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March 8, 2023A SUSTAINABLE MODEL FOR OPTIMAL ALLOCATION OF OIL TANKERS

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nIntroduction

nCrude oil shipping is a critical network of global commerce involving oil tankers. However, according to Gupta and Grossmann (2012, p.6824), the transit of crude oil normally leads to accidents especially when oil tankers are unable to control propulsion or steering. Such incidents take place almost on daily basis but they are rarely reported. In addition, these types of accidents can have serious environmental effects such as oil spills and may cause loss of lives. Various algorithms in maritime shipping have been used for optimal allocation of crude oil tankers. For instance, control centres and ships utilize the automatic identification system (AIS) to monitor tug vessels in an intelligent way. However, such methods are not sustainable especially when the traffic of oil tankers is high.

nMethodology

nThe literature review on sustainable model for optimal allocation of oil tankers is limited because the optimal allocation of oil vessel is still a developing topic. In fact, most of the models do not pay close attention on the issue of sustainability. For this reason, a number of publications and journals have covered this issue. therefore, the literature reviewed for sustainable model for optimal allocation of oil tanker is founded on three kinds of publications.

nFirst, the paper included and analyzed all journal articles having the term “model or algorithm for optimal allocation of oil tankers” in the title. Similarly, all the research papers from reputable databases such as Science Direct and Emerald. It also analyzed data from International Journal of Transportation Engineering and Journals of logistics and transportation reviews. Such journals discussed the sustainability of different models used in optimal allocation of oil tankers. They also discussed how each model attempted to address emerging risks and shortcomings in the industry. Secondly, the paper analyzed studies on the supply chain management on the issue. Thirdly, it included research from reliable research institutes such as European Journal of Operational Research in order to acquire better understanding on the topic of discussion. Furthermore, studies on mathematical modelling and algorithms were included to determine the emerging challenges.

nMixed Integer Programming (MIP) Model

nVarious studies have examined the utilization and sustainability of mixed-integer programming model (MIP). Agra, Christiansen and Delgado (2013, p.113) argued that mixed-integer programming is a mathematical algorithm, which enables optimal assignment by merging discrete and continuous variables. The model is beneficial in the optimal allocation of oil tankers particularly in the event of complex control and planning challenges pertaining to both discrete and continuous decisions. The research by Agra, Christiansen and Delgado (2013, p.115) noted that MIP has been used for a long period. Fortunately, due to the advancement of technology, fast software and computers have enabled its online use. A study conducted by Jiang and Grossmann (2015, p.150) suggested that the core aims of MIP approach are to identify logic and non-convexity. Therefore, the algorithm converts non-convexity through integers and later utilize robust integer optimization instrument to non-convex challenges. The scholars indicated that mixed integer programming could determine the optimal clarifications for difficult planning issues. The algorithm also introduces control that assists in determining uncertainties in oil tanker paths ways. The researcher also highlighted that the control updates plans to incorporate new information. The MIP model can optimize the PWA cost, logic states, and dynamics such as task done, non-convex constraints including avoidance (Engineer et al. 2012, p.107)

nResearch conducted by de Assis and Camponogara (2016, p.374) noted that in order to eliminate the gaps witnessed in the use of MIP model in the optimal allocation of crude oil ships, the online system should be utilized. However, MIP online is still unable to handle cases of large traffic of ships because it is quite slow. The researchers also argued that approaches to fast-track the solution time are usually problem-specific. Agra, Andersson, Christiansen and Wolsey (2013, p.310) demonstrated that there are three common methods to the use of MIP model in optimizing the allocation of crude oil tankers. In this regard, the algorithm includes utilization of past knowledge, estimated cost-to-go, and multi-parametric integer programming.

nAccording to a study by Agra, Christiansen and Delgado (2013, p.116), MIP is quite useful in the shared deployment and routing of a fleet of crude oil vessels. The modelassists in the reduction of operation costs and improves on the competitive advantage. Therefore, the companies are empowered to determine the routes which be served and the types and number of tankers that will be allocated to every route. Such processes are complex since they require consideration of differences in transportation pricing, demand, and diversity of operational features such as carrying capacity, crew requirements, and fuel consumption of every oil tanker.

nRakke, Andersson, Christiansen and Desaulniers (2014, p.386) recommend the use of mixed integer programming model in the crude tankers deployment challenges. The MIP is useful because it solves the challenges of the linear programming model, which normally undertakes that the number of oil tankers accessible to the firm is fixed over the preparation horizon. In addition, the MIP provides a clear account of the routes that may be required. Since the linear programming fails to create new routes, the MIP model can solve the emerging challenges. A similar research by Álvarez Serrano (2010, p.7) initiates an integer-programming model can also be used for optimal allocation of fleets. The model is also useful in dealing with operating costs for each oil tanker route grouping, costs of lay-up, needed service frequencies and vessel-route incompatibilities. An account of all possible routes is necessary. Similarly, the scholars noted that the model regulates the types and number of crude oil tankers to serve every route and the number of tankers that are laid up.

nThe research by Bye and Schaathun (2015, p.1) contended that mixed integer programming integrates the continuous behaviour progression specified by various equations with discontinuous variations specified by distinct event logic. Ideally, these systems in the maritime industry can be recognized as having to rely on discrete decisions related to their operations. However, the researchers highlighted that the process of optimizing allocation through MIP is quite complex and challenging because of the grouping of discrete and continuous variables. Although a wide range of studies has been conducted on the MIP, they are largely centred on heuristic rules created from a ‘common sense strategy that is accountable for certain plant settings. Rakke, Andersson, Christiansen and Desaulniers (2014, p.390) argued that these algorithms are later utilized to gather logic that is then used as a foundation for control rules. However, they argued that the use of this moderately more unstructured process ensures that the generally optimizing allocation for all conceivable scenarios a challenging task. Therefore, the model requires the vessel controller unit to perform many runs. Nevertheless, the studies fail to analyse a sustainable process of optimizing the allocation of ships.

nSeminal work by scholars such as Psaraftis and Kontovas (2013, p.331) determined that mixed integer linear programming (MIP) gaps include optimization issues with a linear impartial function, conditional on linear inequality, and equality limitations. The researchers noted that the benefit of MIP model is that it provides accessibility to proficient solvers that can calculate the multinational optimal solutions in a realistic period.

nPaper Scope and Research gaps

nHowever, most of the studies identified that the MIP model is coupled with several gaps because it does not consider the high uncertainty associated with ocean currents, wave, and weather. In this regard, there is need to integrate parameters and dynamics in every time interval. The receding horizon optimization intends to eliminate some of these constraints.

nModel Predictive control (MPC)

nVarious studies have stressed that model predictive control (MPC) is intended to provide a holistic method optimally allocate the oil tankers and solve the challenges such as multivariable constraints and interactions. A study by Borrelli, Bemporad and Morari (2017, p.14) specified that the control mechanism is intended to offer stabilization to an equilibrium or ship monitoring for a preferred reference trajectory through the feedback control and helps to safeguard the system from potential constraints damages. The researcher contends that the online procedure of MPC steadily enhances a systems vibrant performance while maintaining it within distinct areas of operations. However, one of the drawbacks of MPC is its online computational difficulty. In this respect, the algorithm is rarely implemented on the optimizing allocation for crude oil vessels. The mixed integer dynamic optimisation (MIDO) helps in constant online optimization of mixed processes. The numerical explanations of MIDO problems depend on mathematical techniques initiated to elucidate the mixed integer non-linear programming (MINLP) complications such as bound and branch techniques (de Assis and Camponogara 2016, p.375). According to Gupta and Grossmann (2012, p.6826), over the past few decades, there has been a notable enhancement of the techniques for resolving mixed integer non-linear programming challenges.

nBorrelli, Bemporad and Morari (2017, p.1) claimed that discrete variables that are utilized to explain the hybrid traits signify decisions that have to be taken concerning the operations of the oil tanker. The decisions are normally left out to some kind of control or intelligence procedure. The control of hybrid system then encompasses the initiation or evaluation of these decisions. The researchers also maintained that allocation optimization with continuous/discrete dynamics combined with integer constraints and decisions raise a challenge in the MIDO (Yu-Geng De-Wei and Shu 2013, p.229).

nPrevious research by Brouer et al (2013, p.284) has suggested that model predictive control (MPC) is a category of control models that applies clear process models to forecast the future reaction of a system and monitor a structure to a preferred output utilising optimization as an intermediary step.

nPaper Scope and Research gaps

nThe studies failed to indicate whether the MPC mechanism of oil tankers is founded on a receding horizon viewpoint where a structure of control actions in the future is determined based on the future projected system output. Therefore, it does not show whether allocation is affected by optimization procedure whose aim is to enhance the performance of surveillance. For this reason, the sustainability mechanisms are not analyzed.

nReceding Horizon Genetic Algorithm (RHGA) model

nA study by Bye and Schaathun (2014, p.683) examined the manner in which application of improved receding horizon algorithm (RHGA) model can help to solve the optimization problem in tug fleet. The RHGA is also helpful in the minimization of a danger of drifting accidents in oil tankers. Additionally, the RHGA would assist the vessel traffic services to constantly direct the tugs to new areas in a way that if an oil tanker is unable to find manoeuvrability especially through propulsion or steering failure. RHGA offers a chance to capture the drifting vessel prior to it running aground. The traditional methods of positioning oil tankers using prior experience, wind movements and weather do not offer a viable method especially when the number of oil tankers significantly increases. Therefore, the model becomes untenable for human operators to use this approach (Bye 2012, p.132).

nAccording to Bye and Schaathun (2015b, p.271), the receding horizon genetic algorithm (RHGA) is a sustainable model of address the challenge of tug fleet optimization. The model integrates techniques from the computational intelligence and control theory to iteratively strategize oil tankers movement routes for every distinctive tug. The model is calculated by a cost function, which is optimized through a genetic algorithm (GA). The scholars also demonstrated that RHGA has a number of benefits because it provides a better suboptimal allocation of oil vessels at every run. Nonetheless, the main gap of this model is that it sometimes generates inexact solutions. Moreover, a research by Bye and Schaathun (2015a, p.166) highlighted that the receding horizon mixed integer programming algorithm (RHMIPA) model is more advanced because it provides exact optimal allocation with a minimal cost function. Again, the RHMIPA has illustrated slower computational calculation in comparison with the empirical RHGA.

nMore importantly, the RHMIPA and RHGA are useful tools to deal with problems associated with tug fleet optimization. Rodrigues, Morabito, Yamashita, Silva and Ribas (2017, p.794) noted that these models could be utilized to uniformly set the oil tankers at the base stations along the coastline. Moreover, both are advantageous because they reduce the cost function since they have an active tug oil tanker patrol system that outdoes traditional systems where tugs are put in standby for the event to occur.

nPaper Scope and Research gaps

nA number of researches did not address the sustainability component of the RHGA model. Therefore, it they failed to assess how the model will reduce cost of allocation or eradicate environmental pollution caused by oil tankers.

nReceding Horizon Mixed Integer Programming (RHMIP) Model

nA study by Assimizele, Oppen and Bye (2013, p.803) examined different sustainable models that can be used effectively for optimal vibrant allocation of oil tankers. The researchers observed that vessel operators at the Norwegian coasts lack mathematical models or computer algorithms, which can assist them to solve the challenge of active reserve allocation. In this respect, they proposed the use of receding horizon mixed integer programming (RHMIP) model because it plays a significant part in optimal assignment of oil tankers. Most importantly, this model incorporates features from linear programming and predictive control. The researchers used simulations to tests the effectiveness of RHMIP. The results indicated that this model is of high quality and improves the performance. Therefore, it could be sustainably used as an operative decision maintenance instrument in the oil tanker allocation (Bye, van Albada, and Yndestad 2010, p.115).

n A recent study by Qi and Song (2012, p.863) indicated that receding horizon mixed integer programming (RHMIP) model could be used to resolve the certain challenge witnessed in the use of traditional methods when allocating the oil tankers. The study also noted that it helps in predicting the future position of the oil tanker and the resultant drift trajectories. Furthermore, the findings of the study by Brouer et al (2013, p.287) noted that RHMIP model can be useful in unravelling various challenges such as vigorous oil tanker optimization especially on resource allocation and platform supply vessels both on land and offshore. Receding horizon optimization is extensively acknowledged as a very pragmatic strategy with great performance. For instance, the study conducted by Wang and Meng (2012, p.617) demonstrated that it is a very effective approach to real-world control difficulties. The literature illustrated that most essential theoretical and practical challenges can be expressed in the receding horizon control (RHC) framework.

nSustainability component of RHMIP Model

nSome scholars such as Moura et al (2013, p.5) have also proposed that RHC model comprises two key steps. The first level encompasses projection of future system actions based on the existing measurements and a scheme model. Secondly, they noted that the way out of an optimization difficulty for defining upcoming values of the dependent variables bound by constraints. Therefore, the algorithm helps to give answers to optimization trouble in the discrete time over the period in a manner that a performance index cleared over the deliberated moment is optimized based on operational constraints.

nWang et al (2014, p.50) argued that the main challenge in the oil tankers optimal allocation is that tug vessels are forced to travel no quicker than their best speed, which creates a restriction on the number of oil tankers assigned to a certain tug vessels. After the optimal regulator system is calculated, only the first device sample is executed, shifting of the horizon is started. Consequently, the new status of the network is estimated and a new optimization difficulty is resolved to utilize the new data. Eventually, the RHC standard presents feedback control and hence strength to variations in the environment.

nReduction of distance

nThe research by Barnawi (2015, p.10) describes that the RHMIP model is designed in a manner that can minimize the distances between patrol points and nearest cross points in the preparation horizon. The time is equal to reducing the rescue time in case all patrol tugs have equal highest speed. In fact, the findings of the study implied that this represents a logical option that attempts to increase the number of oil vessels that can be salvaged. Furthermore, the research by Dekker et al (2012, p.672) argued that in MIP model provides a cost function, which is achieved by introducing some variables. The advantages of RHMIP are that pay close attention to different variables, set, and parameters such as tug vessels and oil tankers sets. Some of the parameters, which are included in this model, include the oil tanker and tug vessels maximal speeds as well as cross point of projected trajectory of a given oil tanker. Others parameters included include the initial position of both the oil tanker and tug vessel, drift period taken by an oil tanker, length of preparation horizon (Hennig et al. 2012, p.765). The decision variables include the direction and location of tug vessels as well as the distance between tug vessel and drifting potential of the oil tanker. Based on Wang and Meng (2012, p.619) argument, MIP model is normally utilized as an optimization segment in the RHMIP procedure. In addition, the model has various constraints, which are applied to calculate the maximal direction and speed of every tug vessel at a given period. Other variables in the model are exploited to optimally allocate every tug vessel to one oil tanker. Notably, the algorithm also includes constraints to outline limits on the decision variables.

nIdeal allocation of resources

nPrevious literature has discovered that the RHMIP is a sustainable model, which can be used in the ideal allocation of resources to the oil tankers because it pays close attention to various functions and variables. Qi and Song (2012, p.864) noted that it incorporates the time function, which is used in the planning for the anticipated drift trajectory for every oil tanker that is projected to pass the patrol line after a given period. For instance, if an oil tanker begins drifting in a certain time, the RHMIP model provides speed and direction to its assigned tug vessel at every period such that their distance is reduced in the shortest time possible. Therefore, the tug vessel will be proactive in its movement to ensure that adequate time is available to salvage any oil tanker that is drifting.

nPromotes preparations

nZahedian-Tejenaki and Tavakkoli-Moghaddam (2015, p.231) noted that RHMIP model could be used sustainably because it incorporates the variant for MIP model, which pays close attention to the stationary tug vessels. Therefore, the algorithm assists in better preparation in the event an oil tanker starts drifting. More importantly, this variant provides an optimal assignment of immobile tug vessels especially to the oil tankers. A similar study by Díaz-Parra et al (2013, p.13) argued that RHMIP model is efficient as compared to other models because it reduces the time before a drifting crude oil tankers are optimally assigned to the tug vessels. Additionally, the algorithm is essential because reduces the mean distance before an oil tanker is rescued.

nReduces GHGs Emissions

nMore importantly, the RHMIP model is highly sustainable because it is able to minimize the tug vessels speed based on its parameters and variables. Researchers such as Akyuz et al (2017, p.135) argued that global maritime is responsible for more than 2.7 per cent of the total carbon dioxide emissions. Therefore, the model is critical at operational and tactical level because it deals with the problem of speed in the industry. In this respect, tug vessels had an operational speed of 5km/h in all situations. The investigators argued that this is quite slower relative to the 30km/h top speed. According to Jiravanstit and Tharmmaphornphilas (2017, p.146), a limitation on the highest consumption of fuel per day by the tug vessels may possibly be integrated into the model. Nevertheless, restricting the consumption of fuel would lead to an adjustment between the long-lasting possible environmental effect and short-term carbon dioxide emissions contributed by oil tankers, which are drifting that could not be salvaged in a given period.

nConsiders the existing weather conditions

nBrouer et al (2013, p.289) established that RHMIP is also more robust as compared to other models such as MIP. For instance, the researcher noted that in most cases, the speed of the tug vessel might be affected by various factors such as ocean currents, and wave heights hence leading to deviation from the expected location and distance of the tugs ships. In this respect, the model eliminates the challenge through the receding horizon regulator mechanism particularly at the planning interval. Indeed, the model pays close attention to the existing information about the tanker and tugs vessel location. Likewise, the algorithm also considers the weather conditions at the time, which means these factors, will be integrated determining the velocity of the tug (Barnawi 2015, p.11).

nConclusion

nBrouer, Dirksen, Pisinger, Plum and Vaaben (2013, p.362) argued that RHMIP model could be very beneficial in reducing the oil tanker accidents because it incorporates variables such as characteristics and type of an oil tanker before the misfortune occurs. Furthermore, the model can also assess the area of the coastline that oil spill can happen. Therefore, the ability to recognize the oil tankers weight and the high-risk zone will be useful in the optimal allocation. Such functions can also be integrated into the RHMIP model. Indeed, the model is useful because it helps to reduce accidents caused by oil tanker hence play a critical part in reducing oil spillage. Furthermore, such model is sustainable because it reduces the cost of rescuing the oil tankers, which are drifting. Through optimal allocation of tug vessels to oil tankers, the environmental degradation is reduced in the seaports. For these reasons, RHMIP offers sustainable means of optimal allocation of resources to identified oil tankers, which are likely to cause accidents.

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