Figures (15)  Tables (11)

    • Figure 1. 

      Space-time diagram of BACAP with SSE allocation.

    • Figure 2. 

      Shore operations of MASS and manned vessels.

    • Figure 3. 

      Berth allocation model for Mixed-Strategy and Separated-Strategy.

    • Figure 4. 

      The flowchart of the GA + ALNS algorithm combined with Q-learning.

    • Figure 5. 

      The example of chromosome structure.

    • Figure 6. 

      Single-point crossover.

    • Figure 7. 

      Multi-point crossover.

    • Figure 8. 

      Endpoint mutation.

    • Figure 9. 

      Two-point mutation.

    • Figure 10. 

      Space-time diagram of (a) Mixed-Strategy and (b) Separated-Strategy.

    • Figure 11. 

      Convergence comparison of algorithms.

    • Figure 12. 

      Berth allocation schemes at YICT under Mixed-Strategy and Separated-Strategy. (a) $ \left| V\right| $ = 30 Mixed-Strategy; (b) $ \left| V\right| $ = 30 Separated-Strategy; (c) $ \left| V\right| $ = 40 Mixed-Strategy; (d) $ \left| V\right| $ = 40 Separated-Strategy.

    • Figure 13. 

      The impact of MASS quantity on cost composition and carbon emissions.

    • Figure 14. 

      The impact of the change in the quantity of SSE on total cost and carbon emissions.

    • Figure 15. 

      The impact of the change in the quantity of MASS-available berths on total cost.

    • PaperBAPQCAPSSEMethodVessel type
      Zhang & Wang[13]√SolverMASS
      Zhen et al.[15]√√CGManned vessel
      Tang et al.[11]√√LNSManned vessel
      Yu et al.[16]√√√N-NSGA-IIManned vessel
      Guo et al.[12]√√ALNSManned vessel
      Wang et al.[17]√√√AICSAManned vessel
      Martin-Iradi et al.[23]√ALNSManned vessel
      Yue et al.[18]√√NSGA-IIIManned vessel
      Shen et al.[14]√SAManned vessel + MASS
      This study√√√GA + ALNSManned vessel + MASS

      Table 1. 

      Literature review.

    • Vessel typesSailingAnchoringBerthing
      Diesel-powered vessels with SSEMEa fuelAEb fuelAE fuel/SSE
      Diesel-powered vessels without SSEME fuelAE fuelAE fuel
      Hybrid-powered MASSME fuelStored electricitySSE
      Electric-powered MASSStored electricityStored electricitySSE
      a Main engine. b Auxiliary engines.

      Table 2. 

      The type of energy consumed by different types of ships at different periods[26].

    • NotationExplanation
      Sets
      $ V $The set of vessels, $ V=\left\{1,\;2,\;3,\;\cdots ,\;\left| V\right| \right\} $, where $ \left| V\right| $ is the number of vessels, $ i\in V $
      $ B $The set of berths, $ B=\left\{1,2,3,\cdots ,\left| B\right| \right\} $, where $ \left| B\right| $ is the number of berths, $ b\in B $
      $ Q $The set of QCs, $ Q=\left\{1,2,3,\cdots ,\left| Q\right| \right\} $, where $ \left| Q\right| $ is the number of QCs, $ q\in Q $
      $ T $The set of time units, $ T=\left\{1,2,3,\cdots \left| T\right| \right\} $, where $ \left| T\right| $is the planning horizon, $ t\in T $
      Parameters
      $ {C}_{1} $Unit cost of waiting berth at anchorage
      $ {C}_{2} $Unit cost of using the quay cranes
      $ {C}_{3} $The SSE unit price
      $ {C}_{4} $The fuel oil unit price
      $ {C}_{5} $Unit cost of delay penalty
      $ {C}_{6} $Labor cost per unit time
      $ \lambda $Reward factor of using SSE service during berthing
      $ {L}_{i} $Length of vessel $ i $
      $ {L}_{b} $Length of berth $ b $
      $ {A}_{i} $Arrival time of vessel $ i $
      $ {K}_{i} $Number of loading or unloading containers of vessel $ i $
      $ {D}_{i} $The expected departure time of vessel $ i $
      $ q_{\mathrm{i}}^{\min } $Minimum number of quay cranes assigned to vessel $ i $
      $ q_{i}^{\max } $Maximum number of quay cranes assigned to vessel $ i $
      $ \eta $Speed of quay cranes
      $ {E}_{i} $Auxiliary engine power of vessel $ i $
      $ {N}^{s} $The total number of terminal stevedores
      $ {N}^{c} $The total number of terminal tally clerks
      $ Crew_{s}^{mass} $The number of stevedores in each crew assigned to MASS
      $ Crew_{c}^{mass} $The number of tally clerks in each crew assigned to MASS
      $ Crew_{s}^{m} $The number of stevedores in each crew assigned to manned vessel
      $ Crew_{c}^{m} $The number of tally clerks in each crew assigned to manned vessel
      $ M $A large positive number
      Auxiliary variables
      $ Eq{v}_{i} $Binary, 1 if vessel $ i $ is adapted to SSE supplied, else 0
      $ Eq{v}_{b} $Binary, 1 if berth $ b $ is equipped with SSE, else 0
      $ M{A}_{i} $Binary, 1 if vessel $ i $ is MASS, else 0
      $ B_{b}^{mass} $Binary, 1 if berth $ b $ is MASS available berth, else 0
      Decision variables
      $ {S}_{i} $Berthing time of vessel $ i $
      $ {P}_{i} $Berth allocated to vessel $ i $
      $ {d}_{i} $Departure time of vessel $ i $
      $ W_{itq}^{s} $Integer, allocate the number of stevedores of
      quay crane $ q $ for vessel $ i $ at time $ t $
      $ W_{itq}^{c} $Integer, allocate the number of tally clerks of
      quay crane $ q $ for vessel $ i $ at time $ t $
      $ {O}_{i} $Binary, 1 if vessel $ i $ uses SSE during the berthing time, else 0
      $ {X}_{itb} $Binary, 1 if vessel $ i $ is allocated to berth $ b $ at time $ t $, else 0
      $ {Y}_{itq} $Binary, 1 if quay crane $ q $ is assigned to vessel $ i $ at time $ t $, else 0
      $ {Z}_{ijb} $Binary, 1 if vessel $ i $ and vessel $ j $ are allocated to the same berth $ b $ and vessel $ j $ is served after vessel $ i $, else 0

      Table 3. 

      Notations of the model.

    • Score Criteria description
      3 Find a better solution or equal to the optimal solution after using the ALNS operators
      1.5 Find a better solution or equal to the current solution after using the ALNS operators
      0 Find a solution that is worse than the current solution after using the ALNS operators

      Table 4. 

      The score of destroyed and repaired operators.

    • Parameters Value Ref.
      $ {C}_{1} $ 800 US${\$} $/h Wang et al.[34]
      $ {C}_{2} $ 240 US${\$} $/h Model assumption
      $ {C}_{3} $ 0.15918 US${\$} $/kWh Peng et al.[33]
      $ {C}_{4} $ 0.13382 US${\$} $/kWh Peng et al.[33]
      $ {C}_{5} $ 2400 US${\$} $/h Wang et al.[34]
      $ {C}_{6} $ 40 US${\$} $/h Model assumption
      $ \eta $ 30 TEU/h Model assumption
      $ \lambda $ 0.4 HPA[30]
      $ M $ 100,000 Model assumption
      $ {c}^{e} $ 0.54 kg/kWh Hall[35]
      $ {c}^{f} $ 0.6412 kg/kWh Hall[35]

      Table 5. 

      Values of some parameters.

    • $ \left| V\right| $ $ \left| B\right| $ $ \left| Q\right| $ $ \left| B_{b}^{mass}\right| $ Gurobi solving results GAP (%)
      Mixed-Strategy Separated-Strategy
      $ Ob{j}_{1} $ (US${\$} $) Times (s) $ Ob{j}_{2} $ (US${\$} $) Times (s)
      6 4 9 1 154,678.04 1.76 158,881.69 1.70 2.65
      6 12 2 151,661.30 0.94 152,258.62 0.60 0.39
      8 15 3 151,661.30 0.96 151,661.30 0.91 0.00
      10 18 4 151,661.30 1.14 151,661.30 1.02 0.00
      8 4 9 1 192,980.09 2.58 222,112.94 2.23 13.12
      6 12 2 189,577.96 2.19 190,560.66 0.92 0.52
      8 15 3 189,577.96 1.98 189,577.96 1.54 0.00
      10 18 4 189,577.96 2.41 189,577.96 2.15 0.00
      10 4 9 1 308,054.41 54.73 334,629.59 3.35 7.94
      6 12 2 269,410.28 2.08 296,034.98 2.00 8.99
      8 15 3 269,410.28 3.31 295,052.28 2.46 8.69
      10 18 4 269,410.28 2.93 269,410.28 2.68 0.00
      15 4 9 1 435,356.64 60.47 537,437.17 10.52 18.99
      6 12 2 398,567.20 29.29 400,147.21 3.94 0.39
      8 15 3 398,567.20 30.48 398,567.20 7.91 0.00
      10 18 4 398,567.20 9.87 398,567.20 8.89 0.00
      20 4 9 1 727,758.10 1,641.2 889,589.73 627.49 18.19
      6 12 2 − 3,600 − 3,600 −
      8 15 3 − 3,600 − 3,600 −
      10 18 4 − 3,600 − 3,600 −
      Average 285,086.91 307,395.8 7.26

      Table 6. 

      Gurobi solution results.

    • Cost (US${\$} $) $ \left| V\right| $ 8 10 15 20 Average GAP (%)
      Total cost Mixed 192,980.09 308,054.41 435,356.64 727,758.1 363,765.46 15.1
      Separated 222,112.94 334,629.59 537,437.17 889,589.73 428,530.22
      Waiting cost Mixed 2,400 11,200 12,000 50,400 15,680 51.2
      Separated 11,200 19,200 36,800 88,000 32,160
      QCs cost Mixed 23,184 31,104 41,808 56,016 34,147.2 18.8
      Separated 23,184 31,104 43,440 57,648 34,800
      Energy cost Mixed 29,676.09 42,190.41 58,628.64 87,582.1 48,338.26 13.9
      Separated 33,208.94 46,365.59 69,477.17 106,981.73 56,130.22
      Delay cost Mixed 120,000 103,200 175,200 256,800 446,400 15.8
      Separated 141,600 120,000 189,600 321,600 549,600

      Table 7. 

      Key costs calculated under Mixed-Strategy and Separated-Strategy.

    • $ \left| V\right| $ Carbon emissions (kg) GAP (%)
      Mixed-Strategy Separated-Strategy
      6 111,899.76 116,708.76 4.12
      8 140,946.12 157,873.8 10.72
      10 200,422.92 219,132.36 8.54
      15 269,819.52 329,159.04 18.03
      20 412,487.16 507,615.36 18.74
      Average 227,115.1 26,6097.9 14.65

      Table 8. 

      Comparison of carbon emissions between tow berth allocation strategies.

    • Algorithm Our method ALNS GA
      $ \left| V\right| $ Case $ Ob{j}_{1} $ CT (s) Gap $ Ob{j}_{2} $ CT (s) Gap $ Ob{j}_{3} $ CT (s) Gap
      6 1 156,378.04 5.55 1.09 157,044.07 5.81 1.51 158,442.37 1.85 2.38
      2 152,876.58 5.63 0.79 153,481.17 7.88 1.19 154,641.17 2.00 1.93
      3 152,229.14 5.65 0.37 153,043.34 10.61 0.90 154,297.42 1.92 1.71
      4 151,917.81 6.38 0.17 153,312.35 7.75 1.08 154,205.57 1.97 1.65
      8 1 195,932.36 6.71 1.51 198,024.80 7.45 2.55 203,866.44 2.37 5.34
      2 192,382.78 6.87 1.46 195,104.03 8.63 2.83 207,339.07 1.85 8.57
      3 191,648.06 6.86 1.08 194,461.90 11.24 2.51 202,450.95 2.42 6.36
      4 191,184.36 6.78 0.84 193,666.21 15.72 2.11 201,704.02 2.52 6.01
      10 1 316,972.67 7.67 2.81 334,296.79 12.38 7.85 350,287.69 3.04 12.06
      2 276,229.36 7.80 2.47 291,651.20 14.48 7.63 306,379.28 2.84 12.07
      3 275,324.49 7.91 2.15 285,127.84 18.96 5.51 301,053.86 3.02 10.51
      4 275,012.08 8.70 2.04 281,047.88 21.74 4.14 298,938.24 3.84 9.88
      15 1 453,425.37 11.45 3.98 469,563.09 21.57 7.28 493,484.25 4.29 11.78
      2 414,993.68 11.29 3.96 428,555.32 25.07 7.00 452,447.37 4.51 11.91
      3 416,609.86 10.73 4.33 425,594.14 31.25 6.35 442,073.82 4.43 9.84
      4 414,493.16 11.80 3.84 422,031.97 30.39 5.56 442,394.65 4.02 9.91
      20 1 771,630.94 17.76 5.69 801,368.39 30.28 9.19 881,017.78 5.98 17.40
      2 651,233.08 20.77 − 697,908.48 41.27 − 727,124.39 6.01 −
      3 629,316.41 22.37 − 652,647.68 54.01 − 672,714.46 5.95 −
      4 627,808.35 25.65 − 644,477.01 49.39 − 661,304.62 5.69 −
      30 1 1,044,593.77 29.68 − 1,377,603.23 68.11 − 1,667,353.24 9.43 −
      2 932,048.17 36.26 − 999,053.32 86.65 − 1,345,368.42 9.03 −
      3 921,896.12 37.47 − 968,950.33 106.33 − 1,120,027.34 8.75 −
      4 917,101.77 41.94 − 963,263.93 100.25 − 1,114,765.17 8.96 −
      40 1 1,574,540.08 54.04 − 1,701,024.87 155.63 − 2,340,866.86 18.76 −
      2 1,341,607.22 66.72 − 1,588,796.82 161.82 − 2,063,518.60 19.35 −
      3 1,189,445.17 68.39 − 1,562,007.22 165.73 − 1,808,089.58 18.85 −
      4 1,060,306.03 70.96 − 1,300,407.35 209.49 − 1,512,966.78 23.36 −
      Average 567,469.18 22.13 2.27 628,339.81 52.85 4.42 729,968.69 6.68 8.19

      Table 9. 

      Comparison of results of different algorithms.

    • Parameters Value
      Total number of berths 20
      Total number of QCs 85
      Total number of MASS-available berths 3
      Total number of SSE facilities 6
      The planning horizon 168
      Total number of vessels 30, 40
      Total number of MASSs 8, 10
      Total number of manned vessels equipped
      with SSE reception facilities      		 6, 8

      Table 10. 

      Parameter settings based on the real environment of YICT.

    • $ \left| V\right| $ Strategies Novel GA + ALNS GA + ALNS ALNS GA
      $ Ob{j}_{1} $ CT (s) $ Ob{j}_{2} $ CT (s) $ Ob{j}_{3} $ CT (s) $ Ob{j}_{4} $ CT (s)
      30 Mixed 876,010.54 48.3 917,101.77 46.2 933,979.66 77.4 935,903.24 34.5
      Separated 876,281.38 50.5 917,310.26 54.4 935,664.19 85.1 936,230.78 40.3
      40 Mixed 1,187,623.68 62.8 1,223,508.41 64.9 1,305,649.48 94.3 1,317,627.52 56.7
      Separated 1,218,904.03 65.2 1,292,038.28 70.6 1,334,883.52 98.7 1,352,913.46 60.4
      Average 1,039,704.91 56.7 1,087,489.68 59.03 1,127,544.21 88.87 1,135,668.75 47.98

      Table 11. 

      Results of different algorithms at YICT under Mixed-Strategy and Separated-Strategy.