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Table 3 Notation of the RCPSP-ROC

From: Profit-oriented scheduling of resource-constrained projects with flexible capacity constraints

Indices and (ordered) sets
 \(j \in \mathcal {J}\) Activities \(\mathcal {J}=\{0, 1, \ldots , J, J+1 \}\)
 \(t, \tau \in \mathcal {T}\) Periods \(\mathcal {T}=\{0, 1, \ldots , T\}\)
 \(r \in \mathcal {R}\) Renewable resources \(\mathcal {R}=\{1, \ldots , R \}\)
 \(\mathcal {P}_j \subseteq \mathcal {J}\) Set of immediate predecessors of activity j
 \(d_j\) Duration of activity j
 \(EFT_j\) Earliest finishing time of activity j
 \(LFT_j\) Latest finishing time of activity j
 \(k_{jr}\) Required units of resource r while executing activity j
 \(K_r\) Capacity of resource r
 \(\overline{z}_r\) Overtime limit of resource r
 \(\kappa _r\) Per-unit cost for overtime of resource r
 \(u_t\) Revenue for project completion at the end of period t
Decision variables
 \(x_{jt}\) \(= \left\{ {\begin{array}{*{20}c} {1,} & {{\text{if}}\;{\text{activity}}\;j\;{\text{is}}\;{\text{finished at the}}\;{\text{end}}\;{\text{of}}\;{\text{period}}\;t} \\ {0,} & {{\text{otherwise}}} \\ \end{array} } \right.\)
 \(z_{rt}\) Amount of overtime of resource r used in period t