1. Operations Management Module 3 Productivity Efficiency Effectiveness Markov chains

2. Productivity

3. Productivity measures are useful for
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 3

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

5. 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

6. Assuming the level of input is the same, has the productivity gone up or down during 2011 -2012 ?
Output
Year
No. of tyres produced
16,000
20,000
Life of a tyre in km.
15,000
Price of a tyre in rupees
2,000
1600

7. No. of tyres – 25 % increase
No. of tyre – km = 6.66% decrease
Monetary output = constant
Depends on what is being measured
- Customer satisfaction
- Market share

8. Different Productivity Measures
Labour productivity (partial measures )
Capital productivity (partial measures )
Raw materials productivity (partial measures )
Total factory productivity index
Multi factor

9. Labour Productivity = Gross value added Average daily employment
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

10. India’s real productivity has increased by 65 % from 1998 – 2006
China’s real productivity has increased by 180 % from 1998 – 2006

11. “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

12. Capital Productivity = Output Capital
Where capital includes land, buildings,plant, machinery etc. Does not include working capital

13. Raw Materials and Fuel Input Productivity
Gross ex factory value of output
Combined value of raw materials, fuel etc

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

16. Q. If 180 pieces are produced at a standard price of Rs
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 ?

17. Productivity =
180 * 150 =

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

19. Best mfg co.’s in india L & T Bombay Dyeing HLL Aditya Birla
Jindal Steel
Toyota
Haldia

20. Efficiency & 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 %.

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

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

23. 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.

24. Applications
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

25. Statistical Parameter Estimation Reminder
Data set
Model
Parameters: Θ
The basic paradigm:

26. Markov 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

27. Markov Process Simple Example
Weather:
raining today 40% rain tomorrow
60% no rain tomorrow
not raining today 20% rain tomorrow
80% no rain tomorrow
Stochastic FSM:
rain
no rain
0.6
0.4
0.8
0.2

28. Markov Process Simple Example
Weather:
raining today 40% rain tomorrow
60% no rain tomorrow
not raining today 20% rain tomorrow
80% no rain tomorrow
The transition matrix:
Stochastic matrix:
Rows sum up to 1
Double stochastic matrix:
Rows and columns sum up to 1

29. Markov Process Coke vs. Pepsi Example
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.
transition matrix:
coke
pepsi
0.1
0.9
0.8
0.2

30. Markov Process Coke vs. Pepsi Example (cont)
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[ PepsiCokeCoke ] + Pr[ Pepsi Pepsi Coke ] =
0.2 * * = 0.34
Pepsi  ?
?  Coke

31. Markov Process Coke vs. Pepsi Example (cont)
Given that a person is currently a Coke purchaser, what is the probability that he will purchase Pepsi three purchases from now?
0.9 * * 0.66 = 0.219

32. Markov Process Coke vs. Pepsi Example (cont)
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?
Pr[X3=Coke] = 0.6 * * =
Qi - the distribution in week i
Q0=(0.6,0.4) - initial distribution
Q3= Q0 * P3 =(0.6438,0.3562)