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arXiv · 2210.02434

A flow-based formulation for parallel machine scheduling using decision diagrams

Daniel Kowalczyk·Roel Leus·Christopher Hojny·Stefan Røpke
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Abstract

We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally non-uniform, periods and do not exclude all optimal solutions, but they constrain solutions to adhere to a canonical form. The new formulation has numerous variables and constraints, and hence we apply a Dantzig-Wolfe decomposition in order to compute the linear programming relaxation in reasonable time; the resulting lower bound is stronger than the bound from the classical time-indexed formulation. We develop a branch-and-price framework that solves several instances from the literature for the first time. We compare the new formulation with the time-indexed and arc-time-indexed formulation by means of a series of computational experiments.

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Daniel Kowalczyk, Roel Leus, Christopher Hojny, Stefan Røpke. 2022-10-05. A flow-based formulation for parallel machine scheduling using decision diagrams. https://arxiv.org/abs/2210.02434

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