1 / 13

Assignment Problem

Assignment Problem. Definition. Assignment Problem is a balanced transportation problem in which all supplies and demand are equal to 1. The Hungarian Method.

zaynah
Download Presentation

Assignment Problem

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Assignment Problem

  2. Definition Assignment Problem is a balanced transportation problem in which all supplies and demand are equal to 1

  3. The Hungarian Method • Find the minimum element in each row af the m x m cost matrix. Construct a new matrix by subtracting from each cost the minimum cost in its row. For the new matrix, find the minimum cost in each column. Construct a new matrix (called the reduced cost matrix) by subtracting from each cost the minimum cost in its column

  4. 2. Draw the minimum number of lines (horizontal and/or vertical) that are needed to cover all the zero’s in the reduced cost matrix. If m lines are required, an optimal solution is available among the covered zeros in the matrix. If fewewr than m lines are needed, proceed to step 3

  5. 3. Find the smallest nonzero element (call its value k) in the reduced cost matrix that is uncovered by lines drawn in step 2. Now subtract k from each uncover element of the reduced cost matrix and add k to each element that is covered by two lines. Return to step 2

  6. Example Machineco has 4 machines and 4 jobs to be completed. Each machine must be assigned to complete one job. The time required to set up each machine for completing each job is shown in the table. Machineno wants to minimize the total setup time needed to complete the four job

  7. Solution Xij = 1 if machine i is assgned to meet the demand of job j Xij= 0 if machine I is not assigned to meet the demand of job j

  8. Formulation of the problem Min z = 14 x11 + 5 x12+ 8x13 + 7x14+ …+ 6x43+ 10x44 s.T x11+ x12+ x13+ x14 = 1 (machine constraint) x21+ x22+ x23+ x24 = 1 x31+ x32+ x33+ x34= 1 x41+ x42+ x43+ x44= 1 x11 + x21 + x31 + x41 = 1 (job constraint) x12+ x22+ x32+ x42= 1 x13+ x23+ x33+ x43= 1 x14+ x24+ x34+ x44= 1

  9. Table 1 minimum row

  10. Table 2 Setelahpengurangan row minimum Min Column

  11. Table 3 SetelahPengurangan Column minimum K = 1 (nilaiterkecil di antaracel yang tidaktertutupgaris) Cel yang tidaktertutupgarisdikurangi 1, yang ditutup 2 garisditambah 1

  12. Table 4 Solusi optimal : x12 = 1, x33 = 1, x41 = 1, x24 = 1

More Related