From: Holistic tactical-level planning in liner shipping: an exact optimization approach
Parameter | Value |
---|---|
Number of port rotations: n1 (port rotations) | 3 |
Number of ports of call under port rotation r: \( {n}_r^2,r\in R \) (ports) | 6 |
Number of available vessel types: n3 (vessel types) | 2 |
Number of available TWs at port p of port rotation r: \( {n}_{rp}^4,r\in R,p\in {P}_r \) (TWs) | 3 |
Number of available HRs at port p of port rotation r during TW t: \( {n}_{rp t}^5,r\in R,p\in {P}_r,t\in {T}_{rp} \) (HRs) | 4 |
Maximum port service frequency: Ï•max (days) | 14 |
Number of vessels of type v available in company’s own fleet for deployment: \( {q}_v^{own-m},v\in V \) (vessels) | [3; 4] |
Number of vessels of type v available for chartering: \( {q}_v^{\mathit{\operatorname{char}}-m},v\in V \) (vessels) | [5; 6] |
Maximum sailing speed: Ï‘max (knots) | 25 |
Minimum sailing speed: Ï‘min (knots) | 15 |
Fuel consumption coefficient: αv, v ∈ V | [3; 3.2] |
Fuel consumption coefficient: γv, v ∈ V | [0.012; 0.014] |
Coefficient of the container demand sensitivity to the vessel sailing speed at port p of port rotation r: \( {\alpha}_{rp}^{dem},r\in R,p\in {P}_r \) | U[400; 1,800] |
Coefficient of the container demand sensitivity to the vessel sailing speed at port p of port rotation r: \( {\beta}_{rp}^{dem},r\in R,p\in {P}_r \) | U[1,250; 3,000] |
Portion of import containers at port p of port rotation r: Importrp, r ∈ R, p ∈ Pr (%) | U[40; 60] |
Total quantity of containers on board a vessel before it is moored at the first port of call under port rotation r: \( {QC}_r^{SEA-0},r\in R \) (TEUs) | U[4,000; 7,000] |
Handling productivity under HR h during TW t at port p of port rotation r for vessels of type v: phrpthv, r ∈ R, p ∈ Pr, t ∈ Trp, h ∈ Hrpt, v ∈ V (TEUs/hour) | U[50; 125] |
Average weight of cargo inside a standard 20-ft container: AWC (tons) | 11 |
Empty weight of a vessel of type v: LWTv, v ∈ V (tons) | [48,000; 50,000] |
Total cargo carrying capacity of a vessel of type v: TWCv, v ∈ V (tons) | [144,000; 150,000] |
Arrival TW duration: \( \left[{\tau}_{rp t}^{end}-{\tau}_{rp t}^{st}\right]\forall r\in R,p\in {P}_r,t\in {T}_{rp} \) (hours) | U[12; 24] |
Emission factor in sea: EFSEA (tons of emissions/ton of fuel) | 3.082 |
Emission factor at port p of port rotation r under HR h for vessel type v: \( {EF}_{rphv}^{PORT},r\in R,p\in {P}_r,h\in {H}_{rpt},v\in V \) (tons of emissions/TEU) | 0.01729 for h = 180 |
Unit vessel operational cost for vessel type v: \( {c}_v^{oper},v\in V \) (USD/day) | [39,000; 43,000] |
Unit chartering cost for vessel type v: \( {c}_v^{char},v\in V \) (USD/day) | [59,000; 65,000] |
Unit handling cost for vessel type v at port p of port rotation r during TW t under HR h: \( {c}_{rp t hv}^{hand},r\in R,p\in {P}_r,t\in {T}_{rp},h\in {H}_{rp t},v\in V \) (USD/TEU) | U[200; 500] |
Unit late arrival cost for port p of port rotation r: \( {c}_{rp}^{late},r\in R,p\in {P}_r \) (USD/hour) | U[5,000; 8,000] |
Unit fuel cost: cfuel (USD/ton) | 200 |
Unit inventory cost: cinv (USD/TEU/hour) | 0.25 |
Unit emission cost: cemis (USD/ton) | 32 |
Unit freight rate for delivery to port p of port rotation r: \( {c}_{rp}^{rev},r\in R,p\in {P}_r \) (USD/TEU) | U[1,000; 2,500] |