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

Elham Mardaneh; Ryan Loxton; Qun Lin; Phil Schmidli

doi:10.3934/jimo.2017009

Article Contents

2017, Volume 13, Issue 4: 1601-1623. Doi: 10.3934/jimo.2017009

This issue Previous Article Next Article On subspace properties of the quadratically constrained quadratic program

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: October 31, 2015

Revised: April 30, 2016

Published: November 2017

Abstract Full Text(HTML) Figure(7) / Table(9) Related Papers Cited by

Abstract

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.

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

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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

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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

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

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Figure 4. Historical and optimized vessel schedules for Scenario 1

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Figure 5. Historical and optimized vessel schedules for Scenario 2

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Figure 6. Historical and optimized vessel schedules for Scenario 3

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Figure 7. Historical and optimized vessel schedules for Scenario 4

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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 $\delta^k(t)$

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Table 1. 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	-

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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

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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

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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

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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

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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

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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%

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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%

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