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However, this formulation is computationally difficult to solve optimally using an exact approach.
A decomposition based algorithm was developed and combined with enhancement strategies to solve optimally large scale instances.
In general, supply chain models naturally lead to complex, large-scale mathematical models which are hard to solve optimally in most real cases.
Most instances are found difficult to solve optimally while our metaheuristic can find the best known or close to the best known solution in a short time.
The forest-level management problem addressed is complex, if not impossible to solve optimally, with current computing technologies, as integer decision variables are assumed.
Optimal solutions can be obtained in small sizes, however, large-sized problems are hard to solve optimally in a reasonable time.
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Moreover, since the bilevel model is difficult to be solved optimally and its optimal solution may not be stable, we provide a heuristic algorithm for the bilevel model able to always find a stable solution.
The key feature of the problem at hand is that it does not possess optimal substructure, that is, it cannot be solved (optimally) by an efficient combination of optimal solutions of its smaller subproblems.
However, this combinatorial optimization problem can be solved optimally in a reasonable CPU only when very small instances are considered.
The multi-level lot-sizing (MLLS) problem is a combinatorial optimization problem which can only be solved optimally within reasonable delays when small instances are considered.
It is commonly accepted that the underlying optimization problems, which are non-convex in general, can be solved optimally only for a limited set of problems and utilities in reasonable time.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com