3
$\begingroup$

I'm trying to develop a heuristic to solve a scheduling problem. The difficult for me is to treat the time as a variable.

There are 2 variables related to time, $b_{ij}$ and $f_{ij}$, being the time that the machine j begin and end the job $i$ respectively. It's used like this because the model has a demand constraint (see below), that is attended with the time that the machines do job $i$, and each machine has a specific capacity ($q_j$). There is also in the model a binary variable $x_{ij}$ that says if the machine $j$ do the job $i$.

$$\sum_j \bigg((f_{ij} - b_{ij}) * q_j * x_{ij}\bigg) \geq Demand_i, \forall i$$

In this problem, all the jobs needs to be processed only one time by whatever machine.

If anyone knows which kind of scheduling problem it is... It'll be a great help.

$\endgroup$
2
$\begingroup$

I think it is similar to the Flexible Job Shop Scheduling Problem as one of the students in my research collaborators group discussed a similar model with me, while developing a customized MOEA for solving the multi-objective flexible job-shop scheduling problem (FJSP). Please refer to the following preprint and see if it is helpful for you:

Wang, Y., van Stein, B., Emmerich, M., & Bäck, T. (2020). A Tailored NSGA-III Instantiation for Flexible Job Shop Scheduling. arXiv preprint arXiv:2004.06564. [pdf]

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.