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A mixed-integer linear programming model for optimal vessel scheduling in offshore oil and gas operations

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  • This paper introduces a non-standard vehicle routing problem (VRP) arising in the oil and gas industry. The problem involves multiple offshore production facilities, each of which requires regular servicing by support vessels to replenish essential commodities such as food, water, fuel, and chemicals. The support vessels are also required to assist with oil off-takes, in which oil stored at a production facility is transported via hose to a waiting tanker. The problem is to schedule a series of round trips for the support vessels so that all servicing and off-take requirements are fulfilled, and total cost is minimized. Other constraints that must be considered include vessel suitability constraints (not every vessel is suitable for every facility), depot opening constraints (base servicing can only occur during specified opening periods), and off-take equipment constraints (the equipment needed for off-take support can only be deployed after certain commodities have been offloaded). Because of these additional constraints, the scheduling problem under consideration is far more difficult than the standard VRP. We formulate a mixed-integer linear programming (MILP) model for determining the optimal vessel schedule. We then verify the model theoretically and show how to compute the vessel utilization ratios for any feasible schedule. Finally, simulation results are reported for a real case study commissioned by Woodside Energy Ltd, Australia's largest dedicated oil and gas company.

    Mathematics Subject Classification: Primary: 90B06; Secondary: 90B10, 90C11, 90C27.

    Citation:

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  • Figure 1.  An example of our arrival/departure time convention: if $d_i^k=3$, then a vessel arriving during period 2 and can depart any time from period 6 onwards

    Figure 2.  An example of base servicing with $d_{\text{base}}^k=2$. Closed periods are shaded in grey. After arriving at the base, the vessel must stay for at least $\delta^k(t)=5$ periods to complete the service. For option (i), $\omega_{\text{base}}^k=2$ since the 3 closed periods during service are not considered active periods. For option (ii), $\omega_{\text{base}}^k=5$ since the 3 closed periods are considered active periods

    Figure 3.  Woodside's offshore facilities in the North West Shelf region and Carnarvon Basin

    Figure 4.  Historical and optimized vessel schedules for Scenario 1

    Figure 5.  Historical and optimized vessel schedules for Scenario 2

    Figure 6.  Historical and optimized vessel schedules for Scenario 3

    Figure 7.  Historical and optimized vessel schedules for Scenario 4

    Algorithm 1 Returns the value of $\delta^k(t)$
    Set $t\rightarrow t'$         ▷Initialization step; $t'$ is the period counter
    Set $0\rightarrow d$        ▷Initialization step; $d$ is the working period counter
    while $d < d_{\text{base}}^k$ do         ▷Iterate for $d_{\text{base}}^k$ working periods
        Set $t'+1\rightarrow t'$         ▷Increment period counter
        if $t'>T$ then
            Set $+\infty\rightarrow\delta^k(t)$        ▷Insufficient time to conduct base service
            return $\delta^k(t)$
        else if $t'\in\mathcal{O}_{\text{base}}$ then
            Set $d+1\rightarrow d$        ▷Increment working period counter if base is open
        end if
    end while
    Set $t'-t\rightarrow\delta^k(t)$                                                        ▷Calculate $\delta^k(t)$
    return $\delta^k(t)$
     | Show Table
    DownLoad: CSV

    Table 1.  Distances (in nautical miles) between facilities

    Karratha Angel Goodwyn Nganhurra Ngujima-Yin North Rankin Okha Pluto
    Karratha-68.478.4180.0175.075.065.095.9
    Angel68.4-38.4188.4181.727.510.075.0
    Goodwyn78.438.4-155.0155.912.530.038.4
    Nganhurra180.0188.4155.0-5.0165.0170.0117.5
    Ngujima-Yin175.0181.7155.95.0-160.0165.0112.5
    North Rankin75.027.512.5165.0160.0-18.450.0
    Okha65.010.030.0170.0165.018.4-65.0
    Pluto95.975.038.4117.5112.550.065.0-
     | Show Table
    DownLoad: CSV

    Table 2.  Service requirements for Scenario 1

    Facility Day Demand Time Window Duration Suitable Vessels Off-take?
    Ngujima-Yin 1 300 m2 0:00-24:00 30 hours OSV Yes
    Goodwyn 2 100 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 2 200 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 3 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 6 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 6 250 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 8 300 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 9 100 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 9 200 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 9 100 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 10 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 16 250 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 16 300 m2 0:00-24:00 30 hours OSV Yes
    North Rankin 16 250 m2 0:00-24:00 3 hours PSV, OSV No
    Pluto 17 100 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 19 200 m2 0:00-24:00 30 hours OSV Yes
    Goodwyn 20 100 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 20 200 m2 0:00-24:00 3 hours PSV, OSV No
     | Show Table
    DownLoad: CSV

    Table 3.  Service requirements for Scenario 2

    Facility Day Demand Time Window Duration Suitable Vessels Off-take?
    Goodwyn 1 200 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 2 200 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 3 200 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 4 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 5 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 5 150 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 5 100 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 6 150 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 7 100 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 7 100 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 8 200 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 9 100 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 9 200 m2 0:00-24:00 30 hours OSV Yes
    Okha 11 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 12 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 12 150 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 13 200 m2 0:00-24:00 30 hours OSV Yes
    Goodwyn 14 250 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 15 250 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 18 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 19 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 19 150 m2 0:00-24:00 3 hours PSV, OSV No
     | Show Table
    DownLoad: CSV

    Table 4.  Service requirements for Scenario 3

    Facility Day Demand Time Window Duration Suitable Vessels Off-take?
    Angel 1 200 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 1 250 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 1 250 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 3 250 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 3 250 m2 0:00-24:00 3 hours PSV, OSV No
    Angel 4 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 4 100 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 4 100 m2 0:00-24:00 30 hours OSV Yes
    North Rankin 5 100 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 7 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 8 150 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 8 200 m2 0:00-24:00 30 hours OSV Yes
    North Rankin 8 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 10 150 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 11 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 12 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 14 150 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 14 100 m2 0:00-24:00 3 hours PSV, OSV No
    Pluto 14 300 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 15 150 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 17 100 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 17 100 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 18 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 19 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 21 250 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 21 100 m2 0:00-24:00 3 hours PSV, OSV No
     | Show Table
    DownLoad: CSV

    Table 5.  Service requirements for Scenario 4

    Facility Day Demand Time Window Duration Suitable Vessels Off-take?
    Goodwyn 1 250 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 1 250 m2 0:00-24:00 30 hours OSV Yes
    North Rankin 1 250 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 3 150 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 3 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 3 150 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 4 150 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 5 150 m2 0:00-24:00 30 hours OSV Yes
    Goodwyn 7 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 7 150 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 8 200 m2 0:00-24:00 3 hours PSV, OSV No
    Pluto 9 250 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 10 150 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 11 100 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 11 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 11 100 m2 0:00-24:00 3 hours PSV, OSV No
    Pluto 12 100 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 13 100 m2 0:00-24:00 30 hours OSV Yes
    Goodwyn 14 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 14 150 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 15 200 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 16 200 m2 0:00-24:00 3 hours PSV, OSV No
    Ngujima-Yin 17 150 m2 0:00-24:00 3 hours PSV, OSV No
    Goodwyn 18 150 m2 0:00-24:00 3 hours PSV, OSV No
    Nganhurra 18 150 m2 0:00-24:00 3 hours PSV, OSV No
    North Rankin 18 150 m2 0:00-24:00 3 hours PSV, OSV No
    Angel 21 300 m2 0:00-24:00 3 hours PSV, OSV No
    Okha 21 100 m2 0:00-24:00 3 hours PSV, OSV No
     | Show Table
    DownLoad: CSV

    Table 6.  Model dimensions in terms of binary variables (BVs), continuous-valued variables (CVs), and constraints

    Original Model Simplified Model
    BVs CVs Constraints BVs CVs Constraints
    Scenario 1 1,646,568 1,646,569 1,646,870 206,868 20,571 207,167
    Scenario 2 2,069,928 2,069,929 2,070,258 292,443 31,582 292,771
    Scenario 3 2,541,672 2,541,673 2,542,030 322,105 35,540 322,461
    Scenario 4 2,795,688 2,795,689 2,796,060 330,484 39,859 330,853
     | Show Table
    DownLoad: CSV

    Table 7.  Optimal fuel consumption for Scenarios 1-4

    Total Fuel Use (L)
    Historical Initial Optimized Improvement
    Scenario 1 108,620 107,560 97,440 10.29%
    Scenario 2 124,460 113,880 96,040 22.83%
    Scenario 3 139,500 138,400 125,820 9.81%
    Scenario 4 170,680 168,960 148,640 12.91%
     | Show Table
    DownLoad: CSV

    Table 8.  Optimal vessel utilization for Scenarios 1-4

    Deck-space Utilization Time Utilization
    PSV OSV 1 OSV 2 PSV OSV 1 OSV 2
    Scenario 1 100% 100% 100% 30% 37% 31%
    Scenario 2 80% 88% 89% 26% 31% 31%
    Scenario 3 100% 78% 83% 51% 33% 27%
    Scenario 4 92% 96% 100% 45% 41% 43%
     | Show Table
    DownLoad: CSV
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