# June 2003

## Question Paper of CS 51 – Operations Research of June 2003 from IGNOU

1. a. Explain briefly any two of the following OR techniques: (6)

i. Linear Programming

ii. CPM

iii. M/< / ? 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

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 34 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

6 3 -1 0 -3

X 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)

6.a. The following is the pay-off matrix (in rupees) for the two persons zero-sum game:

Player B

I II III

Player A

I -3 4 -1

II 3 1 5

III -1 -5 11

Using Minmax criterion, find the best strategy for each player. (7)

b. Determine which course of action Player B will not use in the following game. Obtain the best strategy for each of the two players and value of the game. (8)

Player B

I II III

Player A

I -3 1 7

II 4 1 -2