Operations Management Module 3 Productivity Efficiency Effectiveness Markov chains

Productivity

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

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

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 20,000 Life of a tyre in km. 15,000 Price of a tyre in rupees 2,000 1600

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

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

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

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 Capital Where capital includes land, buildings,plant, machinery etc. Does not include working capital

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

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

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 ?

Productivity = 180 * 150 4000+20000+ 12000 = 0.75

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

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

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 %.

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

Markov 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.

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

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

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

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

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

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

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 * 0.9 + 0.8 * 0.2 = 0.34 Pepsi  ? ?  Coke

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 * 0.17 + 0.1 * 0.66 = 0.219

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 * 0.781 + 0.4 * 0.438 = 0.6438 Qi - the distribution in week i Q0=(0.6,0.4) - initial distribution Q3= Q0 * P3 =(0.6438,0.3562)