SEQUENCING PROBLEM. Assignment

Transcription

1 SEQUENCING PROBLEM Questions 1. Describe General sequencing problem. 2. Explain the principal assumptions made while dealing with sequencing problems. 3. Write a short note on the sequencing decision problem for n jobs on two machines. 4. What is no passing rule in a sequencing algorithm? Explain the principal assumptions made while dealing with sequencing problems. 5. Explain Johnson algorithm for processing n jobs 2 machine problem. 6. Explain Johnson algorithm for processing n jobs 3 machine problem. 7. Explain Johnson algorithm for processing n jobs m machine problem. 8. Write an algorithm to process 2 jobs through m machines. N Jobs 2 MACHINE Assignment 1. Five Jobs are performed, first on machine X and then on machine Y. The time taken, in hours by each job on each machine is given below: Job A B C D E Time on Machine X Time on Machine Y Determine the optimum sequence of jobs that minimizes the total elapsed time to complete the jobs. Also compute idle time for each machine. 2. A book binder has one printing press, one binding machine, and manuscripts of a number of books. The time required performing the printing and binding operations on each book are shown below. The binder wishes to determine the order in which the books should be processed, so that the total time required to process all books is minimized, find idle time For each machine. Book Printing Time (Hours) Binding Time (Hours) We have seven jobs each of which has to go through the machine M1 and M2 in the order M1, M2. Processing times (in hours) are given as: Job Machine M Machine M

2 Determine a sequence of these jobs that will minimize the total elapsed time T. Also find Idle time for each machine. 4. Seven jobs are to be processed through two machines A and B. Processing times ( in hours) are given below: Jobs Machine A Machine B Determine the optimum sequence for the jobs,total elapsed time and idle time on each machine. 5. In the machine shop, 8 different products are being manufactured each requiring time on 2 machines A and B as given below: Product Time(in min.) on machine A Time(in min) on machine B I II III IV V VI VII VIII Decide the optimum sequence of processing of different products in order to minimize the total manufacturing time for all the products. 6. A manufacturing company processes 6 different jobs on two machine A and B. Number of units of each job and its processing times on A and B are given below: Job Units of Processing Time each job Machine A (minutes) Machine B (minutes) Find the optimal sequence, the total minimum elapsed time and idle time for each machine.

3 N Jobs 3 MACHINE 1. A ready-made garment manufacturer has to process 7 items through two stages of production viz. cutting and sewing. The times taken for each of these items at the different stages are given below in appropriate units. Item Cutting time Sewing time (i) Find an order in which these items are to be processed through these stages so as to minimize the total processing time. (ii) Suppose the third stage of production is added, viz.. pressing and packing, with processing time for these times as follows: Item Pressing and packing time Find an order in which these 7 items are to be processed so as to minimize the time taken to process all the items through all the three stages. 2. Six jobs have to be processed at three machines A, B and C in the order ABC. The time taken by each job on the three machines is given below. Each machine can process only one job at a time: Jobs Processing Time A (in hours) B On machines C Determine the optimum sequence for the jobs and total elapsed time. 3. Find the sequence that minimizes the total elapsed time required to complete the following tasks. Each job is processed in the order ABC. Job Machine A Machine B Machine C Find a sequence that minimizes the total elapsed time required to complete the following tasks. A B C D E F G Time on Machine Time on Machine Time on Machine A manufacturing firm works 80 hours a week and has a capacity of overtime work to the extent of 40 hours in a week. It has received seven orders to be processed on three machines A, B and C, in the order ABC to be delivered in a week s time from now. The process times are recorded in the given table:

4 Jobs Machine A Machine B Machine C The manager, who, in fairness, insists on performing the jobs in the sequence in which they are received, is refusing to accept an eighth order, which requires 14, 4 and 10 hours respectively on A, B and C machines, because, according to him, the eighth jobs would require a total of 122 hours for processing, which exceeds the firm s capacity. Advise him. Processing n Jobs through m Machines 1. Find an optimal sequence for the following sequencing problems of four jobs and five machines when passing is not allowed of which processing time (in hours) is given below: Job Machine A M1 M2 M3 M4 M5 A B C D Solve the following sequencing problem giving an optimal solution when passing is not allowed. Machine Job A B C D E M M M M Find an optimal sequence for the following sequencing problem of four jobs and five machines (when passing is not allowed) of which processing time (in hrs.) is as follows: Job Machine M Machine M Machine M Machine M Machine M Also find the total elapsed time.

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