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We propose various ways to improve the Benders master problem and the feasibility cuts.
In these column generation approaches, the master problem is often of a set partitioning type.
In the proposed procedure, the master problem will be developed using the surrogate constraints.
An L-shaped decomposition with an additional decomposition step in the master problem is proposed.
To enhance the computational efficiency, a relaxed linear programming (LP) formulation of the master problem is proposed.
This is achieved by decomposing the master problem and solving only the much smaller sub-problems resulting from decomposition.
The master problem determines the assignment of platforms to wells and the planning subproblem calculates the timing for fixed assignments.
We decompose the problem to separate the location decisions in the master problem from the inventory decisions in the subproblem.
Then, we present a new restrict-and-decompose scheme to further decompose the Benders master problem by part.
At each iteration, the sample average approximation method is applied to the NLP sub-problem and MILP master problem.
We show that the main constraints of the master problem can be replaced by the strongest surrogate constraint.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com