Assignment 2: Operations Management - Forecasting and Control Charts

This document presents solutions to Assignment 2 from the College of Administrative and Financial Sciences, focusing on Operations Management. The assignment covers two main questions. The first question involves calculating the mean, UCL, and LCL for a given dataset and constructing a control chart to determine if a process is in statistical control. The second question deals with forecasting techniques, including the five-month moving average, weighted moving average, and exponential smoothing, applied to a dataset of weekly demand. The solution provides step-by-step calculations and explanations for each method, along with a discussion of the underlying assumptions of these forecasting models. Finally, the document includes a bibliography of relevant academic sources.

Assignment 2
College of Administrative and Financial Sciences

Table of Contents
Answer to question 1..................................................................................................................3
Answer to question 2:.................................................................................................................4
Bibliography...............................................................................................................................6

Answer to question 1
The given data set is mentioned as below:
0.01 0.01 0.0 0.04 0.01 0.01
0.00 0.01 0.02 0.02 0.03 0.03
[a] The mean proportion defective is calculated as
p=( 0.01+ 0.01+0.0+0.04 +0.01+0.01+0.0+0.01+0.02+0.02+ 0.03+0.03)
12
Or, p = 0.19/12
Or, p = 0.015833333
The UCL can be calculated as
UCL=0.015833333+ 3∗ √ 0.015833333∗(1−0.015833333)
12
Or, UCL = 0.123939666
The LCL can be calculated as
L CL=0.015833333−3∗
√ 0.015833333∗(1−0.015833333)
12
Or, LCL = -0.092272999
[b] Control Chart
UCL Data LCL CL
0.1239
4 0
-
0.0923
0.0158
3
0.1239
4 0.01
-
0.0923
0.0158
3
0.1239
4 0.02
-
0.0923
0.0158
3
0.1239
4 0.02
-
0.0923
0.0158
3
0.1239
4 0.03
-
0.0923
0.0158
3
0.1239
4 0.03
-
0.0923
0.0158
3
0.1239
4 0.01
-
0.0923
0.0158
3
0.1239
4 0.01
-
0.0923
0.0158
3
0.1239
4 0
-
0.0923
0.0158
3
0.1239 0.04 - 0.0158

4 0.0923 3
0.1239
4 0.01
-
0.0923
0.0158
3
0.1239
4 0.01
-
0.0923
0.0158
3
1 2 3 4 5 6 7 8 9 10 11 12
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Control Chart
UCL Data LCL CL
[c] Statistical control is a
State of a stabilized production process in which only common causes of variation remain (all
special causes of variation having been removed), as evidenced on a control chart by the
absence of (1) data points beyond the control limits, and (2) non-random patterns of variation.
Here, all the points are within the control limits. Therefore, it can be concluded that the
process is in control.
Answer to question 2:
The given data set is
Week 1 2 3 4 5 6
Demand 649 524 561 738 511 590
[a] The five months moving average for months 5 and 6 is given by
M5 = (649+524+561+738+511)/5 =596.6
M6 = (524+561+738+511+590)/5 =584.8

The forecast for month seven is just the moving average for the month before that i.e. the
moving average for month 6 = M6 = 584.8
[b] The demand for week 7 using a three-period weighted moving average can be calculated
as
Week 7 demand = 0.5*590 + 0.3*511 + 0.2*738
= 595.9
[c] The demand for week 7 using exponential smoothing can be calculated as below:
Ft+1 = α*Dt + (1 - α) * Ft
Where, Dt is the actual value
Ft is the forecasted value
α is the weighing factor, which ranges from 0 to 1
t is the current time period.
Here, D6 =590
F6 = 602
α = 0.1
therefore, F7 = 0.1*590 + 0.9*602 = 600.8
[d] The basic assumption behind averaging and smoothing models is that the time series is
locally stationary with a slowly varying mean.

Bibliography
Heizer, J., 2016. Operations management, 11/e. Pearson Education India.
Hitt, M.A., Xu, K. and Carnes, C.M., 2016. Resource based theory in operations management
research. Journal of Operations Management, 41, pp.77-94.
Reid, R.D. and Sanders, N.R., 2019. Operations management: an integrated approach. John
Wiley & Sons.
Slack, N., 2018. Essentials of operations management. Pearson UK.