OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)
OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)
7th Edition
ISBN: 9780077835439
Author: Roger G Schroeder, M. Johnny Rungtusanatham, Susan Meyer Goldstein
Publisher: McGraw-Hill Education
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Chapter 10, Problem 6P

Using the data in problem 2, prepare exponentially smoothed forecasts for the following cases:

  1. a. α = .1 and F1 = 90
  2. b. α = .3 and F1 = 90

a)

Expert Solution
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Summary Introduction

To develop: The exponential smoothed forecast

Introduction:

Exponential smoothing:

In the exponential smoothing forecast method, older data are given lesser importance, and newer data are given more importance. It is efficient in making short-term forecasts.

Explanation of Solution

Given information:

Forecast for period 1 (F1) = 90

Smoothing constant (α) = 0.1

Period Dt
1 92
2 127
3 106
4 165
5 125
6 111
7 178
8 97

Formula for exponential smoothing:

FPeriod=Ft+[α(Dt-Ft)]FPeriod=Forecast for the period calculated.Ft=ForecastedsalesDt=Previousdemandα=Smoothingconstant

Calculation of forecast:

The forecast for period 1 is 90.

Period 2:

F2=F1+[α(D1-F1)]=90+[0.1(92-90)]=90+(0.1×2)=90+0.2=90.2

The forecast for period 2 is 90.2.

Period 3:

F3=F2+[α(D2-F2)]=90.2+[0.1(127-90.2)]=90.2+(0.1×36.8)=90.2+3.68=93.9

The forecast for period 3 is 93.9.

Period 4:

F4=F3+[α(D3-F3)]=93.9+[0.1(106-93.9)]=93.9+(0.1×12.1)=93.9+1.21=95.1

The forecast for period 4 is 95.1.

Period 5:

F5=F4+[α(D4-F4)]=95.1+[0.1(165-95.1)]=95.1+(0.1×70.1)=95.1+7.01=102.1

The forecast for period 5 is 102.1.

Period 6:

F6=F5+[α(D5-F5)]=102.1+[0.1(125-102.1)]=102.1+(0.1×22.9)=102.1+2.29=104.4

The forecast for period 6 is 104.4.

Period 7:

F7=F6+[α(D6-F6)]=104.4+[0.1(111-104.4)]=104.4+(0.1×6.6)=104.4+0.66=105

The forecast for period 7 is 105.

Period 8:

F8=F7+[α(D7-F7)]=105+[0.1(178-105)]=105+(0.1×73)=105+7.3=112.3

The forecast for period 8 is 112.3.

b)

Expert Solution
Check Mark
Summary Introduction

To develop: The exponential smoothed forecast

Introduction:

Exponential smoothing:

In the exponential smoothing forecast method, older data are given lesser importance, and newer data are given more importance. It is efficient in making short-term forecasts.

Explanation of Solution

Given information:

Forecast for period 1 (F1) = 90

Smoothing constant (α) = 0.3

Period Dt
1 92
2 127
3 106
4 165
5 125
6 111
7 178
8 97

Formula for exponential smoothing:

FPeriod=Ft+[α(Dt-Ft)]FPeriod=Forecast for the period calculated.Ft=ForecastedsalesDt=Previousdemandα=Smoothingconstant

Calculation of forecast:

The forecast for period 1 is 90.

Period 2:

F2=F1+[α(D1-F1)]=90+[0.3(92-90)]=90+(0.3×2)=90+0.6=90.6

The forecast for period 2 is 90.6.

Period 3:

F3=F2+[α(D2-F2)]=90.6+[0.3(127-90.6)]=90.6+(0.3×36.8)=90.6+10.92=101.5

The forecast for period 3 is 101.5.

Period 4:

F4=F3+[α(D3-F3)]=101.5+[0.3(106-101.5)]=101.5+(0.3×4.5)=101.5+1.35=102.9

The forecast for period 4 is 102.9.

Period 5:

F5=F4+[α(D4-F4)]=102.9+[0.3(165-102.9)]=102.9+(0.3×62.1)=102.9+18.63=121.5

The forecast for period 5 is 121.5.

Period 6:

F6=F5+[α(D5-F5)]=121.5+[0.3(125-121.5)]=121.5+(0.3×3.5)=121.5+1.041=122.6

The forecast for period 6 is 122.6.

Period 7:

F7=F6+[α(D6-F6)]=122.6+[0.3(111-122.6)]=122.6+(0.3×(-11.6))=122.6-3.48=119.1

The forecast for period 7 is 119.1.

Period 8:

F8=F7+[α(D7-F7)]=119.1+[0.3(178-119.1)]=119.1+(0.3×58.9)=119.1+17.67=136.8

The forecast for period 8 is 136.8.

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OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)

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