A question on Project Management

Given below is a WBS of a project.

 

              

Activity	Activity time in days	Immediate Predecessors
a	30	--
b	20	--
c	15	a
d	18	b
e	32	b
f	25	c, d
g	22	c, d
h	17	e, g
i	8	e
j	15	i

 

 Draw an activity network diagram for this project and find the critical path by finding earliest time and latest time of various events. What is the project completion time?

A question on forecasting (time series)

The recorded number of claims in motor insurance in last 7 months are as follows:

 

35, 70, 45, 20, 50, 80 and 60.

 

Use moving average method to forecast the number of claims for next 3 months based on past 4 months data. The actual numbers of claims in 8^th and 9^th months are 100 and 30 respectively. 

 

Take a smoothing factor of 0.3 to forecast the 10^th month data using exponential smoothing forecasting technique. Don’t change the forecast of previous months.

Simulation Problem

A health insurance product is designed targeting persons working in Education sector. The age profile of people who has taken this policy is as follows:

 

21- 35 years     25%

35+ - 45 years 30%

45+ - 55 years 25%

55+  years       20%

 

Probability of claim is 0.2 in all the age groups however the claim amount varies linearly between Rs. 15000 to Rs. 80000 for age up to 45 years and between Rs. 30000 to Rs. 200000 for age above 45 years. Do a simulation run of length 10 to understand the claim pattern.

 

Use following random numbers 5971, 9987, 1741, 7431, 188, 5333, 3680, 4883, 5036, 5407, 2763, 7194, 3395, 3632, 1109, 9943, 6690, 6408

Class test questions on Simplex method 8th Nov 2011

 

1.                  Below Simplex Table is not a basic feasible solution table.  Why?

Convert that to a basic feasible solution table.

 

 

	p	x1	x2	x3	s1	s2	s3	R.H.S.
P	1	0	0	-10	80	30	0	15000
x2	0	0	3	27	45	18	0	183
x1	0	1	0	12	73	24	0	115
s3	0	0	0	-15	27	-12	-1	-40

 

 

2.                  Below Simplex Table is an optimal table.  Why?

It also has alternate optimal.  Find that. (No need to prepare the complete table.)

 

Since it has an alternate optimal, it has infinite number of optimal solution.  Can you provide some expression to find as many optimum solutions as you want in this case? (send this by mail to get upto 10 marks from the class involvement part.  Deadline: 9/11/11, 5 PM)

 

 

	p	x1	x2	x3	s1	s2	s3	R.H.S.
P	1	25	0	0	10	0	0	7500
x3	0	-15	10	1	8	0	0	305
s2	0	12	25	0	-5	1	0	670
s3	0	3	15	0	12	0	1	320

 

 

 

Sensitivity analysis in Linear programming

This tutorial will be helpful in understanding sensitivity analysis. This seems to be very close to the way we were discussing in the class. Also see other pages on the site.

 

http://fisher.osu.edu/~croxton_4/tutorial/

 

Linear Programming Resource

Contents available at below site nicely explain Linear Programming, graphical method and Simplex method. You may also like to navigate through other pages of the site.

 

http://www.me.utexas.edu/~jensen/ORMM/methods/unit/linear/index.html

Linear Programming- Graphical Method- Test question

A Carpenter manufactures tables and chairs. He has all the resources in abundance except wood and nails. The profitability and resource requirements for the two products are given in following table. The availability of resources per day is also given. How many tables and chairs he should manufacture daily so that his profit is maximized? Formulate the linear programme and solve that using graphical method.

 

	Table	Chair
Profit/unit->	20$	30$	Availability/day v
Wood/unit in kg.	40	30	1200
Nails/unit in number	25	40	1000

 

If the profit/unit on table increases and rest of the data remains same, find the increased value of profit/unit on table so that the optimum product mix doesn’t change.