, Simulation And Forecasting
From above section statements, there are clearly illustrate that LP, Simulation and
Forecasting are all mathematical method models, which require the best model building and
model choice. In these three models, the LP is a middle linkage between Simulation and
Forecasting. Reich (2013) reviewed that LP is limited by formulations in supply chain
especially. The different formulations are decided by various supply chains and demand
relationship.
Similarly, Luedtke (2010) agree that chance- constraints would raise decomposition approach
and programming simulation with valid methods. It is recommended link figure 15 of these
three models. The Forecasting is aimed that to create a future data of demand, which is for
sake of introduction of the formal approach.
Comparison with Forecasting, Oliveira (2016) thinks that hybrid simulations containing
normative models and empirical applications can be useful to represent the reality of supply
chains, generating alternative solutions that improve supply chain performance. Hence,
according to the staff and production lines to distribute capacity and ensure the best supply
and demand constraints of whole manufacturing processes.
Nonetheless, Carotenuto et al. (2014) argue that the efficiency of modelling and simulation
are based on the accuracy of the forecasting methodology. Therefore, making accurate
assumptions is a significant part of modelling process. The basis of accurate forecasting and
simulation, the LP will develop a cost-effective production scheduling in order to achieve
minimum cost.

37
Figure 15: The Link between Forecasting, Simulation and LP.
In this LC case, the demand comes from Forecasting section. After 5 steps building and
check, it clearly indicate the next 18 months’ demand data. Based on this data, the LC have
estimated the future demand constraints so LC could make properly production schedule to
ensure meet the future demand. In order to answer process question, LC should assume a
series of production problems. However, a number of decisions variables (90) cause an
analysing difficulty because the supply is impacted by time and other factors, such as staff
numbers, relationships and work efficiency.
Thus, LC cases have to find other tools to evaluate the model feasible solution. In this case,
Linear Programming plays an important role in these modelling building. It can solve
complicated issues like the relationship of demand, supply and stock. In other words, the LP
could support a comparison between over- production and under- production. In addition to
that, the objective function is necessarily for LC minimum total cost, but different reasons
would influence various situations in different environments. Hence, in the next section, LC
will continue to discuss what scenarios would give rise to the fluctuation of capacity,
profitability and cost.
6. Scenarios Analysis
Among analysing the existing production capacity, it nearly meets the predicted demand for
next six months (from November 2016 to April 2017) for operators' time and stock kept the
lower level. According to simulation and LP result, the total supply from the five production
line is 2017 batches in October 2016, and the simulation result reveals that two inspectors in
LC can inspect 3442 batches in total per month, where 2868 (2 x 150 x 65% / 0.068) batches
can be done by the normal time and 574 (2 x 30 x 65% / 0.068) batches can be done by the
overtime for working. Thus, in these scenarios analysis, we undertake that inspectors’ time is
enough for next two years because they can meet current inspection demand without using
any overtime.
Forecasting
(Demand)
Simulation
(Supply)
Linear
Programming
(Minimize the cost)

38
However, for the purpose of achieving the cost-effective for the company, there are two
primary reasons to conduct the Scenarios analysis.
1. As can be seen from Table 36, LC utilising almost all overtime of operators, the demand
for the five production lines are nearly meet. Namely, from the conclusion in Table 37, there
are only two operation lines produced a slightly lower level of batches than demand, the
Wallet in Dec-16 and the Camcorder in Jan-17.
2. Overtime was 1.5 times cost of the standard production cost. Scenarios analyses in this
section focus on situations which might reduce the cost of production for the Leicester Cases.
Table 36: Current production schedule
Table 37: Current supply and demand situation
The following Scenario 1 to Scenario 9, it can refer to Appendix 5.2-5.9. All of its
production capacities are meet demand.
6.1. Scenario 1
 Two operators and increase efficiency to 75%
The Scenario 1 (Appendix 5.2) considers to increasing working efficiency from 65% to 75%
among training operators or draw up incentive mechanism like performance related pay.
Therefore, LC does not need to use overtime production to meet the demand. Improving the
efficiency of the production line, the overall cost of production is reduced by 6.17%
comparing with the current situation.
Along with the Table 38 conclusion, Scenario 1 uses very little overtime production, which
only on Wallet (76 batches) and Accessory (9 batches) in November 2016 and Camcorder (17
Supply vs Demand Supply vs Demand Supply vs Demand Supply vsDemandSupplyvs Demand Supply vs Demand
Wallet 794 = 794 803 < 826 682 = 682 712 = 712 692 = 692 808 = 808
Digibag 452 = 452 508 = 508 471 = 471 434 = 434 407 = 407 349 = 349
SLR 367 = 367 396 = 396 396 = 396 248 = 248 219 = 219 279 = 279
Camcorder 343 = 343 362 = 362 356 < 370 317 = 317 225 = 225 228 = 228
Accessory 309 = 309 310 = 310 207 = 207 200 = 200 251 = 251 248 = 248
Product
Nov-16 Dec-16 Jan-17 Feb-17 Mar-17 Apr-17
Oct-16 641 402 317 297 244 130 0 0 5 29
Nov-16 647 431 397 297 247 129 86 80 59 49
Dec-16 650 431 398 293 244 109 85 0 60 48
Jan-17 644 427 304 297 155 73 32 0 20 0
Feb-17 651 328 0 166 203 0 0 80 59 48
Mar-17 637 264 199 169 199 130 85 80 59 49

39
batches) on December 2016, and the total store level each month over the six months is
merely less than 60 each month.
Table 38: Two operators and increase efficiency to 75%
Current cost Scenario 1 cost Change rate
1330161 1248029 -6.17%
6.2. Scenario 2 (Best option)
 Based on Scenario 1, add one part-time operator only
Based on the Scenario 1 analysis, Leicester Cases should consider adding one more part-time
operator for the whole production line because Scenario 1 concludes that the overtime
production only needed at Wallet, Camcorder and Accessory production line but in the
different month. According to Scenario 1 solver results, on November 2016, overtime
production on wallet was 22.8 hours ( 76 batches x 0.3 hours ) and on Accessory was 7.2
hours (9 batches x 0.8 hours ). Therefore, there was only need 30 hours overtime to meet the
demand; LC could consider the employed a part-time operator to work at the different
production line. However, LC need consider making a proper training on a part-time operator
ensure he/she can working for the different product line.The summaries of the feasible
solution for scenario 2 reveals that scenario will reduce the cost by 6.48%.
Table 39: Based on Scenario 1, add one part-time operator only
1330161 1243931 -6.48%

40
According to Table 39 above, production without overtime can meet the demand of the
market for Nov-2016 to Apr-2017. Thus, this situation assumption is feasible. The inventory
cost might be very low for the same reason as Scenario 1.
6.3. Scenario 3
 Add one more operator to each production line, efficiency 65%
Table 40: Add one more operator to each production line, efficiency 65%
1330161 1242846 -6.56%
In this scenario, add one more operator in an original position, which would cause zero
overtime production and zero inventory. Basically, from above Table 40 can distinctly show
that three operators increase the production capacity. It is a fall rate when to compare with
current cost, the change rate archive 6.56%. However, this scenario is considering a fixed
demand. Once the demand relationship unstable, when the demand appears shrinkage, LC has
to pay more salary for extra operators. Hence, it is easy to raise the cost in a labour cost.
Another problem is oversupply because 3 operators would completely satisfy supply and 65%
efficiency will manufacture more products. On the other hand, the total cost result solved by
LP are not considering the unused labour cost which suggested there are significantly labour
cost for LC employed one more operator to each product line and add one more operator to 3
might cause redundant personnel.

41
6.4. Scenario 4
 Add 0.5 operator to each production line, efficiency 65%
Table 41: Add 0.5 operator to each production line, efficiency 65%
1330161 1243065 -6.55%
Comparison with scenario 3, scenario 4 will decrease 0.5 operators in each production line
when the work efficiency is 65%. From above Table 41, it is indicated that overtime
production also is zero, but the inventory (wallet) in the first month with 14 surplus stock. In
this case, the total cost was declined 6.55% compared with current cost. If use this way, add
0.5 operators, it would play the similar role with scenario 3. The scenario 4 and scenario 3
have 0.01% change rate difference. Nonetheless, the scenario 4 is the more flexible operating
method. When production capacity is enough, LC could recruit a part time operator or
production capacity is not meet demand; LC could hire an operator. By contrast, this
scenario could save more labour cost than scenario 3 . Overall, append 0.5 operator is more
moderate.
6.5. Scenario 5
 Reduce five product line’s rework rate
- 1st
time reduce to 10%; 2nd
reduce to 5%
By improving quality control process, LC should draw up strict and systematic training to
every operator. Hence, the firm can aim to reduce the rework rate and improve the
productivity. Scenario 5 based upon the assumption that the 1st rework rate can be reduced to
10% and the 2nd rework rate reduces to 5% on average. Thus the total cost of production is
3.82% lower than the current situation.
From the conclusion of Table 42, LC need a high amount of overtime on Wallet production
line, and some of the months , Digibag, Camcorder and Accessory production line also
require operators to work overtime. To summarise, the linear programming finds
mathematics solution, but, in reality, it might not unachievable because operators might be
upset by a long time working hours.

42
Table 42: Reduce five product line’s rework rate
1330161 1279332 -3.82%
6.6. Scenario 6
 Based upon the Scenario 5, add one more operator on Wallet production line
only
Since Wallet production line would need overtime production every month from the Scenario
5 result has shown, Leicester Cases could consider adding one more operator on Wallet
production line only to moderate the work in the overtime. Comparing with Scenario 5, this
option shows a better cost-efficiency result (5.19% > 3.82%).
Table 43: Based upon the Scenario 5, add one more operator on Wallet production line
1330161 1261086 -5.19%
Apart from the Table 43, the cost on another production line still including the overtime
production, however, to some degree, this scenario offers a better solution while there is a
risk of uncertain reduce the demand due to the flexibility of operators to work for overtime.
On the other hand, if operators do not intend to work overtime, the demand will not be able to
meet. To conclude, Scenario 6 is one of the candidate options to Leicester Cases because
save more cost and provide flexibility to reaction to the market.

43
6.7. Scenario 7
 Reducing rework rate- 1st
time reduce to 7%; 2nd
reduce to 3%
If the rework rate can be reduced further from Scenario 5, the bargain is further better than
output in Scenario 5 (4.05% > 3.82%). Due to that operator have more time to produce rather
than rework. However, there still need overtime production to meet demand, especially on
Wallet demand. Nevertheless, there is a challenge for LC reduce 1st time rework rate to 7%
and 2nd rework rate to 3%.
Table 44: Reducing rework rate- 1st time reduce to 7%; 2nd reduce to 3%
1330161 1276249 -4.05%
6.8. Scenario 8
 Based on 2 operators with 75% efficiency using demand from November 2017 to
April 2018
By changing the demand, this assumption exams whether the Scenario 1’s working capacity
can meet the demand in next twelve months. Amend the order quantity on the ground of
Scenario 1 is for several reasons. Firstly, scenario 1 improves the capacity among improving
the efficiency. Thus, Leicester Cases does not need to employ another operator which might
increase cost in the firm. Also, the Scenario 2’s capacity is very close to the break-even point
between supply and demand even through. Namely, it is much cheaper than Scenario 1 output.
The reason for choosing demand from November 2017 to April 2018 is to give management
a clear comparison for the same period in the year.
Table 45: 2 operators with 75% efficiency using demand from Nov 2017 to Apr 2018

44
1330161 1292643 -2.82%
Appendix 5.9 is the output of the Scenario 8 and from the table above, the capacity plausibly
meets the demand with some overtime working if the holistic demand increases 3% (six-
month forecasting demand different/ following six-month forecasting demand). The
production cost is lower than current situations
.
6.9. Scenario 9
 Cut number of inspectors (from 2 to 1.5); efficiency 65%
According to simulation analysis, the inspector takes average 0.068 hours inspect one batch
product. As the result, two inspectors could inspect 3442 batches in total per month where
normal time inspect 2868 (2 x 150 x 65% / 0.068) and overtime inspect 574 (2 x 30 x 65% /
0.068) batches. However, according to analysis the current production capacity, the total
production was 2017 batches in October 2016. Therefore, there have idle time 58 {(2868-
2017) x 0.068} hours for two inspectors.Therefore, LC could consider use inspector idle time
to increase the operator capacity.
Table 46: Scenario comparison
Plans Meet Demand Cost Decreased
Scenario 1 YES 1248029 -6.17%
Scenario 2 YES 1243931 -6.48%
Scenario 3 YES 1242846 -6.55%
Scenario 4 YES 1243065 -6.55%
Scenario 5 YES 1279332 -3.82%
Scenario 6 YES 1261086 -5.19%
Scenario 7 YES 1276249 -4.05%
Scenario 8 YES 1292643 -2.82%
Based on the above analysis, we can see from Table 46, combined with all of the cost factors,
the Scenario 2 and 6 will be a good option for LC to minimise the total cost.

45
7. Limitation Of Using The Models
7.1. Limitations Of Forecasting
Limitations have risen from assumptions while building models. Firstly, historical data is the
only information that would generate the forecasting data, but there would be no guarantee
that what events may have occurred in the past would take place in the future. This
assumption makes a good starting point but cannot solely base decisions on using forecasting
data only (Carver and Nash, 2009).
Secondly, forecasting bias is when the forecaster uses the soft information to produce data
through personal opinions to make patterns which makes allowances for current market
conditions but finding out if the forecaster is biased or not is virtually impossible and to
understand to wisely use the data produced (Fildes, 2011). For instance, during data and
model selection.
Also, making a decision on a weak forecast can affect a company into financial ruin (Carver
and Nash, 2009). The forecasted data cannot combine their impact or use it as a variable. This
statement is known as a "theoretical knot", management merely relies on historical data, but
with this information a company can use the tools such as forecasting to give vital
information about the future.
Moreover, it is known that there is no place to implement unexpected events (political
changes and weather conditions). Assumptions often made while do not have sufficient
evidence to back up the assumption itself, lots of activity occurs in pure confidentiality in
which forecasted data can only happen with accessible public data. Religious festivals change
yearly and move a week ahead, but this still does not justify how people would react to this
change (Chen, Xia and Tian, 2014).
Business can produce different scenarios depending on the interpretation of the data
predicted, and management can rely on the forecasting result as a reference demand and
combine their experience to give a ruffle prediction for future demand. Thus, LC can position
capacity for manufacturing line accurately and achieve the cost-effective management
approach.
7.2. Limitations Of Simulation
While doing these simulation models, every production line considered independently.
Therefore, it assumes that these two operators in one production line cannot work for other
production lines. In other words, if one lines facing capacity shortage problems, for example,
Wallet, they can not share the capacity from another line., but in actuality production process,
operators might switch between production line.

46
As using the software package to simulate the process, there are some drawbacks need to take
into consideration. To begin with, the analyst conducts the process requires a significant
amount of time to get the result; therefore, it might be expensive for Leicester Cases.
Furthermore, Leicester Cases should consider the degree that they can rely on the experts for
the simulation results. Additionally, the simulation model cannot completely recreate in a real
life situation, and it would need to acknowledge that not every possible situation has included
in the model can happen in the actual situation. Thus, this would depend on the judgement of
the person using the software and understand how to change elements to make a good
simulation model (Fraser, 2013)., simulation cannot provide a precise result for management
use because results are system response and it 's hard to measure.
7.3. Limitation Of Linear programming
The primary limitation for LP is that Solver only allows one hundred constraints and two
hundred variables. Which means if LC intends to add one more production line, the Solver
might not solve the problems. For instance, at the current situation, the model supports to
involve the inspectors’ time as constraints for every month. However, it has being removed
from the model since the limits of constraints were exceed the one hundred constraints in the
Excel “Solver” package. Leicester Cases might consider purchasing solver software, but it
might be very expensive.
Apart from the linear programming itself, there are several limitations in the model. Firstly,
the objective function is very hard to conclude, because, from a holistic review, the cost need
including all the production line at all the months as well as storage cost. Therefore, there is a
risk of human error during the model building process. Besides, the LP technique bases on
the hypothesis that there is a linear relationship between inputs and outputs. However, this
relationship is not always clear in the reality. In other words, there might have a quadratic
relationship between cost and sales of bags.
Furthermore, the LP is highly mathematical technique; hence, this approach requires an
explicitly specified variable. In this case, the quantity of production from each production
line at each month. The problem can be solved with a complex method to a simple method,
by the software but it requires a significant amount of calculation. In reality, most of LP
models present a trial and error solution, and its hard to find out the optimal solutions for the
reason of economic complexities. In the case of LC, analyst tries out several scenarios for the
purpose of providing various options to the management team for production decision
making.
Specifying an objective function is not an easy task as of which understanding the problem
and putting it into a mathematical form had to be done through experience and checking it
makes sense. If the objective function is wrong, the whole model would not be understood,
and wrong answers can be produced falsifying information for supporting documents related.
In addition to these understanding social, instructional, financial constraints has to be

47
correctly understood as theory cannot be put into figures very quickly and may not be directly
expressible as linear inequalities (Neumaier and Shcherbina, 2004).
The assumption of linear programming can be very misleading and more bias to inflate
results admired, an example could be the economy unpredictability on sales, but in the LP the
economy would be consistent and predictable. This assumption would be the relationship
between input and output, production and cost, and production and total revenue are expected
to be linear. The relationships between input and outputs are not always "linear" in real life
most relations are non-linear (Neumaier and Shcherbina, 2004).
Linear programming is a complicated method, which based on mathematical technique, LP
models produce a trial of expected outcome and error situations (Schrijver, 1998). When in
real life it is difficult to find optimal solution to various business cases and changing a
business case, may have started from the very beginning as old constraints would not be
understood with new business case problems
Factors such as uncertainty and weather conditions cannot be taken into consideration this
would mean that what the result would be can only be within a perfect operating condition
(Schrijver,1998).
Some situation of LP can have too many possibilities to fit into the formula; LP has no Gut
instinct and needs to review LP conclusions before acting on them (Schrijver, 1998). Once a
problem has been resolved concerning the objective function, and the constraints have been
applied to it, it becomes difficult to edit any changes in the data set, arising on account of any
change in the choice parameter this absence the anticipated flexibility (Vanderbei, 2008).
To summarise, all assumptions made during model building process leads to the limitation of
the model for some degree. Therefore, Leicester Cases management team takes the
mathematic model results as a reference to the operational management process. At the same
time, when using the mathematical modelling, these limitations show what to be aware of
exactly.

48
8. Recommendations
In this recommendation chapter, it covers in-depth assessment of the findings obtained in LC.
These recommendations cover both technical and Human Resource aspect for LC through
applying the three models. Where relevant, it will refer to related examination and highlight
the contributions of this report. Secondly, it discusses the main scenario which is highly
advised to be implemented to obtain minimum cost.
Changing the layout
A Process layout is, similar resources and processes are situated together, this is because of
convenience and the utilisation of transferring of the resources is improved (Staff know
where products are). When products information and Staff flow through the operation, it will
take a specific route to one product line to another. All staff have different needs when using
this layout taking the different route each time.
LC is recommended, to uses the process layout because the company serving different
production lines attracting different staff working on the facilities. All staff would use
different parts of the company at different times. LC Example is producing the Accessory bag,
the staff would be in the production of making the bag but may need to get more material by
having a process layout, would have a convenient poisoning of flow and layout for and ease
for staff, in which they follow a route for time saving.
In relation to the scenario section the most admirable solutions narrow down to the best two,
first increase the efficiently from 65% to 75% with the addition of another operator working
part time and second reduce the first rework rate to 10% and second rework rate to 5% with
also one more operator on the Wallet production line.
Increase efficiency from 65% to 75%
The increase of efficiently which currently is 65% to 75% and adding a part time operator for
all product lines would help fill in gaps where current over time is needed. It is known that
the overtime rate would be more expensive than normal rate of pay hence adding another
operator would be beneficial. In relation to increasing the efficiency levels from 65% to 75%
would be a challenge to LC but can be achieved through on-going training and development.
To adopt learning for efficiently operators can; Job swapping where different operators
understand how to operate each other production lines, E-learning of how to work efficiently
with the time and resources, formal staff training to understand updates to processing and
working standards, and group learning are to be considered as sharing of ideas is more
powerful. With this recommendation considered the new cost would be £1,243,931 rather
than £1,330,161 having a change of -6.48%

Group-5-Business Analysis and Management docx

Group-5-Business Analysis and Management docx

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (20)

Similar to Group-5-Business Analysis and Management docx

Similar to Group-5-Business Analysis and Management docx (20)

Group-5-Business Analysis and Management docx