Register Number: 6847

Total No. of Pages: 3

Name of the Candidate:

P.G. DIPLOMA EXAMINATION - 2010

(APPLIED OPERATIONS RESEARCH)

(paper –IV)

140. NETWORK, REPLACEMENT AND DECISION THEORY MODELS

December) (Time: 3 Hours

Maximum: 100 Marks

Attemptany FIVE questions.
Use of Statistical Tables are permitted. (5 × 20 = 100)

1. The schedule of a project is shown below:

(i) Draw the network diagram for the project.

(ii) Find the earliest, latest time and float for each activity.

(iii)Determine the critical path.

2.The data on normal time, crash time, normal cost, crash cost of a project are given
in the table shown below. Indirect cost is given as Rs. 100 per day. Draw the
network, crash the activities systematically and determine the optimum project
completion time and cost.

3. (a) Machine A costs Rs.36,000. Annual operating costs are Rs.800 for the first year,
and then increase by Rs. 8000 every year. Determine the best age at which to

replace the machine. If the optimum replacement policy is followed, what will be
the average yearly cost of owning and operating the machine?

(b)Machine B costs Rs.40,000. Annual operating costs are Rs. 1600 for the first
year, and then increased by Rs. 3200 every year. The company now has a
machine of type A which is one year old. Should it be replaced with B? If so
when? Assume that both machines have no resale value.

4. The following failure rates have been observed for certain items.

The cost of replacing an individual item is Rs. 1.25. The decision is made to replace all items simultaneously at fixed intervals and also replace individuals as they fail. If the cost of group replacement is 50 paise, what is the best interval for group replacement? At what group replacement per item, would a policy of strictly individual replacement become preferable to the adopted policy.

5. In order to meet an increased demand for the product, a manufacturing company is
considering the following three courses of action:

(i) arrange overtime working (ii) subcontract the production (iii) carry out expansion
of the existing unit.

The correct choice depends largely upon future demand which may be low, medium, or high. The respective probabilities of the future demand are estimated as 0.1, 0.40 and 0.50. A cost analysis reveals the pay offs (profits) shown in the table given below.

Draw the decision tree and indicate the optimal decision and the corresponding expected value.

6. (a) For the following payoff matrix of firm A, determine the optimal strategies for
both the firms and find the value of the game.

(5)

(b) Solve the following 2x2 game:

(15)

7. Solve the following 2x4 game graphically:

8. Solve the following game by the method of matrices.

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