Exact makespan minimization of unrelated parallel machines
Artikel i vetenskaplig tidskrift, 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.

Lagrangian relaxation

variable fixing

unrelated parallel machine problem


binary knapsack


Edvin Åblad

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Ann-Brith Strömberg

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Domenico Spensieri

Chalmers, Industri- och materialvetenskap, Produktutveckling

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik

Open Journal of Mathematical Optimization

27775860 (eISSN)

Vol. 2 2

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

Stiftelsen Fraunhofer-Chalmers Centrum för Industrimatematik, 2017-08-15 -- 2022-09-05.

Stiftelsen för Strategisk forskning (SSF) (RIT15-0025), 2017-08-15 -- 2022-09-05.

Smart Assembly 4.0

Stiftelsen för Strategisk forskning (SSF) (RIT15-0025), 2016-05-01 -- 2021-06-30.


Informations- och kommunikationsteknik




Annan matematik

Robotteknik och automation

Diskret matematik


Grundläggande vetenskaper

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