Table 3 Notations for proposed non-linear transportation system for the sustainable management of OCC.
| Â | Description | Type |
|---|---|---|
Index | ||
 \(c\) | Index for source of corrugated waste from commercial establishments \(\left( {{\text{c}} = 1,2, \ldots ,{\text{ C}}} \right)\) | Integer |
 \(l\) | Index for source for corrugated waste from landfills \(\left( {l = 1,2, \ldots ,{\text{ L}}} \right)\) | Integer |
 \(f\) | Index for corrugated waste recycling facility \(\left( {{\text{f}} = 1,2,{ } \ldots ,{\text{ F}}} \right)\) | Integer |
 \(m\) | Index for corrugated box manufactures \(\left( {m = 1,2,{ } \ldots ,{ }M} \right)\) | Integer |
 \(t\) | Index of mode of conveyance \(\left( {t = 1,2, \ldots ,{\text{ T}}} \right)\) | Integer |
 \(r\) | Index of route \(\left( {r = 1,2,{ } \ldots ,{\text{ R}}} \right)\) | Integer |
 \(n\) | Number of goals | Integer |
 \(Z_{n}\) | Objective function | Integer |
Decision variables | ||
 \(x_{cftr}^{13}\) | Amount of corrugated waste transported from \(c{\text{th}}\) commercial establishment to \(f{\text{th}}\) corrugated waste recycling facility by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Real number |
 \(x_{lftr}^{23}\) | Amount of corrugated waste transported from \(l{\text{th}}\) landfill to \(f{\text{th}}\) corrugated waste recycling facility by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Real number |
 \(x_{fmtr}^{34}\) | Amount of corrugated sheet manufactured by \(f{\text{th}}\) recycling facility transported to \(m{\text{th}}\) cardboard box manufacturer by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Real number |
Parameters | ||
 \(\tilde{A}_{c}^{1}\) | Available amount of corrugated waste at \(c{\text{th}}\) commercial establishment | TS-FBHE |
 \(\tilde{A}_{l}^{2}\) | Available amount of corrugated waste at \(l{\text{th}}\) landfill | TS-FBHE |
 \(\tilde{B}_{f}^{3}\) | Capability of corrugated waste at \(f{\text{th}}\) recycling facility | TS-FBHE |
 \(\tilde{B}_{m}^{4}\) | Demand of corrugated sheets at \(m{\text{th}}\) cardboard box manufacturer | TS-FBHE |
 \(\tilde{E}_{t}\) | Capacity of \(t{\text{th}}\) conveyance | TS-FBHE |
 \(L_{cfr}^{13}\) | Distance from \(c{\text{th}}\) commercial establishment to \(f{\text{th}}\) corrugated waste recycling facility via \(r{\text{th}}\) route | Integer |
 \(L_{lfr}^{23}\) | Distance from \(l{\text{th}}\) landfill to \(f{\text{th}}\) corrugated waste recycling facility via \(r{\text{th}}\) route | Integer |
\(L_{fmr}^{34}\) | Distance from \(f{\text{th}}\) recycling facility transported to \(m{\text{th}}\) cardboard box manufacturer via \(r{\text{th}}\) route | Integer |
 \({\mathfrak{c}}_{cftr}^{13}\) | Unit TE during the transit of corrugated waste transported from \(c{\text{th}}\) commercial establishment to \(f{\text{th}}\) corrugated waste recycling facility by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Integer |
 \({\mathfrak{c}}_{lftr}^{23}\) | Unit TE during the transit of corrugated waste transported from \(l{\text{th}}\) landfill to \(f{\text{th}}\) corrugated waste recycling facility by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Integer |
 \({\mathfrak{c}}_{fmtr}^{34}\) | Unit TE during the transit of corrugated sheet manufactured by \(f{\text{th}}\) recycling facility transported to \(m{\text{th}}\) cardboard box manufacturer by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Integer |
 \({\mathfrak{t}}_{cftr}^{13}\) | Unit TT during the transit of corrugated waste transported from \(c{\text{th}}\) commercial establishment to \(f{\text{th}}\) corrugated waste recycling facility by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Integer |
 \({\mathfrak{t}}_{lftr}^{23}\) | Unit TT during the transit of corrugated waste transported from \(l{\text{th}}\) landfill to \(f{\text{th}}\) corrugated waste recycling facility by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Integer |
\({\mathfrak{t}}_{fmtr}^{34}\) | Unit TT during the transit of corrugated sheet manufactured by \(f{\text{th}}\) recycling facility transported to \(m{\text{th}}\) cardboard box manufacturer by \(t{\text{th}}\) conveyance via \(r{\text{th}}\) route | Integer |
 \(\theta_{1}\) | Tax for carbon emission during transportation | Real |
 \({\mathfrak{e}}_{{CO_{2} }}^{1}\) | Rate of carbon emission of the vehicle per unit item and per unit distance | Real |
 \(\theta_{2}\) | Tax for carbon emission on corrugated waste recycling facility | Real |
 \({\mathfrak{e}}_{{CO_{2} }}^{2}\) | Rate of carbon emission per unit item on corrugated waste recycling facility | Real |
