PCA25C05T · End Semester
Covers all units: Introduction to operations research / Transportation and Assignment Problems / Game Theory / Network Analysis / Queuing Theory and Inventory Control
Answer ANY FIVE Questions
Write any five applications of operations research.
Find the Initial feasible solution to the following transportation problem by North West Corner Rule and Least Cost Method.
| To 1 | To 2 | To 3 | Supply | |
|---|---|---|---|---|
| From 1 | 1 | 2 | 6 | 7 |
| From 2 | 0 | 4 | 2 | 12 |
| From 3 | 3 | 1 | 5 | 11 |
| Demand | 10 | 10 | 10 |
Solve the following assignment problem.
| Salesman \ Area | I | II | III | IV |
|---|---|---|---|---|
| A | 10 | 5 | 13 | 15 |
| B | 3 | 9 | 18 | 3 |
| C | 10 | 7 | 3 | 2 |
| D | 5 | 11 | 9 | 7 |
Solve the following game whose pay-off matrix is given below.
| B1 | B2 | B3 | |
|---|---|---|---|
| A1 | 2 | 4 | 2 |
| A2 | 1 | -5 | -4 |
| A3 | 2 | 6 | -2 |
Solve the 2 x 2 game:
| B1 | B2 | |
|---|---|---|
| A1 | 5 | 1 |
| A2 | 3 | 4 |
Distinguish between PERT and CPM.
Explain the various queueing system briefly.
Explain briefly the various types of inventory.
Answer ALL Questions
Solve the following LPP by graphical method.
Maximize Z = 100 x1 + 40 x2
Subject to the constraints:
5x1 + 2x2 <= 1000
3x1 + 2x2 <= 900
x1 + 2x2 <= 500
and x1, x2 >= 0.
Using simplex method solve the following LPP:
Maximize Z = 3x1 + 2x2 + 5x3
Subject to the constraints:
x1 + 4x2 <= 420
3x1 + 2x3 <= 460
x1 + 2x2 + x3 <= 430
and x1, x2, x3 >= 0.
Solve the following transportation problem.
| Source \ Destination | D1 | D2 | D3 | D4 | Supply |
|---|---|---|---|---|---|
| S1 | 6 | 1 | 9 | 3 | 70 |
| S2 | 11 | 5 | 2 | 8 | 55 |
| S3 | 10 | 12 | 4 | 7 | 90 |
| Demand | 85 | 35 | 50 | 45 |
Solve the following assignment problem.
| Machines \ Jobs | I | II | III | IV | V |
|---|---|---|---|---|---|
| 1 | 1 | 3 | 2 | 3 | 6 |
| 2 | 2 | 4 | 3 | 1 | 5 |
| 3 | 5 | 6 | 3 | 4 | 6 |
| 4 | 3 | 1 | 4 | 2 | 2 |
| 5 | 1 | 5 | 6 | 5 | 4 |
Solve the rectangular game whose payoff matrix is given below.
| 1 | 2 | 3 | |
|---|---|---|---|
| 1 | -1 | -2 | 8 |
| 2 | 7 | 5 | -1 |
| 3 | 6 | 0 | 12 |
Solve the following game graphically.
| Player A \ Player B | B1 | B2 | B3 | B4 | B5 |
|---|---|---|---|---|---|
| A1 | 2 | -1 | 5 | -2 | 6 |
| A2 | -2 | 4 | -3 | 1 | 0 |
Draw the network and determine the critical path for the given data.
| Activity | 1-2 | 1-3 | 1-4 | 2-3 | 2-4 | 3-4 | 3-5 | 4-5 | 4-6 | 5-6 |
|---|---|---|---|---|---|---|---|---|---|---|
| Duration in weeks | 7 | 12 | 4 | 10 | 3 | 5 | 10 | 7 | 4 | 6 |
Also, calculate the total float, free float and independent float of each activity.
Construct the network for the project whose activities and the three time estimates of these activities are given below.
| Activity | 1-2 | 1-3 | 1-4 | 2-4 | 2-5 | 3-4 | 4-5 | 5-6 |
|---|---|---|---|---|---|---|---|---|
| Least time (days) | 3 | 2 | 6 | 2 | 5 | 3 | 1 | 2 |
| Greatest time (days) | 15 | 14 | 30 | 8 | 17 | 15 | 27 | 8 |
| Most likely time (days) | 6 | 5 | 12 | 5 | 11 | 6 | 9 | 4 |
Compute:
i) Expected duration of each activity.
ii) Expected variance of each activity.
iii) Expected variance and standard deviation of the project length.
In a public telephone booth the arrivals are on the average 15 per hour. A call on the average takes 3 minutes. If there is just one phone, find:
i) Expected number of callers in the non empty queue.
ii) Expected number of callers in the system.
iii) Expected waiting time in the queue.
iv) The proportion of the time, the booth is expected to be idle.
The annual demand for an item is 3200 units. The unit cost is Rs. 6, and inventory carrying charges is 25% per annum. If the cost of one procurement is Rs. 150, determine:
(i) Economic order quantity
(ii) Time between two consecutive orders
(iii) Number of orders per year
(iv) The optimal total cost.