Correction to: A heuristic-based non-linear mixed integer approach for optimizing modularity and integrability in a sustainable reconfigurable manufacturing environment

Correction to: The International Journal of Advanced Manufacturing Technology

https://doi.org/10.1007/s00170-020-05366-y

This original article contained a mistake.

C1: The notation table in page 12 is not copied correctly. The correct notations are as follows:

Indices

Operations:

o, o’ = 1, …, TNOP

Configurations:

c, c’ = 1, ..., NC

Machines:

m, m’ = 1, …, NM

Basic modules:

γ = 1, …, BM

Auxiliary modules:

δ =1,..., AM

Parameters

TNOP :

Total number of operations

NC :

Total number of configurations

NM :

Total number of machines

BM :

Number of basic modules

AM :

Number of auxiliary modules

SMAC :

Set of available machines

SCN :

Set of configurations

NI m, c :

Number of interfaces

PRM o :

Precedence Matrix

\( {E}_{PLC}^{m,y} \) :

Energy consumption by controller PLC of γth basic module on the mth machine

\( {E}_{PLC}^{c,\delta } \) :

Energy consumption by controller PLC of δth auxiliary module for the cth configuration

E WASTE :

Energy waste between interfaces

\( {E}_{CHANGE}^{m,m\hbox{'}} \) :

Energy changing machines

\( {E}_{ASS}^{c,\delta } \) :

Energy consumption by assembling δth auxiliary module for the cth configuration

\( {E}_{DIS}^{c,\delta } \) :

Energy consumption by disassembling δth auxiliary module for the cth configuration

E m, γ :

Energy consumption by γth basic module on mth machine

Decision variables

\( {w}_o^{m,c} \) :

1 if the oth operation is being processed by the mth machine using cth configuration, 0 otherwise

\( {\mathrm{x}}_{\mathrm{o},\upgamma}^{\mathrm{m},\mathrm{c}} \) :

1 if the mth machine is using the γth basic module in cth configuration for the oth operation, 0 otherwise

\( {y}_o^{m,{m}^{\prime }} \) :

1 if there has been a change between machine m and m’ in the oth operation, 0 otherwise

\( {\mathrm{u}}_{\mathrm{o},\updelta}^{\mathrm{m},\mathrm{c}} \) :

1 if the mth machine is using the δth auxiliary module in cth configuration in the oth operation, 0 otherwise

\( {z}_{o,\delta}^{m,c} \) :

1 if the δth auxiliary module is assembled on the mth machine in cth configuration in the oth operation, 0 otherwise

\( {v}_{o,\delta}^{m,c} \) :

1 if the δth auxiliary module is disassembled on the mth machine in cth configuration in the oth operation, 0 otherwise

C2: Fig5 in page 19 can be replaced by the following figure.

figurea

The original article has been corrected.

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Correspondence to Hichem Haddou Benderbal.

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The online version of the original article can be found at https://doi.org/10.1007/s00170-020-05366-y

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Massimi, E., Khezri, A., Haddou Benderbal, H. et al. Correction to: A heuristic-based non-linear mixed integer approach for optimizing modularity and integrability in a sustainable reconfigurable manufacturing environment. Int J Adv Manuf Technol 108, 2021–2022 (2020). https://doi.org/10.1007/s00170-020-05533-1

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