An assignment problem can be considered as a special case of transportation problem.
In operational research, the assignment problem is indeed closely related to the transportation problem, but it is not merely a special case; rather, it represents a specific application within the broader framework of optimization.
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The time taken by a TV repair person to repair a TV set is exponentially distributed with mean 30 minutes. She repairs the sets in the order in which they come in. The arrival rate of the sets is approximately Poisson with an average rate of 10 per 8 hours day. Answer the following questions: (5)
i) What is the repair person’s expected idle time each day?
ii) How many jobs are ahead of the arriving set just brought in?
iii) What is probability that there are 2 or more sets in the system?
Customers come to a coffee shop at the average rate of 32 per day (8 hours a day) in Poisson pattern. The waiter employed to serve the customers has left the job. The owner of the shop wants to hire a new the job. The owner of the shop wants to hire a new waiter. Two applicants, Abdul and Raju, have applied for the post. The service times of Abdul and Raju are exponentially distributed with mean 12 minutes and 10 minutes, respectively. Abdul and Raju demand salaries of ₹ 135 and ₹ 165 per day, respectively. If no service is available, the average loss to the owner is ₹ 400 per day. Who among the two should be selected for the job?
निम्नलिखित LPP को हल करने के लिए द्वैती एकधा विधि का प्रयोग कीजिए : 5
z = 3x₁ + x₂ का न्यूनतमीकरण कीजिए
जबकि : 5
x₁ + x₂ ≥ 1
2x₁ + 3x₂ ≥ 2
x₁,x₂ ≥ 0.
An investment company wants to study the investment proposals based on the profit factor. While analyzing a new investment proposal, the company estimated the probability distribution for the profit as follows:
| Profit (in thousands) | 3 | 5 | 7 | 9 | 10 |
| Probability | 0.1 | 0.2 | 0.4 | 0.2 | 0.1 |
एक फैक्टरी में 6 जॉब पूरी होनी हैं। प्रत्येक जॉब को दो मशीनों A और B से AB के क्रम में गुजरना है। जॉब का प्रत्येक मशीन पर प्रक्रिया काल दिया गया है। आपको वह अनुक्रम निकालना
है जिससे कुल व्यतीत समय T न्यूनतम हो, T का मान क्या है ?
| जॉब | मशीन A | मशीन B |
| j1 | 1 | 5 |
| j2 | 3 | 6 |
| j3 | 8 | 3 |
| j4 | 5 | 2 |
| j5 | 6 | 2 |
| j6 | 3 | 10 |
Listed in the table below are the activities and sequencing requirements necessary for the completion of a project.
| Activity | Predecessor | Duration in weeks |
| A | __ | 6 |
| B | A | 24 |
| C | A | 6 |
| D | A | 12 |
| E | A | 9 |
| F | C,D,E | 18 |
| G | B,F | 12 |
| H | G | 24 |
Write the dual of the following LP problem:
Min.
Subject to