Exact makespan minimization of unrelated parallel machines
Journal article, 2021

We study methods for the exact solution of the unrelated parallel machine problem with makespan minimization, generally denoted as R||Cmax. Our original application arises from the automotive assembly process where tasks needs to be distributed among several robots. This involves the solutions of several R||Cmax instances, which proved hard for a MILP solver since the makespan objective induces weak LP relaxation bounds. To improve these bounds and to enable the solution of larger instances, we propose a branch–and–bound method based on a Lagrangian relaxation of the assignment constraints. For this relaxation we derive a criterion for variable fixing and prove the zero duality gap property for the case of two parallel machines. Our computational studies indicate that the proposed algorithm is competitive with state-of-the-art methods on different types of instances. Moreover, the impact of each proposed feature is analysed.

variable fixing

binary knapsack

Lagrangian relaxation

makespan

unrelated parallel machine problem

Author

Edvin Åblad

Fraunhofer-Chalmers Centre

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Ann-Brith Strömberg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Domenico Spensieri

Chalmers, Industrial and Materials Science, Product Development

Open Journal of Mathematical Optimization

2777-5860 (eISSN)

Vol. 2 1-15 2

Smart Assembly 4.0

Swedish Foundation for Strategic Research (SSF) (RIT15-0025), 2016-05-01 -- 2021-06-30.

Interlinked combinatorial and geometrical optimization problems in an autonomous automotive manufacturing industry

Fraunhofer-Chalmers Centre, 2017-08-15 -- 2022-09-05.

Swedish Foundation for Strategic Research (SSF) (RIT15-0025), 2017-08-15 -- 2022-09-05.

Areas of Advance

Information and Communication Technology

Production

Subject Categories

Computational Mathematics

Other Mathematics

Robotics

Discrete Mathematics

Roots

Basic sciences

More information

Latest update

8/25/2021