Om Assignemnt #1

Asad Asad

Assignment 1 Solutions

October 12, 2018

Question 1)

1. 1.13: 

Productivity per worker=2.344 loaves per hour.

Demand=1500 per month, units produced per hour = 1500 / 160 = 9.375 units per hour.

N of workers = 9.375 / 2.344 = 4

New demand =1500*1.25 = 1875 per month = 1875 / 160 = 11.71875 units per hour.

With the same labor productivity, the number of persons required will be 11.71875 / 2.344 = 5. 5-4 =1 extra worker.

1. 1.14: Determine hourly rate.

If I am an hourly employee already then, the hourly rate will be listed on my paycheck. If it is salaried based, the amount of money made per hour can be determined by dividing the gross pay by the number of hours reflected on the paycheck. An example of this would be if the paycheck shows a 2-week period, the gross pay would be divided by 80 hours. The standard workweek is 40-hours so any hours worked over or under would not be considered for salaried based employees.

1. Determine Overtime hourly rate.

Overtime is usually calculated by a pay and half of your normal hourly rate. So overtime is paid at the rate of 1.5 times the normal rate per hour. An example would be if you made $10 per hour during a regular work period, the overtime rate would be $15.

1. Determine how many hours you work in one year.

If you are a full-time employee, you will usually work 40 hours per week. The base salary will be the hourly rate times 2080 hours which can be derived from 40 hours per week times 52 weeks per year. If you work overtime then the overtime hourly rate must be multiplied to the number of total overtime hours worked. This will then be added to that total to your base salary which gives the annual salary. Those who are salaried based do not get compensated for hours worked over 40

     e.

As a tipped employee, you will need to add your tips for the year to the base salary to determine your annual salary.

    1.17:

The labor productivity = products sold/ labour hour  = (52*90+80*198)/(8*45) = $57/ hour

Question 2)

    4.2:

[pic 1]

The WMA method is more accurate because the difference between the forecast plot of WMA method and actual values are actually less than the difference of the MA method.

4.3

[pic 2]

4.5

(a) Moving average = sum demand in 2 yr period/2

Moving average for Nxt yr = (3800+3700)/2 = 3,750 Miles

(b) MEAN ABSOLUTE DEVIATION (MAD) = Sum(|Dt-Ft|)/n

where Dt is demand in Period t & Ft is Forecasts in period t So Moving Avge for Y3 ie F(3) = (3000+4000)/2 = 3500

& D3 = 3400

So Mving Avge for Y4 ie F(4) = (4000+3400)/2 = 3700

& D4 = 3800

So Mving Avge for Y5 ie F(5) = (3400+3800)/2 = 3600

& D5 = 3700

So MAD = Sum(|3500-3400|+|3700-3800|+|3600-3700|)/3

ie MAD = (100+100+100)/3 = 100

(c) Weighted moving average = sum (weight in period n)*(demand in period n)/Sum weights

So Weighted moving average Y6 =

((3800*0.4)+(3700*0.6))/(0.4+0.6) = 3,740

MEAN ABSOLUTE DEVIATION (MAD) = Sum(|Dt-Ft|)/n

where Dt is demand in Period t & Ft is Forecasts in period t

So Wtd Mving Avge for Y3 ie F(3)

= (3000*0.4+4000*0.6)/(0.4+0.6) = 3600

& D3 = 3400

So Wtd Mving Avge for Y4 ie F(4)

= (4000*0.4+3400*0.6)/(0.4+0.6) = 3640

& D4 = 3800

So Wtd Mving Avge for Y5 ie F(5)

= (3400*0.4+3800*0.6)/(0.4+0.6) = 3640

& D5 = 3700

So MAD = Sum(|3600-3400|+|3640-3800|+|3640-3700|)/3

ie MAD = (200+160+60)/3 = 140

(d)Exponential Smoothing F(t)

F(t) =F(t-1)+a*(A(t-1) -F(t-1))

SO F(1) = 3000 + 0.5*(3000-3000) = 3000

F(2) = 3000 + 0.5*(4000-3000) = 3500

F(3) = 3500 + 0.5*(3400-3500) = 3450

F(4) = 3450 + 0.5*(3800-3450) = 3625

F(5) = 3625 + 0.5*(3700-3625) = 3663

So Forecast is 3663 mile

4.6

[pic 3]

b)

i) Forecast as per naïve method

Naïve method assumes demand in the next period is equal to the demand in the recent period.

Now substitute January month demand 20 with December’s demand i.e. 23. As mentioned above whatever the demand in December is equal to the demand in January so 23 is considered

Hence according to naïve method the forecast for January is 23.

ii) To forecast as per three month moving average method

F=(month1+month2+month3)/3

=21.33

iii) To forecast as per sixth month weighted average method

Moving Average=17*0.1+18*0.1+20*0.1+20*0.2+23*0.3

=20.6

iv) To forecast exponential smoothing for September month

a=0.3

FOctober=0.3*20+0.7*18=18.6

FNovember=0.3*20+0.7*18.6=19.02

FDecember=0.3*21+0.7*19.02=19.614

FJanuary=0.3*23+0.7*19.614=20.63

v) To forecast trend projection of the F13