References
55
When i and j are set to the same row, these constraints together with (3.12) make
d ij = |x j − x i |. Since the advantage of these constraints is unclear, we retained the
nonoverlap constraints (3.13), which are a common feature of all layout problems.
The MRFLP has received fairly limited attention in the operations research
literature to date. The MILO formulation for MRFLP in Sect. 3.2.1 was proposed
in Chung and Tanchoco (2010); their model also explicitly accounts for clearances
between departments. This model was later corrected in Zhang and Murray (2012).
The formulation in Sect. 3.2.2 was introduced in Anjos and Vieira (2021), where
Theorem 3.1 and Corollary 3.1 are proved. Total unimodularity is a classical topic
in integer optimization. The results quoted in Sect. 3.2.3 are from Nemhauser and
Wolsey (1988, Section III.2), where the reader can find a wealth of information
about TU matrices and their applications.
The theoretical results and the ILO formulation for the MREFLP given in
Sect. 3.4 were presented in Anjos et al (2018), which also discusses their specialization for the DRFLP. The MILO formulation for the CAP presented in Sect. 3.5.1
was introduced in Amaral (2012).
The models for k-PROP in Sect. 3.5.4 and for the FR-MRFLP in Sect. 3.3 were
introduced in Fischer et al (2019). They presented these models in the opposite
order: first, a model for the k-PROP is introduced, and then the FR-MRFLP is
considered. Together with these models, Fischer et al (2019) present an algorithm
(based on the enumeration of row assignments) that allows them to solve the
MRFLP and k-CAP. They develop strategies for reducing the number of possible
row assignments. As of the time of writing, this is the most efficient strategy for
instances of the MRFLP and k-CAP.
The SDO model, the theoretical results, and the k-PROP approach for the
MRFLP in Sect. 3.6 were presented in Hungerländer and Anjos (2015). They prove
several results to reduce the number of spacing departments needed and hence
improve the computational performance of the SDO approach.
References
Ahonen H, de Alvarenga A, Amaral A (2014) Simulated annealing and tabu search approaches for
the corridor allocation problem. Eur J Oper Res 232(1):221–233
Amaral ARS (2012) The corridor allocation problem. Comput Oper Res 39(12):3325–3330
Amaral ARS (2013) Optimal solutions for the double row layout problem. Optimization Letters
7(2):407–413
Anjos MF, Vieira MVC (2021) Mathematical optimization approach for facility layout on several
rows. Optimization Letters 15:9–23
Anjos MF, Fischer A, Hungerländer P (2018) Improved exact approaches for row layout problems
with departments of equal length. Eur J Oper Res 270(2):514–529
Chung J, Tanchoco JMA (2010) The double row layout problem. Int J Prod Res 48(3):709–727
Fischer A, Fischer F, Hungerländer P (2019) New exact approaches to row layout problems. Math
Programm Comput 11:703–754
Heragu SS (2008) Facilities design. CRC Press
55
When i and j are set to the same row, these constraints together with (3.12) make
d ij = |x j − x i |. Since the advantage of these constraints is unclear, we retained the
nonoverlap constraints (3.13), which are a common feature of all layout problems.
The MRFLP has received fairly limited attention in the operations research
literature to date. The MILO formulation for MRFLP in Sect. 3.2.1 was proposed
in Chung and Tanchoco (2010); their model also explicitly accounts for clearances
between departments. This model was later corrected in Zhang and Murray (2012).
The formulation in Sect. 3.2.2 was introduced in Anjos and Vieira (2021), where
Theorem 3.1 and Corollary 3.1 are proved. Total unimodularity is a classical topic
in integer optimization. The results quoted in Sect. 3.2.3 are from Nemhauser and
Wolsey (1988, Section III.2), where the reader can find a wealth of information
about TU matrices and their applications.
The theoretical results and the ILO formulation for the MREFLP given in
Sect. 3.4 were presented in Anjos et al (2018), which also discusses their specialization for the DRFLP. The MILO formulation for the CAP presented in Sect. 3.5.1
was introduced in Amaral (2012).
The models for k-PROP in Sect. 3.5.4 and for the FR-MRFLP in Sect. 3.3 were
introduced in Fischer et al (2019). They presented these models in the opposite
order: first, a model for the k-PROP is introduced, and then the FR-MRFLP is
considered. Together with these models, Fischer et al (2019) present an algorithm
(based on the enumeration of row assignments) that allows them to solve the
MRFLP and k-CAP. They develop strategies for reducing the number of possible
row assignments. As of the time of writing, this is the most efficient strategy for
instances of the MRFLP and k-CAP.
The SDO model, the theoretical results, and the k-PROP approach for the
MRFLP in Sect. 3.6 were presented in Hungerländer and Anjos (2015). They prove
several results to reduce the number of spacing departments needed and hence
improve the computational performance of the SDO approach.
References
Ahonen H, de Alvarenga A, Amaral A (2014) Simulated annealing and tabu search approaches for
the corridor allocation problem. Eur J Oper Res 232(1):221–233
Amaral ARS (2012) The corridor allocation problem. Comput Oper Res 39(12):3325–3330
Amaral ARS (2013) Optimal solutions for the double row layout problem. Optimization Letters
7(2):407–413
Anjos MF, Vieira MVC (2021) Mathematical optimization approach for facility layout on several
rows. Optimization Letters 15:9–23
Anjos MF, Fischer A, Hungerländer P (2018) Improved exact approaches for row layout problems
with departments of equal length. Eur J Oper Res 270(2):514–529
Chung J, Tanchoco JMA (2010) The double row layout problem. Int J Prod Res 48(3):709–727
Fischer A, Fischer F, Hungerländer P (2019) New exact approaches to row layout problems. Math
Programm Comput 11:703–754
Heragu SS (2008) Facilities design. CRC Press