The Assignment Problem is a special type of transportation problem, where the objective is to minimize the cost or time of completing number of jobs(activities) by number of workers(resources).
|
|
Job (activity) |
|
Worker
(resource)
|
`J_1` |
`J_2` |
`J_3` | Supply |
|
`W_1` |
`c_11` `(x_11)` |
`c_12` `(x_12)` |
`c_13` `(x_13)` |
1 |
|
`W_2` |
`c_21` `(x_21)` |
`c_22` `(x_22)` |
`c_23` `(x_23)` |
1 |
|
`W_3` |
`c_31` `(x_31)` |
`c_32` `(x_32)` |
`c_33` `(x_33)` |
1 |
| Demand |
1 |
1 |
1 | |
Here, `c_(ij)` represents the cost of assignment of worker(resource) i to job(activity) j and
`x_(ij)` represents the assignment of worker(resource) i to job(activity) j
`x_(ij)={(1,"if worker i is assigned to job j"),(0,"otherwise"):}`
General Mathematical Model
minimize `sum_{i=1}^{n}\ sum_{j=1}^{n} c_(ij)*x_(ij)`
subject to
`sum_{j=1}^{n} x_(ij)= 1` (worker availability)
`sum_{i=1}^{n} x_(ij)= 1` (job requirement)
and `x_(ij)=` 0 or 1
Solution of Assignment Problem can be found using
- Simplex method
- Transportation problem method
- Hungarian method
Notes :
- Number of workers = Number of jobs.
- Each worker is assigned only one job.
- Each worker is independently capable for handling any job.
- Assigning criteria is either minimizing cost or maximizing profit.
This material is intended as a summary. Use your textbook for detail explanation.
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