Indira Gandhi National Open University (IGNOU) 2005 Diploma Computer Applications Operations Research - CS51 - Question Paper

CS - 51 : Operations Research 1. a. discuss briefly any 2 of the subsequent OR techniques: (6)
i. Linear Programming
ii. CPM
iii. M/< / eight queing model
iv. Dynamic Programming

b. Product Mix Problem: provide the Linear Programming formulation of the subsequent problem:

The products A and B are produced in 3 machine centers X, Y and Z. every product involves operation of every of the machine centers. The time needed for every operation unit amount of every product is provided below: Time available at machine centers X, Y and Z are 100, 77 and 80 hours respectively. The profit per unit of every of A and B is Rs. 12 and Rs. three respectively. (3)

Product
Machine Centers
Profit Per Unit


X
Y
Z


A
10
7
2
12

B
2
3
4
3



c. Enumerate different important steps in OR study and explain 1 of the steps briefly: (4)

d. discuss the subsequent concepts in situation of Linear Programming / OR ( 3)
i. Objective Function
ii. Convex Polygon
iii. Redundant Constraint

e. discuss the subsequent in situation of Transportation issue (not exceeding 3 phrases for each):
i. Stepping Stone Method
ii. Degenerate Transportation issue
iii. The replaced Distribution Method

f. discuss the subsequent in situation of Assignment issue (not exceeding 3 phrases for each): (3)
i. Balanced Assignment issue
ii. Hungarian Method
iii. an Infeasible Assignment

g. Company XYZ produces 2 products. The maximum sales potential for product one and product two are 30 units and 40 units respectively. Write the goal constraints for achieving the sales goal by incorporating the deviational variables. (3)

h. discuss the subsequent concepts in situation of Dynamic Programming (not exceeding 3 phrases for each): (3)
i. Principle of Optimality
ii. State
iii. Stage

j. discuss the subsequent in situation of Inventory Control: (2)
i. Decoupling
ii. VED classification
iii. Delivery Lag

2. Solve the Product Mix issue provided 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 4 territories, He has 4 candidates of varying experience and capabilities and assesses the possible profit in suitable units for every salesman in every territory as provided below: Salesman
Territories


T1
T2
T3
T4

S1
25
27
28
37

S2
28
34
29
40

S3
35
24
32
33

S4
24
32
25
28


obtain an assignment that maximizes the profit(15)

4. a. Determine the optimum strategies and the vale of the game from the subsequent two x m pay-off matrix game for X: (8)
Y
6 three -1 0 -3
X three two -4 two -1


b. An item is sold for Rs. 25 per unit and it costs Rs. 10. Unsold items can be sold for Rs. four every. It is presumed that there is no shortage penalty cost besides the lost revenue. The demand is known to be any value ranging from 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 every item truly held in inventory plus Rs. 0.02 per year per unit based on the maximum number of units in inventory. compute the Economic Order volume (EOQ). If lead time is 20 days, obtain 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, obtain the economic lot size per run, number of runs per year and total related cost. (8)

6.a. The subsequent is the pay-off matrix (in rupees) for the 2 persons zero-sum game: Player B

Player A

I
II
III

I
-3
4
-1

II
3
1
5

III
-1
-5
11

Using Minmax criterion, obtain the best strategy for every player. (7)

b. Determine which course of action Player B will not use in the subsequent game. find the best strategy for every of the 2 players and value of the game. (8)

Player B

Player A

I
II
III

I
-3
-1
7

II
4
1
-2

Earning:   Approval pending.