# Assignment problem using Hungarian method

There are five jobs to be assigned to five machines and associated cost matrix is as follows $$\begin{matrix} \text{Machine} & 1 & 2 & 3 & 4 & 5 \\ \text{Job A} & [11, &17, &8, &16, &20] \\ \text{Job B} & [9, &7, &12, &6, &15] \\ \text{Job C} & [13, &16, &15, &12, &16] \\ \text{Job D} & [21, &24, &16, &28, &26] \\ \text{Job E} & [14, &10, &12, &11, &15] \end{matrix}$$ The question is now: Find the assignment of machines to jobs that will minimize the total cost?

I solved it using the Hungarian method but for job A and D I had only one zero that too in the same column. I don't know how to solve further if this happens.

• Since this looks a lot like a homework question, it would be best to show you intermediate steps of your attempt to solve it Jun 18, 2019 at 9:20
• As a note, I voted to reject a tag edit of "self-study" because I think that would be a meta-tag. Not sure that we fully settled on that as a policy, but I think we were leaning that direction. (or.meta.stackexchange.com/questions/163/…) Also, welcome to OR.SE, @Tango! Jun 18, 2019 at 14:15
• @E. Tucke At Cross Validated stats.stackexchange.com , self-study tag is applied to all homework problems, and even for questions requesting help understanding passages in textbooks, even f being used in self-study outside any courses. Jun 18, 2019 at 23:12
• @MarkL.Stone Sounds good! The tag seems accurate; it's more that it's a meta-tag. If the community wants to go that direction, that's fine by me. Jun 19, 2019 at 12:13

I assume you're applying the matrix version of the algorithm. When you happen to have only one $$0$$ for A and D the matrix is \begin{align*} \pmatrix{2&9&0&8&8\\2&1&6&0&5\\0&4&3&0&0\\4&8&0&12&6\\3&0&2&1&1} \end{align*} Now continue with Step 3: cover all zeros minimally, and adjust the weights. After that step you will find a solution.
• The least uncovered element will be $2$. Note that line $5$ will be unmarked after step 3. Jun 19, 2019 at 5:14