# A Crew Scheduling Model to Incrementally Optimize Workforce Assignments for Offshore Wind Farm Constructions

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## Abstract

**:**

## 1. Introduction

## 2. Process Description

#### 2.1. Planning and Scheduling of Offshore-Operations

#### 2.2. Conclusion and Research Gap

## 3. Literature Review and Requirements Analysis

#### 3.1. Description of the Investigated Crew Scheduling Problem

#### 3.2. Requirement-Analysis

**Working hours and rest periods:**International and national laws impose strict regulations on working hours and rest periods that the crew scheduling needs to satisfy. These regulations differ, e.g., for national, European, or international laws, and are highly dependent on the country the vessel sails for or the crew aboard. Moreover, a single vessel might need to cover different rules for different types of personnel. For example, German laws differ between the actual vessel crew and crews that perform “offshore duties”, i.e., in the case of this article, the project crews [27,28]. Generally, these laws define maximum workloads per day and week, minimum pause and rest periods, and often the maximum time persons can spend offshore. Accordingly, this requirement states that the crew scheduling should handle different sets of rules for a single vessel, preferably defined for each person or crew.

**Crew Roles and Qualification:**Most of the literature refers to personnel qualification in one way or another. These qualifications range from basic assignments (the person can do a job or not), i.e., the definition of crew roles, to more sophisticated levels of qualification that the optimizer needs to satisfy for each job. Accordingly, each model should at least allow a binary assignment of required and offered roles for jobs and personnel. As this article assumes a fixed sequence of jobs for crew scheduling, the models should also ensure that each job’s minimum qualification level can be guaranteed. Underqualification might result in delays that interfere with the given plan.

**Availability and Worker Health:**As noted above, a single installation cycle with an average vessel takes about one week before the vessel returns to the base port. Consequently, worker availability and unplanned interruptions due to sickness can severely influence the installation or induce additional costs for crew transfers. Several authors highlight the rough working conditions at sea, which induce a high risk of accidents or additional risks of sickness due to the confined living situation on a vessel [29,30]. Accordingly, this requirement states that crew scheduling for offshore constructions should offer a mechanism to deal with this highly unpredictable situation by imposing monitoring and replanning strategies or applying robust planning approaches.

**Types of Contract and Payment:**This requirement ties into previous requirements but extends them by costing. Besides inherently different payments and contract conditions for different crew roles, some authors highlight the ability to book additional personnel on short notice. For example, Leggate et al. [31] differentiate between regular and agency personnel, whereby they use the latter to fill in for higher, unplanned demands at higher costs. Accordingly, this requirement states that each model should allow a specification of different costs per person or crew. Optionally, they should allow the integration of agency crews if requested by the planner.

**Type of Assignment:**As noted above, the type of assignment between personnel, jobs, routes, or vessels imposes a significant requirement for the viability of models in offshore constructions. While most crew scheduling models assign personnel to single vessels or routes (pairing), the article at hand requires the assignment of personnel to single jobs during each trip.

**Influence of Weather and Forecast-Uncertainty:**Most viable models identified during the literature review assign personnel to specific jobs or roles on a vessel. As described in the process description, these jobs depend on the current weather conditions at the open sea, which can change quickly. These conditions influence waiting times between jobs and impose a strong dynamic on the planning as forecasts always include high degrees of uncertainty. Therefore, this requirement states that each model requires a way to include or handle these uncertainties, either directly for crew scheduling or during initial planning.

**Nationality:**Tying into the requirement for crew availability, several authors highlight the nationality of crews as a major influential factor for personnel planning in the offshore domain [31,32]. Local legislation might exclude some nationalities from certain vessels, or planners need to consider visas and transportation for persons. Nevertheless, this article considers this requirement as optional due to its focus on the operative planning level. This article assumes that such questions have been answered before the actual planning, similar to the personnel certification.

#### 3.3. Literature Review on Models for Offshore Crew Scheduling

## 4. Workforce-Management Framework

#### 4.1. Model Design Based on the Requirements and General Assumptions

**Working hours and rest periods:**The proposed model uses the notion of rulesets ($r\in \mathcal{R}$) that it assigns to each person or crew $p\in \mathcal{P}$ as $r={R}_{p}$ to cope with different laws for parts of the overall crew. Each ruleset defines the maximum weekly ($Workloa{d}_{r}^{week}$) and daily (${Workload}_{r}^{day}$) workload, the length of daily rest periods ($Res{t}_{r}$), and the duration (${Break}_{r}^{dur}$), and interval of short breaks (${Break}_{r}^{int}$ ) personnel need to take when working. The use of these rulesets allows differentiating, e.g., between port-side workers, project crews, or vessel crews that fall under different restrictions depending on the country’s laws.

**Crew Roles and Qualification:**In contrast to the articles found in the literature, the proposed model does not rely on a binary role model. Instead, it uses the notion of skills ($s\in \mathcal{S}$). Therefore, it assigns each person a degree of experience for each noted skill as ${S}_{p,s}$ and a minimum required level of experience for each job as ${S}_{j,s}$. This way of denoting capable personnel allows for a great deal of flexibility. Planners can define skills on a very rudimentary level, e.g., “We need persons that can install a blade with an experience of 1.5.”, or on way more detailed levels, e.g., “To install the blade, we need someone who can weld with an experience of 0.7 and someone who can operate the crane with an experience of 1.8”. The optimization model will then select crews that, combined, meet the minimum requirement of skills for each operation.

**Availability and Worker Health:**This requirement splits into two different aspects. First, the dynamic aspect of unavailability due to sickness or accidents. This proposed general approach already covers this aspect by its iterative planning and the described monitoring and rescheduling policy. Second, the requirement includes planned unavailabilities, e.g., due to vacation or on/off periods. The model covers this aspect by including a parameter ($Planne{d}_{p,k}$) in its state. It lists if a person (p) is already planned or unavailable for a given instance (k) within the prediction horizon. In addition to noting general unavailability, the model uses this parameter to block a rescheduling of personnel, e.g., if the plan for one vessel fails, while other vessels still have planned operations for the new prediction horizon left.

**Types of Contract and Payment:**Similar to the rulesets, which already cover most of the contractual characteristics, the model allows assigning costs to each person individually as $Cos{t}_{p}$. By combining the rulesets and skills with the cost parameter, the model provides a versatile way to define different personnel, contract types, and associated costs. For example, by adding a person without limits on their workloads, all skills, and high costs, the model can easily represent the notion of additional agency personnel introduced by Leggate et al. [31].

**Type of Assignment:**The model’s design assigns crews to jobs. As described earlier, the fourth step of the general approach breaks down the provided plans into basic installation, loading, and vessel operations as specified in Table 1 to allow precise assignment with a high level of detail. Therefore, the model uses a set of jobs $j\in \mathcal{J}$. For each job, the model denotes the jobs starting ($Jo{b}_{j}^{start}$) and end time ($Jo{b}_{j}^{end}$), its duration ($Jo{b}_{j}^{dur}$), and its indexed location ($Lo{c}_{j}^{job}$), e.g., if it takes place at the port or a particular vessel. Similarly, it denotes the location of personnel ($Lo{c}_{p}^{per}$). Using these locations, the model calculates a binary matching if a particular person or crew is present at the right location ($AtLo{c}_{p,j}$) as part of the capability requirement.

**Influence of Weather and Forecast-Uncertainty:**Weather conditions strongly affect the overall planning problem and define when an operation can start safely. The proposed approach includes these dynamics in its general approach but not in the actual crew scheduling model. As described earlier, the general approach follows a predictive-reactive approach to first estimate the influence of weather conditions using forecasts, even including their uncertainty. Second, it employs viable monitoring and rescheduling policies to react if the predictions were wrong.

**Nationality:**As described earlier, this article focuses on the operative decision support and, thus, assumes that planners already took care of visa, traveling, and accommodation issues for planned crews or personnel. Thus, the model does not include the nationality of the crews explicitly.

#### 4.2. System State for the Crew Scheduling (Model Parameters)

#### 4.3. Decision Variables and Cost Function

#### 4.4. Constraints

## 5. Experiments and Results

#### 5.1. Scenario Description

#### 5.2. Experimental Results

#### 5.2.1. Base Scenario

#### 5.2.2. Extended Scenario and Computational Times

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- REN21. Renewables 2021 Global Status Report. 2021. Available online: https://www.ren21.net/reports/global-status-report/ (accessed on 14 September 2021).
- BVGassociates. Guide to an Offshore Wind Farm. 2019. Available online: https://bvgassociates.com/publications/ (accessed on 14 September 2021).
- Beinke, T.; Ait Alla, A.; Oelker, S.; Freitag, M. Demand for Special Vessels for the Decommissioning of Offshore Wind Turbines in the German North Sea—A Simulation Study. In Proceedings of the 30th International Ocean and Polar Engineering Conference (ISOPE), Virtual, 1–16 October 2020; Chung, J.S., Akselsen, O.M., Jin, H., Kawai, H., Lee, Y., Matskevitch, D., Eds.; ISOPE: Cupertino, CA, USA, 2020; pp. 480–484. [Google Scholar]
- Breton, S.; Moe, G. Status, Plans and Technologies for Offshore Wind Turbines in Europe and North America. Renew. Energy
**2009**, 34, 646–654. [Google Scholar] [CrossRef] - Dewan, A.; Asgarpour, M.; Savenije, R. Commercial Proof of Innovative Offshore Wind Installation Concepts Using Ecn Install Tool; ECN: Petten, The Netherlands, 2015. [Google Scholar]
- Muhabie, Y.T.; Rigo, P.; Cepeda, M.; D’Agosto, M.A. A Discrete-event Simulation Approach to Evaluate the Effect of Stochastic Parameters on Offshore Wind Farms Assembly Strategies. Ocean Eng.
**2018**, 149, 279–290. [Google Scholar] [CrossRef] - Ait Alla, A.; Oelker, S.; Lewandowski, M.; Freitag, M.; Thoben, K.D. A Study of New Installation Concepts of Offshore Wind Farms by Means of Simulation Model. In Proceedings of the Twenty-seventh International Ocean and Polar Engineering Conference (ISOPE), San Francisco, CA, USA, 25–30 June 2017; Chung, J.S., Triantafyllou, M.S., Langen, I., Eds.; ISOPE: Cupertino, CA, USA, 2017; pp. 607–612. [Google Scholar]
- Vis, I.F.; Ursavas, E. Assessment Approaches to Logistics for Offshore Wind Energy Installation. Sustain. Energy Technol. Assess.
**2016**, 14, 80–91. [Google Scholar] [CrossRef][Green Version] - Oelker, S.; Lewandowski, M.; Ait Alla, A.; Ohlendorf, J.H.; Haselsteiner, A.F. Logistikszenarien Für Die Errichtung Von Offshore-windparks—Herausforderungen Der Wirtschaftlichkeitsbetrachtung Neuer Logistikkonzepte. Ind. 4.0 Manag.
**2017**, 33, 24–28. [Google Scholar] - Rippel, D.; Jathe, N.; Lütjen, M.; Freitag, M. Evaluation of Loading Bay Restrictions for the Installation of Offshore Wind Farms Using a Combination of Mixed-integer Linear Programming and Model Predictive Control. Appl. Sci.
**2019**, 9, 5030. [Google Scholar] [CrossRef][Green Version] - Rippel, D.; Jathe, N.; Becker, M.; Lütjen, M.; Szczerbicka, H.; Freitag, M. A Review on the Planning Problem for the Installation of Offshore Wind Farms. IFAC-PapersOnLine
**2019**, 52, 1337–1342. [Google Scholar] [CrossRef] - Scholz-Reiter, B.; Karimi, H.R.; Lütjen, M.; Heger, J.; Schweizer, A. Towards a Heuristic for Scheduling Offshore Installation Processes. In Proceedings of the 24th International Congress on Condition Monitoringand and Diagnostics Engineering Management. Advances in Industrial Integrated Asset Management, Birmingham, UK, 30 May–1 June 2011; Maneesh, S., Rao, R., Liyanage, J.P., Eds.; COMADEM International: Birmingham, UK, 2011; pp. 999–1008. [Google Scholar]
- Ait Alla, A.; Quandt, M.; Lütjen, M. Simulation-based Aggregate Installation Planning of Offshore Wind Farms. Int. J. Energy
**2013**, 7, 23–30. [Google Scholar] - Kerkhove, L.P.; Vanhoucke, M. Optimised Scheduling for Weather Sensitive Offshore Construction Projects. Omega
**2017**, 66, 58–78. [Google Scholar] [CrossRef] - Ursavas, E. A Benders Decomposition Approach for Solving the Offshore Wind Farm Installation Planning at the North Sea. Eur. J. Oper. Res.
**2017**, 258, 703–714. [Google Scholar] [CrossRef] - Barlow, E.; Tezcaner Öztürk, D.; Revie, M.; Akartunalı, K.; Day, A.H.; Boulougouris, E. A Mixed-method Optimisation and Simulation Framework for Supporting Logistical Decisions during Offshore Wind Farm Installations. Eur. J. Oper. Res.
**2018**, 264, 894–906. [Google Scholar] [CrossRef][Green Version] - Irawan, C.A.; Wall, G.; Jones, D. An Optimisation Model for Scheduling the Decommissioning of an Offshore Wind Farm. OR Spectr.
**2019**, 41, 513–548. [Google Scholar] [CrossRef] - Lange, K.; Rinne, A.; Haasis, H.D. Planning Maritime Logistics Concepts for Offshore Wind Farms: A Newly Developed Decision Support System. Lect. Notes Comput. Sci. Comput. Logist.
**2012**, 7555, 142–158. [Google Scholar] - Beinke, T.; Ait Alla, A.; Freitag, M. Resource Sharing in the Logistics of the Offshore Wind Farm Installation Process Based on a Simulation Study. Int. J. E-Navig. Marit. Econ.
**2017**, 7, 42–54. [Google Scholar] [CrossRef] - Quandt, M.; Beinke, T.; Ait Alla, A.; Freitag, M. Simulation Based Investigation of the Impact of Information Sharing on the Offshore Wind Farm Installation Process. J. Renew. Energy
**2017**, 2017, 11. [Google Scholar] [CrossRef][Green Version] - Cheng, M.Y.; Wu, Y.F.; Wu, Y.W.; Ndure, S. Fuzzy Bayesian schedule risk network for offshore wind turbine installation. Ocean Eng.
**2019**, 188, 106238. [Google Scholar] [CrossRef] - Peng, S.; Szczerbicka, H.; Becker, M. Modeling and Simulation of Offshore Wind Farm Installation with Multi-Leveled CGSPN. In Proceedings of the 30th International Ocean and Polar Engineering Conference (ISOPE), Virtual, 11–16 October 2020; Chung, J.S., Akselsen, O.M., Jin, H., Kawai, H., Lee, Y., Matskevitch, D., Eds.; ISOPE: Cupertino, CA, USA, 2020; pp. 472–479. [Google Scholar]
- Moher, D.; Liberati, A.; Tetzlaff, J.; Altman, D.G. Preferred reporting items for systematic reviews and meta-analyses: The PRISMA statement. PLoS Med.
**2009**, 6, e1000097. [Google Scholar] [CrossRef][Green Version] - van den Bergh, J.; Beliën, J.; de Bruecker, P.; Demeulemeester, E.; de Boeck, L. Personnel scheduling: A literature review. Eur. J. Oper. Res.
**2013**, 226, 367–385. [Google Scholar] [CrossRef] - Gopalakrishnan, B.; Johnson, E.L. Airline Crew Scheduling: State-of-the-Art. Ann. Oper. Res.
**2005**, 140, 305–337. [Google Scholar] [CrossRef] - John, O.; Gailus, S.; Rizvanolli, A.; Rauer, R. An Integrated Decision Support Tool for Hours of Work and Rest Compliance Optimization during Ship Operations. In Proceedings of the 13th International Conference on Computer and IT Applications in the Maritime Industries, COMPIT’14, Redworth, UK, 12–14 May 2014; Bertram, V., Ed.; Schriftenreihe Schiffbau, Technology University Verlag Schriftenreihe Schiffbau: Hamburg, Germany, 2014; pp. 245–257. [Google Scholar]
- Bundesamt für Justiz und Verbraucherschutz. Verordnung über die Arbeitszeit bei Offshore-Tätigkeiten; Bundesamt für Justiz and Verbraucherschutz: Berlin, Germany, 2013. [Google Scholar]
- Bundesamt für Justiz and Verbraucherschutz. Seearbeitsgesetz (SeeArbG); Bundesamt für Justiz and Verbraucherschutz: Berlin, Germany, 2021. [Google Scholar]
- Colli, N.; Mache, S.; Harth, V.; Mette, J. Physische und psychische Gesundheit von Offshore-Beschäftigten. Zentralblatt für Arbeitsmedizin Arbeitsschutz und Ergon
**2017**, 67, 176–178. [Google Scholar] [CrossRef] - Hammer, G.; Röhrig, R. Qualification Requirement Analysis Offshore Wind Energy Industry. Tech. Rep.
**2005**. Available online: http://pcoe.nl/@api/deki/files/1919/=15final_report_qrs.pdf (accessed on 21 October 2021). - Leggate, A.; Sucu, S.; Akartunalı, K.; van der Meer, R. Modelling crew scheduling in offshore supply vessels. J. Oper. Res. Soc.
**2018**, 69, 959–970. [Google Scholar] [CrossRef] - Sucu, S. Solving Crew Scheduling Problem in Offshore Supply Vessels: Heuristics and Decomposition Methods. Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, 2017. [Google Scholar]
- Giachetti, R.E.; Damodaran, P.; Mestry, S.; Prada, C. Optimization-based decision support system for crew scheduling in the cruise industry. Comput. Ind. Eng.
**2013**, 64, 500–510. [Google Scholar] [CrossRef][Green Version] - Damodaran, P.; Mestry, S.; Zuniga, M.; Perez, J.; Brearley, R.; Arteta, B. A mathematical model for scheduling shipboard crew in cruise lines. In Proceedings of the IIE Annual Conference Expo 2010 Proceedings, Boston, MA, USA, 23–25 June 2010. [Google Scholar]
- Sereno, V.M.; Reinhardt, L.B.; Guericke, S. Exact Methods and Heuristics for the Liner Shipping Crew Scheduling Problem. In Computational Logistics; Cerulli, R., Raiconi, A., Voß, S., Eds.; Lecture Notes in Computer Science; Springer International Publishing: Cham, Switzerland, 2018; Volume 11184, pp. 363–378. [Google Scholar] [CrossRef]
- Leggate, A. A Vessel Crew Scheduling Problem: Formulations and Solution Methods. Ph.D. Thesis, University of Strathclyde, Glasgow, Scotland, 2016. [Google Scholar]
- Rizvanolli, A.; John, O. Ein gemischt-ganzzahliges lineares Optimierungs- modell zur Ermittlung des minimal notwendigen Bedarfes an Seefahrern zur Besetzung eines Schiffes. In Entscheidungsunterstützung in Theorie und Praxis; Spengler, T., Fichtner, W., Geiger, M.J., Rommelfanger, H., Metzger, O., Eds.; Springer Fachmedien Wiesbaden: Wiesbaden, Germany, 2017; pp. 87–107. [Google Scholar] [CrossRef]
- Rizvanolli, A.; Heise, C.G. Efficient Ship Crew Scheduling Complying with Resting Hours Regulations. In Operations Research Proceedings 2016; Fink, A., Fügenschuh, A., Geiger, M.J., Eds.; Operations Research Proceedings; Springer International Publishing: Cham, Switzerland, 2018; pp. 535–541. [Google Scholar] [CrossRef]

**Figure 1.**Conventional installation concept [10].

**Figure 2.**Crew Scheduling Procedure extended from Reference [26].

**Figure 4.**General Approach. Extended from Reference [10].

**Figure 7.**Computational time depending on the planning horizon (

**top**) and the number of personnel (

**bottom**).

**Table 1.**Operations, limits, and durations—extended from Reference [10].

Operation | Base-Duration | Max. Wind | Max. Wave | Responsible |
---|---|---|---|---|

[h] | [m/s] | [m] | Crew | |

Load Tower | 3 | 12 ^{1} | 5 ^{1} | Port Crew |

Load Nacelle | 2 | 12 ^{1} | 5 ^{1} | Port Crew |

Load Hub | 1 | 12 ^{1} | 5 ^{1} | Port Crew |

Load Blade | 2 | 12 ^{1} | 5 ^{1} | Port Crew |

Traveling | 4 | 21 | 2.5 | Vessel Crew |

(Re-)Positioning | 1 | 14 | 2.0 | Vessel Crew |

Jack-up/-down | 2 | 14 | 1.8 | Vessel Crew |

Install Tower | 3 | 12 | 2.5 ^{2} | Project Crew |

Install Nacelle | 3 | 12 | 2.5 ^{2} | Project Crew |

Install Hub | 2 | 12 | 2.5 ^{2} | Project Crew |

Install Blade | 2 | 10 | 2.5 ^{2} | Project Crew |

^{1}Mostly omitted by using loading bridges.

^{2}High values due to jack-up stabilizing the vessel.

Publication | Objective | Domain | Horizon |
---|---|---|---|

Damodaran et al. (2010) [34] | Min. Cost | Cruise-Lanes | 1 Year |

Giachetti et al. (2013) [33] | Min. Trip Cost | Cruise-Lanes | 240 Days |

John et al. (2014) [26] | Min. Cost | Shipping Lines | One Trip |

Sereno et al. (2018) [35] | Min. Trip Cost | Shipping Lines | 1 Year |

Leggate (2016) [36] | Min. Cost | Offshore Supply | 3+ Months |

Sucu (2017) [32] | Min. Cost | Offshore Supply | 3+ Months |

Leggate et al. (2018) [31] | Min. Cost and | Offshore Supply | 3+ Months |

Min. Num Changes | |||

Rizvanolli and John (2017) [37] | Min. Crew | Container Transp. | One Trip |

Rizvanolli and Heise (2018) [38] | Min. Crew | Container Transp. | One Trip |

Parameter | Symbol | Unit | Domain |
---|---|---|---|

Sets and Indices | |||

Prediction Horizon $N=P\xb7T$ | $k\in N$ | Hours | ${\mathbb{N}}^{+}$ |

Set of Persons/Crews | $p\in \mathcal{P}$ | Persons | - |

Set of Jobs | $j\in \mathcal{J}$ | Jobs | - |

Set of Locations | $\mathcal{L}$ | Locations | - |

Set of Skills | $s\in \mathcal{S}$ | Skills | - |

Rule Sets | $r\in \mathcal{R}$ | Rulesets | - |

Job Information | |||

Job Start Instance | $Jo{b}_{j}^{start}$ | Hour | ${\mathbb{N}}^{+}$ |

Job End Instance | $Jo{b}_{j}^{end}$ | Hour | ${\mathbb{N}}^{+}$ |

Job Duration | $Jo{b}_{j}^{dur}$ | Hours | ${\mathbb{N}}^{+}$ |

Location of Job | $Lo{c}_{j}^{job}$ | Location | ${\mathbb{N}}^{+}$ |

Assignment of Req. Skills to Jobs | ${S}_{j,s}$ | Experience | ${\mathbb{R}}_{0}^{+}$ |

Personnel Information | |||

Assignment of Ruleset to Persons | ${R}_{p}$ | Index | ${\mathbb{N}}^{+}$ |

Assignment of Skills to Persons | ${S}_{p,s}$ | Experience | ${\mathbb{R}}_{0}^{+}$ |

Cost per Person | $Cos{t}_{p}$ | Currency | ${\mathbb{R}}_{0}^{+}$ |

Ruleset Information | |||

Maximum Daily Workload | ${Workload}_{r}^{day}$ | Hours | ${\mathbb{N}}^{+}$ |

Maximum Weekly Workload | ${Workload}_{r}^{week}$ | Hours | ${\mathbb{N}}^{+}$ |

Rest Period | $Res{t}_{r}$ | Hours | ${\mathbb{N}}^{+}$ |

Length of Breaks | $Brea{k}_{r}^{dur}$ | Hours | ${\mathbb{N}}^{+}$ |

Break Interval (One Break each) | $Brea{k}_{r}^{int}$ | Hours | ${\mathbb{N}}^{+}$ |

Current State Information | |||

Availability of Person | $Planne{d}_{p,k}$ | Unavailable | Binary |

Location of Personnel | $Lo{c}_{p}^{per}$ | Location | ${\mathbb{N}}^{+}$ |

Presence of Person at Job Location | $AtLo{c}_{p,j}$ | At Location | Binary |

Index of Next Week | $WeekStart$ | Hours | ${\mathbb{N}}^{+}$ |

Index of Next Day | $DayStart$ | Hours | ${\mathbb{N}}^{+}$ |

Needs to Start Rest Today | $Paus{e}_{p}^{start}$ | Requires | Binary |

Needs to End Rest Today | $Paus{e}_{p}^{end}$ | Requires | Binary |

Hours Worked Today | $Worke{d}_{p}^{day}$ | Hours | ${\mathbb{N}}^{+}$ |

Hours Worked This Week | $Worke{d}_{p}^{week}$ | Hours | ${\mathbb{N}}^{+}$ |

Free Time at End of the Last Iteration | $Paus{e}_{p}^{last}$ | Hours | ${\mathbb{N}}^{+}$ |

Parameter | Port Crew | Vessel Crew | Project Crew | Agency |
---|---|---|---|---|

Maximum Daily Workload | 14 | 12 | 10 | 24 |

Maximum Weekly Workload | 72 | 48 | 40 | 168 |

Rest Period | 6 | 11 | 11 | 0 |

Length of Breaks | 1 | 1 | 1 | 0 |

Break Interval | 10 | 10 | 8 | 0 |

Number per Location | 5 | 3 | 4 | 1 |

Inst. Tower | Inst. Nacelle | Inst. Blade | Inst. Hub | |
---|---|---|---|---|

Mechanic | 2 | 1 | 2 | 2 |

Electrician | 1 | 2 | 1 | 2 |

Welder | 1 | 0 | 0 | 0 |

Engineer | 1 | 1 | 1 | 1 |

Construction Worker | 2 | 0 | 0 | 0 |

Crane Operator | 1 | 1 | 2 | 2 |

Technician | 1 | 1 | 0 | 1 |

Result | |||
---|---|---|---|

Key-Performance Indicator | All | One Vessel | Two Vessels |

Average Number of Jobs Scheduled | 390.92 | ||

Average Project Duration | 771 h | 1007 h | 535 h |

Average Number of Planning Iterations | 2.75 | 3.17 | 2.33 |

Total Number of Plan Interruptions | 10.0 | 4.00 | 6.00 |

Average Optimization Time per Iteration | 25.25 s | 18.17 s | 32.32 s |

Average Port Crews Required | 3.17 | 3.00 | 3.33 |

Average Vessel Crews Required | 1.50 | 1.00 | 2.00 |

Average Project Crews Required | 3.17 | 2.17 | 4.17 |

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**MDPI and ACS Style**

Rippel, D.; Foroushani, F.A.; Lütjen, M.; Freitag, M. A Crew Scheduling Model to Incrementally Optimize Workforce Assignments for Offshore Wind Farm Constructions. *Energies* **2021**, *14*, 6963.
https://doi.org/10.3390/en14216963

**AMA Style**

Rippel D, Foroushani FA, Lütjen M, Freitag M. A Crew Scheduling Model to Incrementally Optimize Workforce Assignments for Offshore Wind Farm Constructions. *Energies*. 2021; 14(21):6963.
https://doi.org/10.3390/en14216963

**Chicago/Turabian Style**

Rippel, Daniel, Fatemeh Abasian Foroushani, Michael Lütjen, and Michael Freitag. 2021. "A Crew Scheduling Model to Incrementally Optimize Workforce Assignments for Offshore Wind Farm Constructions" *Energies* 14, no. 21: 6963.
https://doi.org/10.3390/en14216963