Contents
What is MILP model?
An MILP model contains constraints for starting times of each task based on the arcs, and for the relationship between the makespan and the starting times of the tasks. An MILP model based on the superstructure gives the optimal solution of the scheduling problem. The minimal makespan is 41 hours for the example.
Why is integer programming NP hard?
In integer programming, you cannot just set the non-pivot columns to 0. The solution is harder (NP-hard) to find. Note also that the solutions are in Q, so this is not directly related to finite/infinite precision.
Why are integer optimization problems typically much harder than linear optimization problems?
However, integer variables make an optimization problem non-convex, and therefore far more difficult to solve. This is because many combinations of specific integer values for the variables must be tested, and each combination requires the solution of a “normal” linear or nonlinear optimization problem.
How long does it take to solve a MILP based problem?
Results demonstrate that MILP-based model could obtain good-quality results in less than 1 hour of CPU time. While, heuristic-based algorithms, were able to decompose the problem in reduced sub-problems that were solved in a moderate CPU time.
Is the MILP solution similar to the milfp solution?
Nilay Shah, in Computer Aided Chemical Engineering, 2020 The MILP and MILFP solutions appear very close in term of SC configuration, where the optimisation driven MILP sets all the storage facilities in the Romanian region. The cost breakdown between the MILP and the MILFP solutions is also comparable.
How is the stochastic MILP problem formulated into a two stage problem?
Using the classical scenario approach, the stochastic MILP problem can be formulated into a two-stage stochastic programming problem (Birge and Louveaux (2010)) as follows: (P) min x 0, x 1, …, x s c 0 T x 0 + ∑ ω ∈ Ω c ω T x ω s. t.
When to use a MILP-based heuristic approach?
An MILP-based model and sequential heuristic approaches were developed for the scheduling of multiple aircraft-parts in the surface-treatment process in the aircraft industry. Results demonstrate that MILP-based model could obtain good-quality results in less than 1 hour of CPU time.