# Special Case of Traveling Sales Man Problem

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The fact that schedule in sequencing problem is unable to return to its actual point till all jobs are accomplished, is the chief difference between sequencing problem and assignment. Thus, as compared to those assignment problems, solving a problem on sequencing is trickier. However, there are certain features which are common to problems of both assignment and sequencing. Thus, with few modifications, a student can easily solve his sequencing problems like that of assignment problems.

The problem of traveling salesman is a type of sequencing problem where it is expected that a salesman will visit all places before he returns to the starting point and finishes his journey in the shortest possible time.

Steps to solve traveling salesman problem

There are certain steps which a salesman needs to adopt to solving this kind of sequencing problem. These steps are-

Step-1:

• By diminishing the problem at first by rows, followed by columns
• If the zero cells in the matrix are placed in a way that they depict possible job sequencing, it is considered as the best solution of this kind of sequencing problem.

Step-2:

If those zero cells in matrix are not placed in a way through which possible solutions can be determined, there occurs a further improvement of these solutions till the point they attain a lower cost schedule. In case those zero cells do not provide the best sequence, then the cells having the next higher value are taken into consideration for achieving the best sequence.

To have a better understanding of this sequencing problems, students are advised to practice sums based on the same. This helps in gaining a better knowledge of a complex topic like this. However, there are few questions which too need special consideration.

Test Questions

1. What do you mean by Johnson’s algorithm?
2. Explain the concept of no passing rule in Johnson’s algorithm of sequencing problem.
3. What is the process of ‘n’ jobs through two machines?
4. Describe the process of ‘m’ jobs on three machines A, B, C in the order of ABC.
5. What are the chief assumptions which need to be considered while solving sequencing problems?
6. What do you mean by processing time?
7. Explain Johnson’s procedure for ascertaining the best sequence for operating ‘n’ job son two machines. Provide justifications of the rules involved in this process.
8. Elucidate the significance of sequencing technique in the process of decision- making. Point out the assumptions which should be considered in simple sequencing problem.
9. What do you mean by job arrival pattern in sequencing?
10. What are the uses of sequencing problem?
11. Explain the steps to solve sequencing problem.
12. How are a number of jobs (n) on 2 machines assigned in a way that it reduces the total elapsed time?
13. Briefly explain the terms-
• No passing rule
• Total elapsed time
• Total idle time
• Processing order
1. Describe the procedure to solve ‘n’ jobs and 3 machine sequencing problem.
2. What is the rule of shortest processing time (SPT)?
3. What do you mean Weight scheduling process time (WSPT)?
4. What are the types of sequencing problem? Justify your answer with examples.
5. Explain sequencing problem with few examples from your daily life.
6. What are the types of priority sequencing rules which are followed in a service system?
7. How can you solve traveling salesman sequencing problem?

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