Table 1 Notations of mathematical formulation.
\(i,h,{i}^{^{\prime}}\) | Index of the jobs, \(i=1,\cdots n\) |
\(j, { j}^{^{\prime}}\) | Index of the operations |
\(k,{k}^{^{\prime}}\) | Index of the machines, \(k=1,\cdots m\) |
\(z\) | Index of machine speed levels |
\({l}_{i}\) | Total number of operations of job \(i\),\({l}_{i}\le m\) |
\(L\) | Total number of speed levels of each machine |
\({O}_{i,j}\) | \(j\) th operation of job \(i\) |
\({t}_{i,j}\) | Processing time of operation \({O}_{i,j}\) |
\({v}_{z}\) | \(z\) th speed of each machine |
\({PM}_{kz}\) | Processing power of machine \(k\) when its machine speed is set to \({v}_{z}\) |
\({PS}_{k}\) | Standby power of machine \(k\) |
\({PST}_{k}\) | Setup power of machine \(k\) |
\({ST}_{ihk}\) | Sequence-dependent setup time for processing job \(h\) immediately after job \(i\) on the same machine \(k\) |
\({ST}_{ohk}\) | Setup time of job \(h\) on machine \(k\) when job \(h\) is the first job processed on machine \(k\) |
\({D}_{i}\) | Due date of the job \(i\) |
\(H\) | Large enough integer |
\({C}_{i,j}\) | Completion time of operation \({O}_{i,j}\) |
\({C}_{i}\) | Completion time of machine \(k\) |
\({C}_{max}\) | Completion time of all jobs |
\({w}_{i}\) | The weight of the job \(i\) |
\({f}_{i}\) | The flowtime of job \(j\) |
\({\mathbb{T}}\) | Set of delayed jobs |
\({\mathbb{C}}\) | Set of completed jobs |
