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