# American Institute of Mathematical Sciences

October 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, [2] F. Alonso, M. J. Alvarez and 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 and 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 and 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 and 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 and 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 and 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 and 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, [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 and 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 and 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 and 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 and 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. doi: 10.1137/1.9780898718515. [19] S. Salhi and 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, [2] F. Alonso, M. J. Alvarez and 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 and 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 and 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 and 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 and 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 and 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 and 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, [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 and 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 and 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 and 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 and 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. doi: 10.1137/1.9780898718515. [19] S. Salhi and 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.
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
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
Woodside's offshore facilities in the North West Shelf region and Carnarvon Basin
Historical and optimized vessel schedules for Scenario 1
Historical and optimized vessel schedules for Scenario 2
Historical and optimized vessel schedules for Scenario 3
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 $\delta^k(t)$
 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 $\delta^k(t)$
Distances (in nautical miles) between facilities
 Karratha Angel Goodwyn Nganhurra Ngujima-Yin North Rankin Okha Pluto Karratha - 68.4 78.4 180.0 175.0 75.0 65.0 95.9 Angel 68.4 - 38.4 188.4 181.7 27.5 10.0 75.0 Goodwyn 78.4 38.4 - 155.0 155.9 12.5 30.0 38.4 Nganhurra 180.0 188.4 155.0 - 5.0 165.0 170.0 117.5 Ngujima-Yin 175.0 181.7 155.9 5.0 - 160.0 165.0 112.5 North Rankin 75.0 27.5 12.5 165.0 160.0 - 18.4 50.0 Okha 65.0 10.0 30.0 170.0 165.0 18.4 - 65.0 Pluto 95.9 75.0 38.4 117.5 112.5 50.0 65.0 -
 Karratha Angel Goodwyn Nganhurra Ngujima-Yin North Rankin Okha Pluto Karratha - 68.4 78.4 180.0 175.0 75.0 65.0 95.9 Angel 68.4 - 38.4 188.4 181.7 27.5 10.0 75.0 Goodwyn 78.4 38.4 - 155.0 155.9 12.5 30.0 38.4 Nganhurra 180.0 188.4 155.0 - 5.0 165.0 170.0 117.5 Ngujima-Yin 175.0 181.7 155.9 5.0 - 160.0 165.0 112.5 North Rankin 75.0 27.5 12.5 165.0 160.0 - 18.4 50.0 Okha 65.0 10.0 30.0 170.0 165.0 18.4 - 65.0 Pluto 95.9 75.0 38.4 117.5 112.5 50.0 65.0 -
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
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
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
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
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
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%
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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