PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB
PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB
11th Edition
ISBN: 9780135226742
Author: HEIZER
Publisher: PEARSON
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Chapter 4, Problem 6P

The monthly sales for Yazici Batteries, Inc., were as follows:

Chapter 4, Problem 6P, The monthly sales for Yazici Batteries, Inc., were as follows: a) Plot the monthly sales data. b)

a) Plot the monthly sales data.

b) Forecast January sales using each of the following:

i) Naive method.

ii) A 3-month moving average.

iii) A 6-month weighted average using .1, .1, .1, .2, .2, and .3, with the heaviest weights applied to the most recent months.

iv) Exponential smoothing using an α = .3 and a September forecast of 18.

v) A trend projection.

c) With the data given, which method would allow you to forecast next March’s sales?

a)

Expert Solution
Check Mark
Summary Introduction

To determine: Plot and represent the monthly sales data in graphical form.

Introduction: Forecasting is used to predict future changes or demand patterns. It involves different approaches and varies with different time periods. A sequence of data points in successive order is known as a time series. Time series forecasting is the prediction based on past events which are at a uniform time interval.

Answer to Problem 6P

The monthly sales data is plotted and represented.

Explanation of Solution

Given information:

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

Table 1

Graph:

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 4, Problem 6P , additional homework tip  1

The data to plot the sales is obtained from Table 1. Graph is plotted with the sales for January to December.

Thus, the sales data points are plotted and the graphical representation of sales data is presented.

b) i)

Expert Solution
Check Mark
Summary Introduction

To determine: Forecast January sales using Naïve method.

Answer to Problem 6P

The forecast for January using Naïve method is 23

Explanation of Solution

Given information:

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

Naïve Approach: This method assumes that the demand for a particular period will be the same as the demand in the most recent period.

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23
January 23

According to the naïve approach, the demand for January will be the same as the demand in the most recent past month. That is, the demand will be the same as that of December. Therefore, the demand for January will be same as the demand of December; 23.

Hence, the forecast for January using naïve approach is 23

ii)

Expert Solution
Check Mark
Summary Introduction

To determine: Forecast January sales using 3-month moving average.

Answer to Problem 6P

The forecast for January using 3-month moving average is 50.67

Explanation of Solution

Given information:

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

Formula to calculate the demand forecast:

Movingaverage=demandinpreviousnperiodsn

Month Sales Moving Average
January 20
February 21
March 15
April 14 42.67
May 13 36.00
June 16 32.00
July 17 33.67
August 18 37.33
September 20 40.33
October 20 43.67
November 21 46.00
December 23 47.67
January 50.67

Excel worksheet:

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 4, Problem 6P , additional homework tip  2

Calculation of the demand forecast for January sales:

Substitute the summation of the values 20, 21, and 23and divide it by the nth period; n=3

Movingaverage=20+21+233=50.67 (1)

The January forecast is 50.67

Hence, the forecast of January sales using 3-month moving average is 50.67

iii)

Expert Solution
Check Mark
Summary Introduction

To determine: Forecast January sales using 6-month weighted moving average.

Answer to Problem 6P

The forecast for January using 6-month moving average is 20.60

Explanation of Solution

Given information:

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

Formula to calculate the demand forecast:

Weightedmovingaverage=((Weightforperiodn)(Demandinperiodn))Weights

Month Sales Weighted moving average
January 20
February 21
March 15
April 14
May 13
June 16
July 17 15.80
August 18 15.90
September 20 16.20
October 20 17.30
November 21 18.20
December 23 19.40
January 20.60

Excel worksheet:

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 4, Problem 6P , additional homework tip  3

Calculation for the demand forecast of January sales:

Weightedmovingaverage=(0.3×23)+(0.2×21)+(0.2×20)+(0.1×20)+(0.1×18)+(0.1×17)0.3+0.2+0.2+0.1+0.1+0.1=20.60 (2)

To calculate the forecast for January, multiply the weights with the sales of recent year, i.e. multiply weight 0.3 with 23, 0.2 with 21, 0.2 with 20, 0.1 with 20, 0.1 with 18 and 0.1 with 17.

Divide the summation of the multiplied values with the summation of the weights i.e. (0.3+0.2+0.2+0.1+0.1+0.1). The corresponding result is 20.60which is the forecasted value for January. Therefore January forecast is 20.60.

Hence, the forecast of January sales using 6-month weighted moving average is 20.60

iv)

Expert Solution
Check Mark
Summary Introduction

To determine: Forecast January sales using exponential smoothing method.

Answer to Problem 6P

The forecast for January using exponential smoothing method is 20.6298

Explanation of Solution

Given information:

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

Smoothingconstant(α)=0.3ForecastofSeptember=18

Formula to calculate the demand forecast

Ft=Ft-1+α(At-1-Ft-1)

Where

Ft=newforecastFt-1=Previousperiod'sforecastα=smoothingconstantAt-1=PreviousperiodactualDemand

Sl. No. Month Sales Forecast
1 January 20
2 February 21
3 March 15
4 April 14
5 May 13
6 June 16
7 July 17
8 August 18
9 September 20 18
10 October 20 18.6
11 November 21 19.02
12 December 23 19.614
13 January 20.6298

Excel worksheet:

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB, Chapter 4, Problem 6P , additional homework tip  4

Calculation of the forecast for October:

Focotber=Fseptember+α(Aseptember-Fseptember)=18+0.3(2818)=18.6

To calculate forecast for October, substitute the value of forecast of September, smoothing constant and difference of actual and forecasted demand of September. The result of forecast for October is 18.6.

Calculation of the forecast for November:

Fnovember=Focotber+α(Aocotber-Focotber)=18.6+0.3(2018.6)=19.02

To calculate forecast for November, substitute the value of forecast of October, smoothing constant and difference of actual and forecasted demand of October. The result of forecast for November is 19.02.

Calculation of the forecast for December:

Fdecember=Fnovember+α(Anovember-Fnovember)=19.02+0.3(2119.02)=19.614

To calculate forecast for December, substitute the value of forecast of November, smoothing constant and difference of actual and forecasted demand of November. Therefore, the forecast for December is 19.614.

Calculation of the forecast for January:

Fjanuary=Fdecember+α(Adecember-Fdecember)=19.614+0.3(2319.614)=20.6298 (3)

To calculate forecast for January, substitute the value of forecast of December, smoothing constant and difference of actual and forecasted demand of December. Therefore, the forecast for January is 20.6298.

Hence, the forecast of January sales using exponential smoothing method is 20.6298

v)

Expert Solution
Check Mark
Summary Introduction

To determine: Forecast January sales using trend projection.

Answer to Problem 6P

The forecast for January using trend projection is 20.754

Explanation of Solution

Given information:

Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23

Formula to calculate the demand forecast

y^=a+bx

Where,

 y^=computed value of the variablea=y-axis interceptb=slope of the regression linex=the independent variable

b=xynx¯y¯x2nx¯2

Where

b=slope of the regression line= summation signx=known values of the independent variablesy=known values of the dependent variables

x¯=average of the x - valuesy¯=average of the y - values= number of data points

Month (x) Sales (y) xy x2
1 20 20 1
2 21 42 4
3 15 45 9
4 14 56 16
5 13 65 25
6 16 96 36
7 17 119 49
8 18 144 64
9 20 180 81
10 20 200 100
11 21 231 121
12 23 276 144
∑=78 ∑=218 ∑=1474 ∑=650

Substituting the values in the above formula

Calculation of average of x values x¯ :

x¯=i=112xn=7812=6.5

Average of x values is obtained by dividing the summation of x values i.e. (1+2+…+12) with the number of period n i.e.12. The value of x¯ = 6.5.

Calculation of average of y values y¯ :

y¯=i=112yn=21812=18.166

Average of y values is obtained by dividing the summation of sales with the number of period n i.e.12. The value of y¯ = 18.166

Calculation of slope of regression line ‘b’:

b=xynx¯y¯x2nx¯2=1,474(12×6.5×18.166)650(12×6.52)=57143=0.398

Summation of product of sales (y) with x values is ∑xy = 1474, product of number of months (n), average of x values and average of y values is obtained i.e. nx¯y¯ =1416.94. Difference between 1474 and 1416.94 is 57.

Summation of square of x values i.e. 650 is subtracted from the product of number of months i.e. 12 with average of x values i.e. 6.5. The resultant value is 143. The slope of regression line is obtained by dividing 57 with 143. The value of ‘b’ is 0.398.

Calculation of y axis intercept ‘a’:

a=y¯-bx¯=18.166-(0.398×6.5)=15.579

The y axis intercept is obtained by the difference between average of y values and values obtained by the product of slope of regression line with average of x values. The resultant value of ‘a’ is 15.579.

Calculation of forecast of January:

y^january=a+bx=15.58+(0.398×13)=20.754 (4)

The January forecast is obtained by summation of the product of slope of regression line and forecasted month, January i.e. 13 with the y-axis intercept. The forecasted value obtained is 20.754.

Hence, the forecast for January sales using trend projection is 20.754

c)

Expert Solution
Check Mark
Summary Introduction

To determine: The best technique among time series methods to forecast March sales.

Explanation of Solution

The calculated results from the data revels that the trend projection (refer to equation (4)) is the best suitable technique to forecast March sales as it is useful in evaluating trends in the data.

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The monthly sales for Yazici Batteries, Inc., wereas follows: a) Plot the monthly sales data.b) Forecast January sales using each of the following:i) Naive method.ii) A 3-month moving average.iii) A 6-month weighted average using .1, .1, .1, .2, .2, and.3, with the heaviest weights applied to the most recentmonths.iv) Exponential smoothing using an a = .3 and aSeptember forecast of 18.v) A trend projection.c) With the data given, which method would allow you toforecast next March’s sales?

Chapter 4 Solutions

PRIN.OF OPERATIONS MANAGEMENT-MYOMLAB

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