OPERATIONS AND RESEARCH MANAGEMENT ASSIGNMENTS
ASSIGNMENT ONE
Mulungushi Manufacturer has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them products 1, 2 and 3. The available capacity on the machines that might limit output is summarised in the following table.
Machine type Available time (Machine hours per week)
Milling Machine 500
Lathe 350
Grinder 150
The number of machine hours required for each unit of the respective products is
Productivity coefficient (in machine hours per unit)
|
Machine Type
|
Product 1
|
Product 2
|
Product 3
|
|
Milling machine
Lathe
Grinder
|
9
5
3
|
3
4
0
|
5
0
2
|
The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be K50, K20 and K25 respectively, on product 1, 2 and 3. The objective is to determine how much of each product X should be produced to maximise profit.
a) Formulate an LP model
b) Find the maximum profit and the amount of each product to be produced using the simplex method.
ASSIGNMENT TWO
A project manager has completed a list of major activities that will be required to install a computer information system in her firm. The list include estimated completion times for activities and precedence relationships
Activity Immediate predecessor Estimated Times (weeks)
A - 2-4-6
D A 6-8-10
E D 7-9-12
H E 2-3-5
F A 3-4-8
G F 5-7-9
B - 2-2-3
I B 2-3-6
J I 3-4-5
K J 4-5-8
C - 5-8-12
M C 1-1-1
N M 6-7-11
O N 8-9-13
End H, G, K, O
A) Construct an AON and AOA diagrams for this project
B) If the project is finished within 26 weeks of its start, the project manager will receive a bonus of K1, 000 and if the project is finished within 27 weeks of its start, the bonus will be K500. Find the probability of each bonus.
ASSIGNMENT THREE
The parts department of a large automobile dealership has a counter used exclusively for mechanics' requests for parts. The time between requests can be modelled by a negative exponential distribution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, and this can be modelled by a poison distribution that has a mean of 15.
a) On average, how many mechanics would be at the counter, including being served?
b) What probability that a mechanic would have to wait for service?
c) If a mechanic has to wait, how long would the average wait be?
d) What percentage of time are the clerks idle?
e) If the clerk represents a cost of K20 per hour and mechanics a cost of K30 per hour, what number of clerks would be optimal in terms of minimising total costs?