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 γ^th basic module on the m^th machine

${E}_{PLC}^{c,\delta }$ :

Energy consumption by controller PLC of δ^th auxiliary module for the c^th configuration

E _WASTE :

Energy waste between interfaces

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

Energy changing machines

${E}_{ASS}^{c,\delta }$ :

Energy consumption by assembling δ^th auxiliary module for the c^th configuration

${E}_{DIS}^{c,\delta }$ :

Energy consumption by disassembling δ^th auxiliary module for the c^th configuration

E ^{m, γ} :

Energy consumption by γ^th basic module on m^th machine

Decision variables

${w}_o^{m,c}$ :

1 if the o^th operation is being processed by the m^th machine using c^th configuration, 0 otherwise

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

1 if the m^th machine is using the γ^th basic module in c^th configuration for the o^th operation, 0 otherwise

${y}_o^{m,{m}^{\prime }}$ :

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

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

1 if the m^th machine is using the δ^th auxiliary module in c^th configuration in the o^th operation, 0 otherwise

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

1 if the δ^th auxiliary module is assembled on the m^th machine in c^th configuration in the o^th operation, 0 otherwise

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

1 if the δ^th auxiliary module is disassembled on the m^th machine in c^th configuration in the o^th operation, 0 otherwise

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

The original article has been corrected.