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    Workers/Machine Jobs: Assignment Problems

    Uploaded by

    sravanicharitha Mamidi
    This document describes an assignment problem to minimize total processing time by assigning jobs to workers. It provides a cost matrix showing the processing time for each job by each worker. It explains that the problem is balanced since there are an equal number of rows and columns. It shows the steps to solve this including finding the reduced cost matrix and using lines to cover all the zeros, determining the optimum assignment schedule. The minimum processing time is calculated and the optimum assignment is displayed.

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    Workers/Machine Jobs: Assignment Problems

    Uploaded by

    sravanicharitha Mamidi
    24 views6 pages
    This document describes an assignment problem to minimize total processing time by assigning jobs to workers. It provides a cost matrix showing the processing time for each job by each worker. It explains that the problem is balanced since there are an equal number of rows and columns. It shows the steps to solve this including finding the reduced cost matrix and using lines to cover all the zeros, determining the optimum assignment schedule. The minimum processing time is calculated and the optimum assignment is displayed.

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    Original Title

    Assignment Problems

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    This document describes an assignment problem to minimize total processing time by assigning jobs to workers. It provides a cost matrix showing the processing time for each job by each worker. It explains that the problem is balanced since there are an equal number of rows and columns. It shows the steps to solve this including finding the reduced cost matrix and using lines to cover all the zeros, determining the optimum assignment schedule. The minimum processing time is calculated and the optimum assignment is displayed.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    24 views6 pages

    Workers/Machine Jobs: Assignment Problems

    Uploaded by

    sravanicharitha Mamidi
    This document describes an assignment problem to minimize total processing time by assigning jobs to workers. It provides a cost matrix showing the processing time for each job by each worker. It explains that the problem is balanced since there are an equal number of rows and columns. It shows the steps to solve this including finding the reduced cost matrix and using lines to cover all the zeros, determining the optimum assignment schedule. The minimum processing time is calculated and the optimum assignment is displayed.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 6

    Assignment problems

    Workers/Machine Jobs
    1 A
    2 B
    3 C
    4 D

    Workers Jobs
    A B C D
    1 10 8 7 12
    2 9 7 13 17
    3 6 7 8 9
    4 11 2 5 10
    m=n
    Assign the jobs for the workers so that the total processing time is minimum.

    Jobs
    Men
    I II III IV V
    A 9 22 58 11 19
    B 43 78 72 50 63
    C 41 28 91 37 45
    D 74 42 27 49 39
    E 36 11 57 22 25

    Since the number of rows is equal to Number of columns in the cost matrix,
    the given assignment problem is balanced.

    Row
    min
    9 22 58 11 19 9
    43 78 72 50 63 43
    41 28 91 37 45 28
    74 42 27 49 39 27
    36 11 57 22 25 11

    Select the smallest cost element in each row and subtract this from all the
    elements of the corresponding row, we get the reduced matrix

    0 13 49 2 10
    0 35 29 7 20
    13 0 63 9 17
    47 15 0 22 12
    25 0 46 11 14
    Select the smallest cost element in each column and subtract this from all the
    elements of the corresponding column,

    0 13 49 2 10
    0 35 29 7 20
    13 0 63 9 17
    47 15 0 22 12
    25 0 46 11 14
    Column 0 0 0 2 10
    min
    we get the reduced matrix:

    cover all the zeros by drawing a minimum number of lines.

    0 13 49 0 0
    0 35 29 5 10
    13 0 63 7 7
    47 15 0 20 2
    25 0 46 9 4

    0 17 49 0 0
    0 39 29 5 10
    9 0 59 3 3
    47 19 0 20 2
    21 0 42 5 0
    I II III IV V
    A 0 17 49 0 0
    B 0 39 29 5 10
    C 9 0 59 3 3
    D 47 19 0 20 2
    E 21 0 42 5 0

    Jobs
    Men
    I II III IV V
    A 9 22 58 11 19
    B 43 78 72 50 63
    C 41 28 91 37 45
    D 74 42 27 49 39
    E 36 11 57 22 25

    Minimum processing time:


    Determine the optimum assignment schedule.

    I II III IV V
    A 8 4 2 6 1
    B 0 9 5 5 4
    C 3 8 9 2 6
    D 4 3 1 0 3
    E 9 5 8 9 5

    I II III IV V
    A
    B
    C
    D
    E

    I II III IV V
    A
    B
    C
    D
    E

    I II III IV V
    A
    B
    C
    D
    E
    MAS company has four jobs to be assigned to 5 machines. Only one job could
    be assigned to one machine. The amount of time in hours required for the jobs
    in machine are given in the following matrix.

    Machines
    Job
    A B C D E
    1 4 3 6 2 7
    2 10 12 11 14 16
    3 4 3 2 1 5
    4 8 7 6 9 6

    Find the optimum assignment of jobs to the machines to minimize the


    total processing time and also find for which machine no job is assigned. What
    is the total processing time to complete all the jobs.

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