1. a. Explain briefly any two of the following OR techniques:
(6)
i. Linear Programming
ii. CPM
iii. M/< / 8 queing model
iv. Dynamic Programming
b. Product Mix Problem: Give the Linear Programming
formulation of the following problem:
The products A and B are produced in three machine
centers X, Y and Z. Each product involves operation
of each of the machine centers. The time required for
each operation unit amount of each product is given
below: Time available at machine centers X, Y and Z
are 100, 77 and 80 hours respectively. The profit per
unit of each of A and B is Rs. 12 and Rs. 3 respectively.
(3)
Product
|
Machine Centers
|
Profit Per Unit
|
| |
X |
Y |
Z |
III |
| A |
10 |
7 |
2 |
12 |
| B |
2 |
3 |
4 |
3 |
| |
|
- |
|
|
c. Enumerate various important steps in OR study and discuss
one of the steps briefly: (4)
d. Explain the following concepts in context of Linear
Programming / OR ( 3)
i. Objective Function
ii. Convex Polygon
iii. Redundant Constraint
e. Explain the following in context of Transportation
Problem (not exceeding three sentences for each):
i. Stepping Stone Method
ii. Degenerate Transportation Problem
iii. The Modified Distribution Method
f. Explain the following in context of Assignment Problem
(not exceeding three sentences for each): (3)
i. Balanced Assignment Problem
ii. Hungarian Method
iii. an Infeasible Assignment
g. Company XYZ produces two products. The maximum sales
potential for product 1 and product 2 are 30 units and
40 units respectively. Write the goal constraints for
achieving the sales goal by incorporating the deviational
variables. (3)
h. Explain the following concepts in context of Dynamic
Programming (not exceeding three sentences for each):
(3)
i. Principle of Optimality
ii. State
iii. Stage
j. Explain the following in context of Inventory Control:
(2)
i. Decoupling
ii. VED classification
iii. Delivery Lag
2. Solve the Product Mix Problem given above as Q.
No 1(b), using either Graphical Method or Simplex Method
of Linear Programming. (15)
3. A sales manager has to assign to four territories,
He has four candidates of varying experience and capabilities
and assesses the possible profit in suitable units for
each salesman in each territory as given below:
Salesman
|
Territories
|
| |
T1 |
T2 |
T3 |
T4 |
| S1 |
25 |
27 |
28 |
37 |
| S2 |
28 |
24 |
29 |
40 |
| S3 |
35 |
24 |
32 |
33 |
| S4 |
24 |
32 |
25 |
28 |
Find an assignment that maximizes the profit(15)
4. a. Determine the optimum strategies and the vale
of the game from the following 2 x m pay-off matrix
game for X: (8)
|
Y |
| X |
6 3 -1 0 -3 |
| 25272837 |
| 3 2 -4 2 -1 |
b. An item is sold for Rs. 25 per unit and it costs Rs.
10. Unsold items can be sold for Rs. 4 each. It is assumed
that there is no shortage penalty cost besides the lost
revenue. The demand is known to be any value between 600
and 1000 items. Determine the optimal number of units
of the item to be stocked. (7)
5.a. An item is used at a uniform rate of 50,000 units
per year. No shortage is allowed and delivery is at
an infinite rate. The ordering, receiving and hauling
cost is Rs. 13 per order, while inspection csot is Rs.
12 per order. Interest costs Rs. 0.056 and deterioration
and obsolescence cost Rs. 0.004 respectively per year
for each item actually held in inventory plus Rs. 0.02
per year per unit based on the maximum number of units
in inventory. Calculate the Economic Order Quantity
(EOQ). If lead time is 20 days, find reorder level.
(7)
b. An item is produced at the rate of 50 units per
day and is consumed at the rate of 25 units per day.
If the set-up cost is Rs. 100 per production run and
holding cost in stock is Rs. 365 per unit per year,
find the economic lot size per run, number of runs per
year and total related cost. (8)
|
