productivity. operations management module 3 productivity efficiency effectiveness markov chains

AMITY GLOBALBUSINESS SCHOOL Bangalore

Operations ManagementModule 3

Productivity Efficiency

EffectivenessMarkov chains


Productivity


• Productivity–A measure of the effective use of resources,

usually expressed as the ratio of output to input• Productivity measures are useful for

–Tracking an operating unit’s performance over time

–Judging the performance of an entire industry or country


Productivity

A measure of the quantity of output per unit of input.Productivity = Amount of Output Amount of InputInput – man hours/ machine hours / material consumed


Traditionally,labour productivity…

Workers productivity = Number of units of output Number of days taken

Group of workers productivity = Tonnes(or kg) of output Number of workers …. Limited view


Assuming the level of input is the same, has the productivity gone up or down during 2011 -2012 ?

Output Year 2010 - 2011 2011- 2012

No. of tyres produced 16,000 20,000Life of a tyre in km. 20,000 15,000Price of a tyre in rupees 2,000 1600


No. of tyres – 25 % increaseNo. of tyre – km = 6.66% decreaseMonetary output = constant

Depends on what is being measured - Customer satisfaction - Market share


Different Productivity Measures

1. Labour productivity (partial measures )2. Capital productivity (partial measures )3. Raw materials productivity (partial measures ) 4. Total factory productivity index5. Multi factor


Labour Productivity

= Gross value added Average daily employmentGross value = Ex factory price – (raw material inputs + fuel + electricity) Average daily employment = Total attendance of all persons, all shifts, all working days / no.

of days worked


• India’s real productivity has increased by 65 % from 1998 – 2006

• China’s real productivity has increased by 180 % from 1998 – 2006


“Because salaries have been cheap, we (India) have never really cared about how much inefficiency really hurts us. In the West, because labour is costly, they do not hire unless compelled to do so”.

- Pramod Bhasin, President & CEO, Genpact


Capital Productivity = Output CapitalWhere capital includes land, buildings,plant, machinery etc. Does

not include working capital


Raw Materials and Fuel Input Productivity

Gross ex factory value of outputCombined value of raw materials, fuel etc


Output Ouput OutputMultifactor Measures ; ; Multiple Inputs Labor+Machine Labor+Capital+Energy


Total Factory Productivity Index = goods and services produced All resources used


Q. If 180 pieces are produced at a standard price of Rs.150 each, with a labour cost of Rs.4000 / -, material cost of Rs. 20,000 and overhead of Rs. 12,000 /- what is the multifactor productivity ?


Productivity = 180 * 1504000+20000+ 12000= 0.75


• Average inventory in India : 50 – 60 days• Average recoveries : 60 – 90 days• Professional management systems are absent • Quantity orientation

AMITY GLOBALBUSINESS SCHOOL BangaloreBest mfg co.’s in india

• L & T• Bombay Dyeing• HLL• Aditya Birla• Jindal Steel• Toyota • Haldia

AMITY GLOBALBUSINESS SCHOOL BangaloreEfficiency & Effectiveness

- Efficiency means doing something at the lowest cost

- It is the ratio of actual output of a process relative to some standard.

For eg. Consider a machine designed to package cereal at a rate of 30 boxes per minute. If an operator actually produces 36 boxes than the efficiency is 120 %.


• Effectiveness means doing the right things to create the most value for the company

AMITY GLOBALBUSINESS SCHOOL BangaloreMarkov Chains

Developed by Russian mathematician Andrei A. Markov. They are a probabilistic models known as stochastic processes.


It is a method of analyzing the current behavior of some variable in an effort to predict the future behavior of that same variable.

It deals with the probabilities of future occurrences by analyzing presently known probabilities.

AMITY GLOBALBUSINESS SCHOOL BangaloreApplications

• Useful in analyzing consumer buying patterns by examining and predicting the behavior of students in terms of their brand loyalty.

• For planning personnel needs• To study stock market movements• etc

AMITY GLOBALBUSINESS SCHOOL BangaloreStatistical Parameter EstimationReminder

• The basic paradigm:Data set

ModelParameters: Θ

AMITY GLOBALBUSINESS SCHOOL BangaloreMarkov Process• Markov Property: The state of the system at time t+1 depends only on the state of the system at time t

X1 X2 X3 X4 X5

x | X x X x x X | X x X tttttttt 111111 PrPr


Weather:• raining today 40% rain tomorrow

60% no rain tomorrow

• not raining today 20% rain tomorrow80% no rain tomorrow

Markov ProcessSimple Example

rain no rain

0.60.4 0.8

0.2

Stochastic FSM:


Weather:• raining today 40% rain tomorrow

60% no rain tomorrow

• not raining today 20% rain tomorrow80% no rain tomorrow

Markov ProcessSimple Example

8.02.06.04.0

P• Stochastic matrix:

Rows sum up to 1• Double stochastic matrix:

Rows and columns sum up to 1

The transition matrix:


• Given that a person’s last cola purchase was Coke, there is a 90% chance that his next cola purchase will also be Coke.• If a person’s last cola purchase was Pepsi, there is an 80% chance that his next cola purchase will also be Pepsi.

coke pepsi

0.10.9 0.8

0.2

Markov ProcessCoke vs. Pepsi Example

8.02.01.09.0

P

transition matrix:


Given that a person is currently a Pepsi purchaser, what is the probability that he will purchase Coke two purchases from now?Pr[ Pepsi?Coke ] = Pr[ PepsiCokeCoke ] + Pr[ Pepsi Pepsi Coke ] = 0.2 * 0.9 + 0.8 * 0.2 = 0.34

66.034.017.083.0

8.02.01.09.0

8.02.01.09.02P

Markov ProcessCoke vs. Pepsi Example (cont)

Pepsi ? ? Coke

8.02.01.09.0

P


Given that a person is currently a Coke purchaser, what is the probability that he will purchase Pepsi three purchases from now?0.9 * 0.17 + 0.1 * 0.66 = 0.219


562.0438.0219.0781.0

66.034.017.083.0

8.02.01.09.03P


•Assume each person makes one cola purchase per week•Suppose 60% of all people now drink Coke, and 40% drink Pepsi•What fraction of people will be drinking Coke three weeks from now?


8.02.01.09.0

P

562.0438.0219.0781.03P

Pr[X3=Coke] = 0.6 * 0.781 + 0.4 * 0.438 = 0.6438

Qi - the distribution in week iQ0=(0.6,0.4) - initial distributionQ3= Q0 * P3 =(0.6438,0.3562)

productivity. operations management module 3 productivity efficiency effectiveness markov chains

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