2017, 13(4): 1601-1623. doi: 10.3934/jimo.2017009

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

1. 

Curtin University, Perth, 6102, Australia

2. 

Woodside Energy Ltd, Perth, 6000, Australia

Received  November 2015 Revised  May 2016 Published  December 2016

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.

Citation: Elham Mardaneh, Ryan Loxton, Qun Lin, Phil Schmidli. A mixed-integer linear programming model for optimal vessel scheduling in offshore oil and gas operations. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1601-1623. doi: 10.3934/jimo.2017009
References:
[1]

AIMMS Modelling Platform, AIMMS B. V., Haarlem, Netherlands, accessed 17 April 2016, <http://www.aimms.com>

[2]

F. Alonso, M. J. Alvarez, J. E. Beasley, A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions, Journal of the Operational Research Society, 59 (2008), 963-976.

[3]

N. Azi, M. Gendreau, J. Y. Potvin, An exact algorithm for a single-vehicle routing problem with time windows and multiple routes, European Journal of Operational Research, 178 (2007), 755-766. doi: 10.1016/j.ejor.2006.02.019.

[4]

N. Azi, M. Gendreau, J. Y. Potvin, An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles, European Journal of Operational Research, 202 (2010), 756-763.

[5]

M. Battarra, M. Monaci, D. Vigo, An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem, Computers and Operations Research, 36 (2009), 3041-3050.

[6]

J. Bisschop, AIMMS Optimization Modelling, Haarlem: AIMMS B. V., 2016.

[7]

J. C. S. Brandão, A. Mercer, The multi-trip vehicle routing problem, Journal of the Operational Research Society, 49 (1998), 799-805.

[8]

D. Feillet, P. Dejax, M. Gendreau, C. Gueguen, An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems, Networks, 44 (2004), 216-229. doi: 10.1002/net.20033.

[9]

B. Fleischmann, The vehicle routing problem with multiple use of vehicles (technical report), Hamburg: Universität Hamburg, 1990.

[10]

Gurobi, Optimizer Reference Manual, Houston: Gurobi Optimization Inc., 2016.

[11]

F. Hernandez, D. Feillet, R. Giroudeau, O. Naud, A new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration, 4OR, 12 (2014), 235-259. doi: 10.1007/s10288-013-0238-z.

[12]

IBM ILOG CPLEX Optimizer, IBM Corporation, New York, USA, accessed 17 April 2016, http://www.ibm.com/software/commerce/optimization/cplex-optimizer>

[13]

IBM ILOG CPLEX Optimization Studio CPLEX User's Manual, New York, IBM Corporation, 2014.

[14]

R. Macedo, C. Alves, J. M. Valério de Carvalho, F. Clautiaux, S. Hanafi, Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model, European Journal of Operational Research, 214 (2011), 536-545. doi: 10.1016/j.ejor.2011.04.037.

[15]

A. Olivera, O. Viera, Adaptive memory programming for the vehicle routing problem with multiple trips, Computers and Operations Research, 34 (2007), 28-47. doi: 10.1016/j.cor.2005.02.044.

[16]

R. J. Petch, S. Salhi, A multi-phase constructive heuristic for the vehicle routing problem with multiple trips, Discrete Applied Mathematics, 133 (2003), 69-92. doi: 10.1016/S0166-218X(03)00434-7.

[17]

E. D. Taillard, G. Laporte, G. Gendreau, Vehicle routeing with multiple use of vehicles, Journal of the Operational Research Society, 47 (1996), 1065-1070.

[18]

P. Toth and D. Vigo, editors, The Vehicle Routing Problem, Philadelphia: SIAM, 2002.

[19]

S. Salhi, R. J. Petch, A GA based heuristic for the vehicle routing problem with multiple trips, Journal of Mathematical Modelling and Algorithms, 6 (2007), 591-613. doi: 10.1007/s10852-007-9069-2.

[20]

A. Şen and K. Bülbül, A survey on multi trip vehicle routing problem, In: Proceedings of the International Logistics and Supply Chain Congress 2008, Istanbul, Turkey.

show all references

References:
[1]

AIMMS Modelling Platform, AIMMS B. V., Haarlem, Netherlands, accessed 17 April 2016, <http://www.aimms.com>

[2]

F. Alonso, M. J. Alvarez, J. E. Beasley, A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions, Journal of the Operational Research Society, 59 (2008), 963-976.

[3]

N. Azi, M. Gendreau, J. Y. Potvin, An exact algorithm for a single-vehicle routing problem with time windows and multiple routes, European Journal of Operational Research, 178 (2007), 755-766. doi: 10.1016/j.ejor.2006.02.019.

[4]

N. Azi, M. Gendreau, J. Y. Potvin, An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles, European Journal of Operational Research, 202 (2010), 756-763.

[5]

M. Battarra, M. Monaci, D. Vigo, An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem, Computers and Operations Research, 36 (2009), 3041-3050.

[6]

J. Bisschop, AIMMS Optimization Modelling, Haarlem: AIMMS B. V., 2016.

[7]

J. C. S. Brandão, A. Mercer, The multi-trip vehicle routing problem, Journal of the Operational Research Society, 49 (1998), 799-805.

[8]

D. Feillet, P. Dejax, M. Gendreau, C. Gueguen, An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems, Networks, 44 (2004), 216-229. doi: 10.1002/net.20033.

[9]

B. Fleischmann, The vehicle routing problem with multiple use of vehicles (technical report), Hamburg: Universität Hamburg, 1990.

[10]

Gurobi, Optimizer Reference Manual, Houston: Gurobi Optimization Inc., 2016.

[11]

F. Hernandez, D. Feillet, R. Giroudeau, O. Naud, A new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration, 4OR, 12 (2014), 235-259. doi: 10.1007/s10288-013-0238-z.

[12]

IBM ILOG CPLEX Optimizer, IBM Corporation, New York, USA, accessed 17 April 2016, http://www.ibm.com/software/commerce/optimization/cplex-optimizer>

[13]

IBM ILOG CPLEX Optimization Studio CPLEX User's Manual, New York, IBM Corporation, 2014.

[14]

R. Macedo, C. Alves, J. M. Valério de Carvalho, F. Clautiaux, S. Hanafi, Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model, European Journal of Operational Research, 214 (2011), 536-545. doi: 10.1016/j.ejor.2011.04.037.

[15]

A. Olivera, O. Viera, Adaptive memory programming for the vehicle routing problem with multiple trips, Computers and Operations Research, 34 (2007), 28-47. doi: 10.1016/j.cor.2005.02.044.

[16]

R. J. Petch, S. Salhi, A multi-phase constructive heuristic for the vehicle routing problem with multiple trips, Discrete Applied Mathematics, 133 (2003), 69-92. doi: 10.1016/S0166-218X(03)00434-7.

[17]

E. D. Taillard, G. Laporte, G. Gendreau, Vehicle routeing with multiple use of vehicles, Journal of the Operational Research Society, 47 (1996), 1065-1070.

[18]

P. Toth and D. Vigo, editors, The Vehicle Routing Problem, Philadelphia: SIAM, 2002.

[19]

S. Salhi, R. J. Petch, A GA based heuristic for the vehicle routing problem with multiple trips, Journal of Mathematical Modelling and Algorithms, 6 (2007), 591-613. doi: 10.1007/s10852-007-9069-2.

[20]

A. Şen and K. Bülbül, A survey on multi trip vehicle routing problem, In: Proceedings of the International Logistics and Supply Chain Congress 2008, Istanbul, Turkey.

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
Table 
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 $\delta^k(t)$
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 $\delta^k(t)$
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-
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-
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
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
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
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
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
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
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
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
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
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
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%
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%
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%
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%
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