Question (1): Assume a 45-hr/week and an hourly wage of €21. Material cost is €15 per running meter and the standard inventory value of output is €173 per unit. Overhead is charged weekly at the rate of €1838 and 0.75 times direct cost. Week | 1 | 2 | 3 | 4 | Output | 636 | 576 | 624 | 644 | Workers | 12 | 11 | 11 | 9 | Material (meter) | 4125 | 3675 | 3930 | 4035 | A. Briefly explain the concept of productivity?

Productivity
Productivity is a measure of the rate at which outputs of goods and services are produced per unit of input (labor, capital, raw materials, etc.). It is calculated as the ratio of the amount of outputs produced to some measure of the amount of input used. Productivity = Quantity of goods and services produced Amount of resources used

As the equation indicates, there are two variables in measuring productivity- the amount of production and amount of resources used. Productivity varies with the amount of production relative to the amount of resources used. Productivity can be increased in several ways, which
Are given below here-

1. Increase production using the same or a smaller amount of resources. 2. Reduce the amount of resources used while keeping the same production or increasing it. 3. Allow the amount of resources used to increase c production increases more. 4. Allow production to decrease as long as the amount of resources used decreases more.

Whichever the method productivity needs be improved as increased productivity contributes to the competitive advantage of an organization. When productivity increases, the company can pay higher remuneration to its employees without boosting inflation. Increased earning without corresponding increase in inflation add to the standard of living of people. Improving productivity also means getting more from given inputs. Higher productivity does not mean adding more inputs but using the resources better. Improving productivity does not mean working harder; its mean working smarter, not just doing things right but doing right things.
Conceptually, productivity is a ‘supply-side’ measure, capturing technical production
Relationships between inputs and outputs. But, implicitly, it is also about the
Production of goods and services that are desired, valued and in demand.

Example: Assume two workers paint 24 tables in 8 hours:- Input: 16 hour of labor (2 workers * 8 hours) Output: 24 painted tables Productivity = output/Input =24 tables / 16 hours =1.5 tables /hour Types of productivity measures

Productivity can be expressed as a physical measure (for example- number of cars
Produced per employee), a monetary measure (for example- thousands of dollars of
Output per hour worked).

In principle, inputs can be broadly defined to cover people's time, their skills, land, raw
Materials, machinery and equipment, energy (for example, electricity) and so on. But, most commonly, inputs are defined in terms of: labor (number of employees or hours of work) and capital (buildings, machinery etc.).

I. Total Productivity Measure- Productivity can be measured with respect to a single input or a combination of inputs. The partial or single factor productivity (or SFP) is defined as the ratio of the volume of output (or value-added) to the quantity of the factor of production for which productivity is to be estimated (e.g., labor productivity or capital productivity).

Total Productivity = Revenues, Profits/All inputs

Total Productivity (includes all inputs in an organization i.e. labor, materials, overheads, capital)

II. Multifactor Productivity Measure-Multifactor productivity (MFP) is the ratio of output to the combined input of labor and capital. Sometimes this measure is referred to as total factor productivity.
MFP is an index of output obtained from more than one of the resources used in prod/service.

Multifactor Productivity= Output/Labor+ Material+ Overhead

Multifactor Productivity (ratio of output to a group of inputs such as labor and material)

III. Partial Productivity Measure- Partial Productivity Measure defined as the ratio of a measure of output quantity to some measure of the quantity of labor used, such as total hours worked.
Partial productivity is concerned with efficiency of one particular characteristic.

Partial Productivity = Total Output / Total Productive Hours Partial Productivity (measures of output against a specific input) E.g. Items made/employee.

Productivity Growth Rate:-

It can be used to compare a process’s productivity at a given time (P2) to the same process’s productivity at an earlier time (P1).

Growth rate = P2 – P1 *100 P1

Why is productivity important?

Productivity growth is important because it contributes to growth in output, income and living standards.

Productivity growth = Output growth – Input growth

Rearranging:

Output growth = Input growth + Productivity growth

That is, input growth and productivity growth both contribute to output growth.
Next, we observe that output growth is equal to income growth (if output is measured as value added). And so, productivity growth leads to income growth in an economy.
Finally, if we measure living standards as GDP per head where P = population, H = hours worked.

Since GDP is both a measure of income and output and since GDP per hour worked is a measure of labor productivity, growth in productivity will raise income per person. In practice, the other term on the right hand side (hours worked per person) only changes gradually and by a relatively small amount over time. Consequently, productivity growth accounts for the most part of growth in average income over the long term.

At a firm or industry level, the benefits of productivity growth can be distributed in a number of different ways:

* To the workforce through better wages and conditions.

* To shareholders and superannuation funds through increased profits and dividend
Distributions.

* To customers through lower prices.

* To the environment through more stringent environmental protection.

* To governments through increases in tax payments (which can be used to fund
Social and environmental programs).

Productivity growth is important to the firm because it means that it can meet its
(Perhaps growing) obligations to workers, shareholders, and governments (taxes and regulation), and still remain competitive or even improve its competitiveness in the market place.

B. Calculate the average multi-factor productivity measure for each of the week’s shown? Multifactor Productivity for 1st Week:- Calculation of overhead charges for 1st week =1838+ (45*21*12+4125*15)*0.75 = 56749.25

Multifactor Productivity= Output/Labor+ Material+ Overhead

=173*636/ (45*21*12+4125*15+56749.25)

=110028/ (11340+61875+56749.25) =0.84 Multifactor Productivity for 2nd Week:- Calculation of overhead charges for 2nd week =1838+(45*21*11+3675*15)*0.75 =50978

Multifactor Productivity= Output/Labor + Material+ Overhead

=173*576/ (45*21*11+3675*15+50578)

=99648/ (10395+55125+50978) =0.85

Multifactor Productivity for 3rd Week:- Calculation of overhead charges for 3rd week =1838+ (45*21*11+3930*15)*0.75 =53846.75

Multifactor Productivity= Output/Labor+ Material+ Overhead

=173*624/ (45*21*11+3930*15+53846.75)

=107592/ (10395+58950+53846.75)

=0.87
Multifactor Productivity for 4th Week:- Calculation of overhead charges for 4th week =1838+ (45*21*9+4035*15)*0.75 =53610.5

Multifactor Productivity= Output/Labor+ Material+ Overhead

=173*644/ (45*21*9+4035*15+53610.5)

=111412/ (8505+60525+53610.5) =0.9

C. Plot the productivity figures estimated against weeks. Briefly explain?

In this graph we are seeing that in week2 productivity increases with respect to week1 by 0.85% and in week3 productivity increases by 0.87% with respect to Week2 then again in week4 productivity increases by 0.9% with respect to week4, means here productivity increases in every week in a successive order.

D. Calculate the growth rate of productivity throughout the weeks. Briefly explain? Calculation of growth rate for given weeks:- Growth rate for 2nd week = Growth rate of week 2nd - Growth rate of week 1st *100 Growth rate of week 1st = 0.85-0.84/0.84*100 =0.01/0.84 =1.19 Growth rate for 3rd week = Growth rate of week 3rd - Growth rate of week 2nd *100 Growth rate of week 2nd =0.87-0.85/0.85*100 = 0.02/0.85*100 =2.35 Growth rate for 4th week = Growth rate of week 4th - Growth rate of week 3rd *100 Growth rate of week 3rd =0.9-0.87/0.87*100 =0.03/0.87 *100 =3.44

Question (2) A. Compute the multi-factor productivity measure for each of the week’s shown. Assume 40 hour weeks and an hourly wage of $12. Overhead is 1.5 times weekly labor cost. Material cost is $ 6 per pound. Week | Output (units) | Workers | Materials (lbs.) | 1 | 30,000 | 6 | 450 | 2 | 33,600 | 7 | 470 | 3 | 32,200 | 7 | 460 | 4 | 35,400 | 8 | 480 | Multifactor Productivity for 1st Week:-

Multifactor Productivity= Output/Labor+ Material =30000 / (2880+4320+2700)

=30000 / 9900

=3.03

Multifactor Productivity for 2nd Week:-

Multifactor Productivity= Output/Labor+ Material

=33600 / (3360+5040+2820)

=33600 / 11220

=2.99

Multifactor Productivity for 3rd Week:-

Multifactor Productivity= Output/Labor+ Material

=32200 / (3360+5040+2760) =33600 / 11160 =2.88

Multifactor Productivity for 4th Week:-

Multifactor Productivity= Output/Labor+ Material

= 35400 / (3840+5760+2880)

= 35400/ 12480

= 2.83

B. What do the productivity figures suggest?

By analyzing the productivity figures here which are coming different in Every week. From 1st to 4th week productivity comes here 3.03, 2.99, 2.88, 2.83. So here productivity in every week here declining.

Question (3). A. A manager checked production records and found out that a worker produced 160 units while working 40 hours. In the previous week, the same worker produced 138 units while working 36 hours. Compute the worker’s productivity.
Growth rate = P2 – P1 / P1
Workers Productivity=Current year productivity -Previous year productivity / Previous year productivity *100 (P1 = 138/36=3.83 for previous year, P2 = 160/40=4 for current year) Growth rate= 4 – 3.83 / 3.83 =4.1
So here growth rate will be 4.1%.

B. Did his productivity increase, decrease or remain the same? Briefly explain. As we see that the worker’s productivity is coming 4.1% so it indicates that here productivity is increasing.

Question (4). Which type of forecasting approach Qualitative or Quantitative is better? Qualitative Forecasting * These approaches are used when historical data are scarce or not available at all. * They generally use expert opinion to predict future events subjectively.

Advantage Useful when historical data either are not available or are scarce.
For example: sales of new product, environment and technology over the long term.

Disadvantage Subjective
Quantitative Forecasting

* These approaches are used when historical data are available. * They generally construct a forecasting model from available data or theory to do forecasts.

Advantage
Objective, once the underlying model or technique has been chosen, the corresponding forecasts are determined automatically. They are fully reproducible by any forecaster.

Disadvantage Need data

Question (5) A commercial bakery has recorded sales in dozen for the products as shown below: Day | Blueberry Muffins | Cinnamon Buns | Cupcakes | 1 | 30 | 18 | 45 | 2 | 34 | 17 | 26 | 3 | 32 | 19 | 27 | 4 | 34 | 19 | 23 | 5 | 35 | 22 | 22 | 6 | 30 | 23 | 48 | : | : | : | : | 12 | 31 | 28 | 26 | 13 | 35 | 29 | 27 | 14 | 34 | 31 | 24 | 15 | 33 | 33 | 22 | A. Predict orders for the following day for each of the products using an appropriate naïve method. Also Plot each data set.
First product Blueberry Muffins forecasting
Blueberry Muffins forecast for 7th day= 1st+2nd+3rd+4th+5th+6th / 6 = 30+34+32+34+35+30 / 6 =32.5
Blueberry Muffins forecast for 8th day= 2nd+3rd+4th+5th+6th +7th / 6 =34+32+34+35+30+32.5 /6 =32.9
Blueberry Muffins forecast for 9th day= 3rd+4th+5th+6th +7th +8th / 6 =32+34+35+30+32.5 +32.9 / 6 =32.78
Blueberry Muffins forecast for 10th day= 4th+5th+6th +7th +8th +9th / 6 =34+35+30+32.5 +32.9+32.78 / 6 =32.8
Blueberry Muffins forecast for 11th day= 5th+6th +7th +8th +9th +10th / 6 =35+30+32.5 +32.9+32.78+32.8 / 6 =32.6

Second product Cinnamon Buns forecasting Cinnamon Buns forecast for 7th day= 1st+2nd+3rd+4th+5th+6th / 6 =18+17+19+19+22+23 / 6 =19.6
Cinnamon Buns forecast for 8th day= 2nd+3rd+4th+5th+6th +7th / 6 =17+19+19+22+23+19.6 / 6 =19.9
Cinnamon Buns forecast for 9th day= 3rd+4th+5th+6th +7th +8th / 6 =19+19+22+23+19.6+19.9 / 6 =20.4
Cinnamon Buns forecast for 10th day= 4th+5th+6th +7th +8th +9th / 6 =19+22+23+19.6+19.9+20.4 / 6 =20.6
Cinnamon Buns forecast for 11th day= 5th+6th +7th +8th +9th +10th / 6 =22+23+19.6+19.9+20.4+20.6 / 6 =20.9 Third product Cupcakes forecasting
Cupcakes forecast for 7th day= 1st+2nd+3rd+4th+5th+6th / 6 =45+26+27+23+22+48 / 6 =31.8
Cupcakes forecast for 8th day= 2nd+3rd+4th+5th+6th +7th / 6 =26+27+23+22+48+31.8 / 6 =29.6
Cupcakes forecast for 9th day= 3rd+4th+5th+6th +7th +8th / 6 =27+23+22+48+31.8+29.6 / 6 =30.2
Cupcakes forecast for 10th day= 4th+5th+6th +7th +8th+9th / 6 =23+22+48+31.8+29.6+30.2 / 6 =30.7
Cupcakes forecast for 10th day= 5th+6th +7th +8th+9th +10th / 6 =22+48+31.8+29.6+30.2+30.7 / 6=32 Day | Blueberry Muffins | Cinnamon Buns | Cupcakes | 1 | 30 | 18 | 45 | 2 | 34 | 17 | 26 | 3 | 32 | 19 | 27 | 4 | 34 | 19 | 23 | 5 | 35 | 22 | 22 | 6 | 30 | 23 | 48 | 7 | 32.5 | 19.6 | 31.8 | 8 | 32.9 | 19.9 | 29.6 | 9 | 32.7 | 20.4 | 30.2 | 10 | 32.8 | 20.6 | 30.7 | 11 | 32.6 | 20.9 | 32 | 12 | 31 | 28 | 26 | 13 | 35 | 29 | 27 | 14 | 34 | 31 | 24 | 15 | 33 | 33 | 22 |
(b.) What should the use of sales data instead of demand imply?

Question (6.) Atlas Ancillaries plans to set up a manufacturing unit for ‘100 HP’ motors. The management has identified Gurgaon and Delhi as the potential areas to set up the unit. The fixed costs per year and the variable costs per unit for Gurgaon are Rs.6, 00,000 and Rs.750 respectively. The costs for Delhi are Rs.7, 50,000 and Rs.650. Each motor is priced at Rs.1500 and the expected sales are 9000 units per year. Which of the two locations will be more profitable for Atlas?
We first calculate the total costs (sum of the fixed and variable costs) at each of Delhi and Gurgaon- Location | Fixed cost / Yr | Variable cost / Unit | Delhi | Rs. 7,50,000 | 650 | Gurgaon | Rs. 6,00,000 | 750 |

Total cost at Delhi= 7,50,000 + 650 =7,50,650
Total cost at Gurgaon= 6,00,000 + 750=6,00,750
Total revenue of the firm= 1500 * 9000 =1,35,00,000
The profits of the company if they were set up in the given locations would be as follows:
Profit at Delhi = 1,35,00,000 - 7,50,650 = 1,27,49,350
Profit at Gurgaon = 1,35,00,000 - 6,00,750 = 1,28,99,250
-------------------------------------------------
So Gurgaon location will be more profitable for Atlas than Delhi

BibLIOGRAPHy- * Production and operation management by- (K.aswathappa and k.shridhara bhat) * Production and operation management by- (R.panneerselvan) * Operation management by- (joseph g.monks)