# Solver for Flexible Job Shop Scheduling Problem

I have a FJSSP that I would like to solve. However, the jobs in this problem have deadlines and in addition there are setup times between two jobs. Because of this, my objective function is not just the makespan but rather a more complex (nonlinear)combination between makespan and tardiness (with respect to given deadlines) of the execution of the jobs.

I was thus wondering which solvers are available right now which offer flexibility to modify my objective functions. Or, in general, how are practitioners tackling these problems in industry currently? Can you please help?

• Would you say, have you had any force to use a non-linear objective function? Is it possible to use e.g. the multi-objective approach, specifically, in the MIP context? Mar 13 at 19:36
• @A.Omidi The problem is that machines can work different number of hours every day and I only care about the day jobs end, so it should be a linear function of a step function . I dont intend to use multiobjective techniques here. Mar 13 at 19:58
• some points: 1) FJSSP is already NP-Hard in its essence and as you pointed out the number of jobs is around $400$, so it becomes more challenging. 2) There are some options to solve such a large-scale problem. First, by using a modified local-search heuristic that can handle your non-linear objective. Second, with the aim of CP/MI(NL)P solvers, and finally with special solvers like LocalSolver or Cp-SAT. (One of the best CP-SAT offered by Google or-tool). Do you try that? Mar 14 at 6:37
• @A.Omidi Thanks! Yes, I am currently exploring the Google OR - tool option with CP SAT. I think the main problem will be to express my custom objective function in terms of the intervals, but we will see. Could you perhaps suggest a cool reference/tutorial on this? I think it would also help other people who have the same question. Thanks again! Mar 14 at 13:20