A long-term fleet renewal problem under uncertainty: A simulation-based optimization approach

Expert Systems With Applications 145 (2020) 113158

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A long-term fleet renewal problem under uncertainty: A simulation-based optimization approach Hasan Hüseyin Turan∗, Sondoss Elsawah, Michael J. Ryan Capability Systems Centre, University of New South Wales, Canberra, Australia

a r t i c l e

i n f o

Article history: Received 25 August 2019 Revised 28 October 2019 Accepted 21 December 2019 Available online 23 December 2019 Keywords: Fleet renewal Simulation-optimization System dynamics Genetic algorithm Scenario discovery

a b s t r a c t In this paper, we model and solve a strategic problem of fleet renewal to meet future operational needs under uncertain conditions. The fleet renewal problem focuses on mainly strategic decisions involving from fleet size, fleet mix and timing of replacement, yet it is essential to consider a significant amount of detail regarding short-term decisions to prevent inferior or infeasible strategies. In this direction, we develop a hybrid simulation model by combining system dynamics (SD) and discrete event simulation (DES) approaches. The standalone use of this model enables the decision maker to analyze the effects of both short- and long-term decisions on availability by simulating the processes that the fleet undertakes through its life-cycle from asset acquisition to retirement. Nevertheless, the simulation neither suggests nor seeks the best renewal strategy(ies). To alleviate this difficulty, we propose a simulation-based optimization that uses a genetic algorithm (GA) to effectively search a very large set of feasible fleet renewal strategies and uses the developed hybrid simulation model to evaluate candidate strategies found by GA. To provide a decision context where the approach has been developed and applied, we use a naval fleet renewal application. The extensive numerical experiments show that the proposed approach not only finds good and robust renewal strategies but also identify critical resources that influence the fleet’s availability. Finally, the robustness of optimized strategies under uncertainty is tested by sensitivity analysis, and mappings between implemented strategies and the fleet performance are constructed by scenario discovery analysis to provide insights for decision makers. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction An important issue in fleet management is the timing of the replacement of the old fleet (i.e., what, when, where)-known as the fleet renewal or transition problem. The fleet renewal problem requires to find the number of assets of each type to maintain in each time period so that a maximal operational fleet availability is achieved with a minimum cost. The renewal decisions can be viewed as a complex, dynamic, and path-dependent problem. First, the performance of decision or investment options changes over time in response to a combination of controllable (e.g., maintenance decisions) and uncontrollable factors (e.g., asset market price). Second, the problem is path-dependent as the range and outcomes of available options is constrained and shaped by past decisions, resulting in suboptimal results (e.g., excessive maintenance costs at later stage

∗

Corresponding author. E-mail addresses: [email protected] (H.H. Turan), [email protected] (S. Elsawah), [email protected] (M.J. Ryan). https://doi.org/10.1016/j.eswa.2019.113158 0957-4174/© 2019 Elsevier Ltd. All rights reserved.

of the investment lifetime) and decision-lockout situations. Third, making acquisition/upgrade plans requires making complex tradeoffs among: (1) short, medium and long term asset management decisions, and (2) multiple objectives (e.g., cost, availability, asset age). It is impossible for decision makers to consider the large set of possible of options (i.e., decision space), and anticipate their effects especially when factoring in future uncertainties (e.g,. changes in the operational requirements). Simulation models are one of the widely used techniques in such situations for modeling complex systems (Lin, Sir, & Pasupathy, 2013). Further, simulation models are also good at capturing uncertainties associated with entities and resources in the system. Thus, we take advantage of these features of simulation models to simulate the life-cycle of a fleet from asset acquisition to asset retirement, as well as to provide an understanding of the relationships between the input and output parameters. The developed simulation model is a combination of system dynamics (SD) and discrete event simulation (DES) methodologies. The hybrid model (SD-DES) contains several sub-modules (e.g., maintenance, workforce, and operations) interacting with

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H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

Fig. 1. The proposed simulation-based optimization approach for the fleet renewal problem.

each other to capture and simulate the dynamic complexities of fleet management issues as shown in Fig. 1 (see Section 4 for details). Due to these interactions and (usually non-linear) interdependencies, it is difficult to anticipate how the system will respond to a range of fleet management strategies. Ignoring these structural properties in the fleet renewal would lead to inadequate system performance (e.g., underutilized assets, high waiting times and idle resources). Fortunately, an SD model is capable of dealing with these complexity features by explicitly capturing the feedback interdependencies among elements of the strategy (Kunc & Morecroft, 2009). Thus, the developed SD-DES model provides an aggregate strategic view (i.e., a holistic approach) of the entire fleet rather than dividing the system into its sub-systems. Each sub-system such as maintenance, workforce and operations of fleet management corresponds to a particular sub-module in the developed SD-DES model. Despite the advantages, simulation models do not provide the capability of finding an optimal fleet renewal strategy. Obtaining optimal fleet renewal strategy may require evaluating a large number of strategies by the simulation model. Here, by strategy, we mean a set of the input variables (also called factors or parameters) that determines the ”design” or ”configuration” of the fleet renewal strategy. Essentially, a strategy is a vector composed of all input variables, which constitutes a large number of possible configurations. In this case, the simulation experiments may become computationally prohibitive due to the total number of runs needed to evaluate all feasible strategies. In addition to the high computational cost, an even higher cost is incurred when the sub-optimal strategy is selected (due to the strategy not achieving operational requirements). Further, the existing traditional analytical approaches are often impractical in solving real-world fleet renewal problems efficiently. As a remedy to this problem, simulationbased optimization (or simulation-optimization) approaches are utilized as powerful problem solving techniques. Simulation-based optimization is an optimization itself; however, it requires addi-

tional mechanisms (i.e., simulation model) to make the entire optimization process much closer to the real-world (Yuan, 2009). In the paper, we adopt a simulation-optimization approach by using a hybrid simulation model integrated with a genetic algorithm (GA) to solve fleet renewal problems. In simulation-based optimization, the outputs (e.g., fleet availability, waiting times and resource utilization) of the simulation model are used by the GA to provide feedback to the simulation model outputs as visualized in Fig. 1. This, in turn, guides further input to the simulation model. The GA effectively and systematically searches a very large set of all feasible strategies, without explicitly evaluating each possibility, to find a strategy(ies) that achieves the best fleet performance. We enhance the traditional GA by improving genetic operators to expand the search space and increase the diversity of the solutions to prevent convergence to a local minimum (see Section 4.1 for details). The simulation-based optimization approach suggested in this paper applies to any fleet renewal. However, to provide a decision context where the methods have been developed an applied, we use a naval fleet application where high-value strategic vessels form a fleet. To our knowledge, the proposed methodology enables decision makers, for the first time, the solution and analysis of a highly complex and significant long-term fleet renewal problem by including all vital activities from the acquisition to the retirement and resource uncertainty. In general, the contributions of this paper are:

(i) developing a SD-DES simulation model that is capable of analyzing both strategic and tactical fleet management decisions under uncertainty, from asset acquisition to retirement; (ii) developing a genetic algorithm that has enhanced genetic operators, which are capable of producing strategies by considering problem characteristics;

H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

(iii) coupling a simulation model with an optimization algorithm to leverage the power of optimization models for finding the best policy, without dealing with a high level of detail or extensive datasets usually need for optimization models; (iv) using a case study to demonstrate the development and application of the proposed framework, along with sensitivity analysis and scenario discovery for analyzing results; and (v) using interactive data visualization tools to summarize managerial implications of large numerical results. The rest of the paper is organized as follows. Section 2 provides a brief literature review on fleet management. Section 3 presents a mathematical formulation for the studied fleet renewal problem. In Section 4, we discuss the solution approach including the details of both simulation and optimization modules. In Section 5, we present an extensive computational study to show applicability and superiority of approach together with managerial insights gained. Finally, Section 6 draws conclusions about the approach and suggests future improvements. 2. Related works Fleet management in general and fleet renewal problems, in particular, have been tackled by a wide range of computational decision analysis techniques from simulation (e.g., discrete-event and SD) through optimization (e.g., linear and integer programming). Thus, there is a very large number of studies regarding the modeling and solution of fleet management related issues. In the section, we present an overview of studies on optimization and simulation applications in fleet management. The review is not meant to be exhaustive, but to provide a good overview of the current state of research in the area and to help contextualize the paper’s contribution in this body of knowledge. One type of approach that has been extensively used for fleet management problems is developing optimization-based models such as mixed-integer programming models, and using analytical methods (e.g.,branch-and-bound) or (meta)heuristic approaches to solve the developed models. For example, Simeonova, Wassan, Salhi, and Nagy (2018) use a mixed-integer formulation to model a heterogeneous vehicle fleet routing problem for the commercial gas delivery industry. They solve the formulated problem with a variant of variable neighborhood search meta-heuristic. Similarly, Bräysy, Porkka, Dullaert, Repoussis, and Tarantilis (2009) solve a fleet size and mix vehicle routing problem via a meta-heuristic developed by authors. Jiang, Ng, Poh, and Teo (2014) and Li, Leung, and Tian (2012) also solve fleet mix and routing related tactical problems with meta-heuristics. Gavranis and Kozanidis (2015) study the maintenance aspects of fleet management to maximize the fleet availability. They also use mixed-integer formulation, but prefer to use an exact analytical approach rather than a heuristic. Monnerat, Dias, and Alves (2019) investigate the crewing problem in a fleet management to minimize the cost of fleet and crew. They use a genetic algorithm to solve the mixed-integer program. A resource allocation problem in the fleet management is studied by Mathew, Khasnabis, and Mishra (2010). The developed mixed-integer programming model allocates yearly resources for the replacement and/or re-building of existing vehicles in the fleet. They use both a genetic algorithm and branch-and-bound approaches to solve the model There are some major shortcomings in optimization-based approaches. First, except for a few (Du, Brunner, & Kolisch, 2016; Fagerholt, Christiansen, Hvattum, Johnsen, & Vabø, 2010; Fagerholt & Lindstad, 20 0 0), most of the models simplify the problem by focusing on a particular aspect of fleet management such as routing or maintenance. Second, to make the optimization problems solvable, they are usually short-term models addressing tactical

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and/or operational issues rather than strategical problems in the fleet management. Last, a few of the optimization models take into account uncertainty; i.e, stochastic elements, associated with assets and environment such as future requirements and costs (Loxton, Lin, & Teo, 2012; Zheng & Chen, 2018) due to arising computational complexity and the need for special tailored algorithms. These weaknesses make this approach unsuitable as a general solving methodology to tackle a wide range of fleet management problems, including the strategic planning problems that are addressed in this study. On the other hand, our approach is capable of dealing with strategic fleet planning problems by considering the uncertainties involved. Further, our approach analyzes each aspect of the fleet management as a part of the whole system rather than treating them independently to reduce the complexity of the problem. This holistic and life-cycle oriented investigating of the strategic fleet planning from acquisition to retirement contributes to the literature. Simulation models are another type of approach that is applied to the different facets of fleet management problems. To illustrate, McLucas, Lyell, and Rose (2006) use a SD simulation to investigate the effects of the interrelationships between availability, maintenance, and available workforce on the fleet readiness. Another SD simulation in fleet management was used by Coyle and Gardiner (1991) to analyze a military fleet maintenance scheduling problem. Adamides, Stamboulis, and Varelis (2004) and Bivona and Montemaggiore (2010) also address implications of both long-term and short-term maintenance decisions on the fleet management by SD simulation models. The works of Caicedo and Diaz (2009); Größler, Bivona, Fuzhuang, and Größler (2015); Mardin and Arai (2011) are some examples of fleet and asset replacement problems that are addressed with simulation models. In contrast to optimization-based approaches, stochastic elements in the fleet management can be treated properly in the simulation models, and interrelations between different aspects of the fleet management can be captured by simulation models as studied by Ahram, Karwowski, Sala-Diakanda, and Jiang (2017); Elsawah, Ryan, Gordon, and Harris (2018). The stand-alone use of the simulation models allows decision makers to examine the performance of a strategy over the planning horizon by setting up ‘what-if’ questions. Nevertheless, none of these simulation models finds an optimal strategy(ies). In this context, we contribute to the fleet management literature by integrating a meta-heuristic optimization algorithm so that optimal strategies are suggested to decision makers at the end of simulation experiments. 3. Problem definition and mathematical model In this section, we define the fleet renewal problem and develop a mathematical model. We consider an organization that needs to replace the existing fleet by acquiring new vessels to operate over a future time horizon. The problem is to find the number of vessels of each type to maintain in each time period so that a maximal operational availability is achieved. The size and composition of a fleet must be carefully chosen by considering both the organization’s future operational needs and the future uncertainties associated with the capacity of resources that organization has (Loxton et al., 2012). If the fleet is too small, then existing vessels have to be over-utilized, leading to increased pressure on the fleet, and therefore causing the risk of failure and high maintenance costs. On the other hand, if the fleet is too large, then some vessels may be under-utilized for a long period. Further, a large fleet requires more resources (e.g., maintenance), which brings additional challenges for the decision maker. These trade-offs require joint optimize both the retirement and acquisition dates of old and new vessels-that is, finding a fleet-transition schedule that maximizes availability by taking into account resource uncertainty.

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H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

In our model, we consider two fleets, namely an old fleet that contains only old type vessels (OLD) and the new fleet that consists of only new type vessels (NEW). We assume these vessels have different characteristics such as maximum operational durations without needing any maintenance, and resource requirements (see Section 5 for the details). We try to find the retirement date for each vessel i type of OLD, tiOLD (∀i ∈ I ), and a commissioning date for each vessel j type of NEW, t NEW (∀ j ∈ J ), where I and j J denote the index sets of OLD and NEW, respectively. We also assume that decision maker has a priori knowledge of the number of acquisitions (i.e., new fleet size |J|) that will take place during the planning period. We also try to find the home-base locations (region) RNEW (∀ j ∈ J ) and ROLD (∀i ∈ I ) for each vessel in the fleet. j i We assume that the length of the planning period is T. It is usually required to complete acquisitions of the new type of vessels in a limited time frame to prevent the new technology becoming obsolete, and to avoid increased maintenance needs due to the aging of the old vessels. The duration of this transition period is denoted as L, where L ≤ T. The availability of a resource (such as the facilities to perform maintenance and crew to operate the vessels) m at time t is modeled with a random variable rm,t that has a probability distribution function p(rm,t ) where M is the set of all stochastic resources m ∈ M and t ∈ [0, T]. When a vessel is performing one of the tasks during the planning period, we call it vessel k is operational at time t under resource availability rm,t and denote with an indicator variable Ok (t|rm,t ) as follows:



1,

Ok (t |rm,t ) =

0,

if vessel k (∀k ∈ I ∪ J ) is operational at time t (t ∈ [0, T ] ) otherwise

We say that the vessel is in the active status if it is not retired yet. We define an indicator variable Nk (t|rm,t ) denoting the activity status of vessel k at time t under resource availability rm,t as follows:



1, if vessel k (∀k ∈ I ∪ J ) is active at time t (t ∈ [0, T ] ) 0, otherwise

Nk (t |rm,t ) =

which implies that Ni (t |rm,t ) = 1 ⇔ tiOLD > t (∀i ∈ I ) and N j (t |rm,t ) = 1 ⇔ t NEW < t ( ∀ j ∈ J ). j Fig. 2 shows a realization of a fleet-transition schedule S and activities included in the life-cycle of vessels. In this illustration,

the old and the new fleet contain two |I| = 2 and three |J| = 3 vessels, respectively. The fleet-transition starts with the commissioning of the first NEW type of vessel at time t1NEW = 5, and ends at the year six. Further, the highest number of the operational vessel is four, which is achieved between years six and seven. We propose two objective functions that decision maker may choose one of them to optimize. The first objective function is to find a feasible fleet-transition schedule, S that maximizes expected average fleet availability E[A(S )]. This objective function can be used when the decision maker has not exact knowledge on the future needs for the number of operational vessels at each time period t. We calculate the average fleet availability A (S|rm,t ) for the given resource availability as follows:

1 A(S|rm,t ) = T and

E[A(S )] =





T t=0

 





Ok (t |rm,t ) dt

(1)

k∈I∪J

A(S|rm,t ) p(rm,t )d

(2)

where  indicates probability space for rm,t . It is not always easy to evaluate the integral in Eq. (2). Hence, we approximate the expected value as follows:

 R 11 E[A(S )]  R T q=1



T t=0





Ok t |

q rm,t



dt

q

where rm,t denotes the sampled value from the distribution rm,t at qth replication and R is the size of the sample (replication number). Another objective function might be to find a feasible fleettransition schedule, S that minimizes expected capability gap E[GAP (S )]. This value is calculated as:

E[GAP (S )] =





T t=0



max{0, γt −



Ok (t |rm,t )} d dt

(4)

k∈I∪J

where γ t denotes the number of operational vessel required at time t during the planning horizon. This objective function is useful when the decision maker has the information about the number of operational vessel required in the future; i.e., the value of γ t ∀t ∈ [0, T]. The same approximation method in the Eq. (3) can be used to find a closed-form numerical value for the E[GAP (S )]. The mathematical model for the stochastic fleet renewal problem is presented between Eqs. (5)-(12). An arbitrary schedule S may not be feasible because it has to satisfy several constraints. The constraint Eq. (6) ensures that the OLD fleet is retired by time T. Similarly, the constraint Eq. (7) guarantees that all NEWs enter the service before the end of the planning period. The constraint Eq. (8) ensures that all acquisitions occur within the transition period L. Further, the constraint Eq. (9) guarantees that the initial acquisition cannot be earlier than tstart . The constraint set Eq. (10) is required to ensure all retirements and acquisitions dates are within the planning period. The home-base locations for fleets have to be one of the existing regions R, which is ensured by Eq. (11). Finally, the legitimacy of probability distributions regarding the availability of resources during the planning period is provided by Eq. (12).

maximize: E[A(S )] or minimize: E[GAP (S )] S

0

(3)

k∈I∪J

subject to: 

S



Ni (T |rm,T ) = 0

(5) (6)

i∈I

N j (T |rm,T ) = |J|

(7)

j∈J

Fig. 2. An illustrative fleet-transition and life-cycle diagram.

0 ≤ max t NEW − min t NEW ≤L j j j∈J

j∈J

(8)

H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

min t NEW ≥ tstart j

(9)

j∈J

∀i ∈ I, ∀ j ∈ J

0 ≤ tiOLD , t NEW ≤T j RNEW , ROLD ∈R j i 0 ≤ p(rm,t ) ≤ 1

∀i ∈ I, ∀ j ∈ J ∀m ∈ M, ∀t ∈ [0, T ]

(10) (11) (12)

4. Solution algorithm In this section, we first discuss details of the GA (i.e., optimization module) used for generating different feasible fleet renewal strategies in Section 4.1. In Section 4.2, we describe the properties of the developed SD and DES models (i.e., hybrid simulation module) run for evaluating fleet renewal strategies produced by optimization module. Fig. 3 shows the flow of the proposed optimization algorithm and its interaction with the simulation module. At each iteration, the GA generates a population of feasible candidate fleet-transition schedules S to find the best retirement and acquisition dates that maximize fleet performance (either, the expected number of available vessels or fleet capability). The simulation module is then invoked to evaluate the fleet performance achieved by each solution generated by GA. Previously generated and evaluated solutions are recorded into a solution database to prevent regenerating and reevaluation these schedules, which improves the runtime and the convergence of the algorithm.

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4.1. The optimization module: A GA GA is a widely implemented meta-heuristic algorithm that is usually used for solving difficult optimization problems (Owais & Osman, 2018). A GA combines elements of directed and stochastic search to explore and exploit the solution space to obtain good solutions; i.e, fleet-transition schedules S. It is an iterative meta-heuristic algorithm that tries to improve results; i.e., fleet availability, continuously. GAs have some unique features such as population-based search and flexibility to hybridize with other applications and heuristics (Mahdavi, Paydar, Solimanpur, & Heidarzade, 2009). Hence, we chose to couple the GA with our simulation model. For any GA implementation following components have to be defined: (i) the solution encoding scheme, (ii) the initial population generation, (iii) a function or model to evaluate the fitness of each member of the population, (iv) the selection mechanism, (v) the genetic operators used to produce the next generations, and (vi) algorithm input parameters; e.g., population size, number of iterations, genetic operator probabilities (Goldberg & Holland, 1988). In the following subsections, we discuss how the traditional GA components are implemented, improved and combined with a simulation model. 4.1.1. The encoding scheme and initial population generation GA is based on an analogy to the phenomenon of natural selection in biology (Goldberg & Holland, 1988). It is required to define a chromosome structure (an encoding scheme) to represent the solutions of the problem. Afterward an initial population

Fig. 3. Flow of the proposed simulation-optimization algorithm.

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Fig. 4. A solution encoding (a chromosome) for a fleet-transition schedule S.

of solutions is generated by using the defined chromosome structure. Each chromosome is made up of a sequence of genes from a certain alphabet. The alphabet can be a set of binary numbers, real numbers, integers, symbols, or matrices (Goldberg & Holland, 1988). In this paper, we use an array coding scheme that has two-parts and two-layers, as shown in Fig. 4, which represents a feasible fleet-transition schedule S. The upper-layer array contains two arrays that consist of |I| and |J| genes, respectively. The context of these genes forms the lowerlayer, which includes information about retirement or acquisition schedules of the asset. The sample solution encoding in Fig. 4 implies that the old fleet contains |I| OLD type assets indexed from 1 to |I|, and the new fleet contains |J| NEW type assets indexed from 1 to |J|. The figure also demonstrates that the retirement date of the first OLD is ”10/11/2020” and the retirement location is ”Region 3”. In the same manner, the commissioning date of the first NEW is ”10/05/2023” and the home base location is ”Region 1”. The home base location attribute is particularly important because this attribute determines where each asset can go for maintenance and licensing activities. After defining the solution representation, a set of initial solutions, a population, are generated. The number of solutions to be included in the population is called population size. The initial population is generated only once at the beginning for the first generation of the GA. For our problem, an individual solution chromosome can be generated randomly by assigning random dates to the first cells of the lower-layer, which corresponds to either retirement or acquisition dates. The retirement dates are drawn from a uniform distribution between 0 and end of the planning period T so that tiOLD ∈ [0, T ] is ensured ∀i ∈ I. Different from the retirement dates, we have to ensure the first acquisition date t1NEW meets transition start time constraint imposed. Therefore, we randomly generate the first acquisition date by sampling from interval [tstart , T]. After assigning the first acquisition date t1NEW ∈ [tstart , T ], the rest of the acquisition dates are assigned randomly with equal probability between t1NEW and t1NEW + L so that:

max t NEW − min ≤ L j j∈J

j∈J

is guaranteed. Similarly, the second cells of the lower-layer; i.e., retirement and acquisition locations, are assigned randomly with equal probability from the available set of regions. 4.1.2. The fitness evaluation and selection procedure A fitness module is used to evaluate and reproduce new fleettransition schedules, called offspring for the next generations. The fitness evaluation is used to measure the goodness of the candidate schedule S in the population with respect to the expected fleet availability. The fitness value of an individual schedule is evaluated by calling the simulation module which models the life-cycle of a fleet from asset acquisition to retirement for a given renewal schedule produced by the GA. The details of the fitness evaluation are provided in Section 4.2. In our implementation, we added a database functionality to prevent computational expensive sim-

ulation model calls to reevaluate already evaluated schedules as shown in Fig. 3. Next, some fleet-transition schedules in the population are selected, based on their fitness values; i.e., fleet availability. In general, schedules providing higher fleet availability (fitter individuals) are more likely to be selected in order to reproduce. That is, inferior solutions with low fitness values are replaced by more fit solutions (Mahdavi et al., 2009). We apply a tournament selection strategy due to the its capability of improving the diversity and convergence of GAs (Aladeemy, Tutun, & Khasawneh, 2017). In the tournament selection, several tournaments are played among a few individuals. The individuals are chosen at random from the population. The winner of each tournament is selected for the next generation. 4.1.3. The genetic operators: Crossover and mutation Genetic operators (e.g., crossover and mutation) are applied to the selected fleet-transition schedules to produce a new population at each generation. This procedure is repeated until a certain number of generations genmax is reached as shown in Fig. 3. Different from the traditional GA algorithm where only one type of crossover used, we use three different crossover schemes that are combinations of widely used single- and two-point crossover operators as depicted in Fig. 5. Fig. 5 a shows a single-point crossover applied on only OLD fleet retirement schedule. In this crossover scheme, two fleettransition schedules, called parents, are selected from the population. Then a number lold between 0 and |I| − 1 is chosen randomly with equal probability as the crossover point. Then, the genes form lold to |I| of both parents that are corresponding the fleet retirements are exchanged to build two new chromosomes (children). In the single-point acquisition crossover, a crossover point lnew is chosen randomly between |I| and |I| + |J| − 1, afterward the genes of both parents from lnew to |I| + |J| are swapped as shown in Fig. 5b. These two operators are intended to keep renewal schedules that have either fitter retirement or acquisition schedules, and perform a local search around the neighborhood of these schedules. Fig. 5c presents the two-point crossover scheme. Different from the previous schemes, the genes regarding both retirements and acquisitions between lold and lnew are exchanged between parents simultaneously. This operator is indented to keep diversity in the population. After crossover, we apply a mutation operation to the randomly selected solutions. Mutation operators can expand the search space and increase the diversity of the solutions to prevent convergence to a local minimum (Krishnasamy, Kulkarni, & Paramesran, 2014). Traditional GA algorithms usually utilize one type of mutation to perform a local search. However, in this study, we develop and try four different mutation operations. The two of mutation operators are designed to search for closer solutions. Among these operators, the first mutation operator picks a gene from the old fleet randomly (with equal probability of selection) and changes that vessel’s retirement date to an arbitrary date between the start and end dates of the planning period. The second mutation operator

H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

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Fig. 5. Visualization of different crossover operators.

arbitrarily chooses a gene from the new fleet and changes that vessel’s commissioning date to a random date between min t NEW and j j∈J

min t NEW + L. The third and the fourth operators are designed to j j∈J

enlarge the search space to prevent trapping in local optima. In the third operator, all of the retirement dates of old fleet reassigned such that





tiOLD ← Uniform min t NEW ,T j j∈J

∀i = 1 , . . . , |I |

This structure prevents very early retirement of the old fleeti.e., the retirement of all old fleet before commissioning of any new fleet asset-to eliminate inferior fleet-transition schedules with lower availability. The next mutation operator reschedules the acquisition dates of all new vessels. In this algorithm, a random date





t ∗ ∈ min tstart , min tiOLD , max tiOLD i∈I



i∈I

is chosen. Afterward, the new acquisition dates are generated as follows:

t NEW ← Uniform(t ∗ , t ∗ + L ) j

∀ j = 1, . . . , |J |

This structure prevents the very late acquisition of the new fleet; i.e., the acquisition of new fleet starts before decommissioning of all old fleet assets. Having the ability to generate close and distant solutions simultaneously provides a more extensive and balanced search on solution landscape. After applying crossover and mutation operations, newly produced solutions are checked and repaired if necessary as shown in Fig. 3. That is, if a schedule does not satisfy constraints in Section 3, it replaced by a random feasible solution. 4.1.4. Implementation details The population size and the number of generations are functions of the size of the problem on hand. The values of these parameters have to ensure convergence. On the other hand, evaluating the fitness of individuals; i.e., simulation calls, is expensive (see Section 5 for algorithm runtime). To balance the runtime and the convergence of GA, we set the population size as 200, and set

the number of generations (genmax ) to 50. We chose crossover and mutation probability as 0.7 and 0.4, respectively. During the reproduction of new schedules, one of three crossover operators is equally likely to be chosen. In the same manner, when a schedule is chosen to mutate, the probability of applying one of the four mutations operations is 0.25. Moreover, the tournament size for selection procedure is decided as 10. 4.2. Fitness evaluation: A hybrid simulation model The evaluation of fitness; i.e., the expected fleet availability E[A(S )] or expected capability gap E[GAP (S )], for a given fleettransition schedule S is not a trivial analytical process since naval vessels are considered complex, dynamic, and multi-level systems with over a decade lifetime. The performance of such systems relies on inter-related, nonlinear, and delayed feedback loops among many independent components, such as operational and maintenance systems, resources (e.g., personnel), and infrastructure systems (e.g., docks). Nonlinearity, time delay, and multi-causality (i.e., in which several individual and environmental factors may interact to cause a particular condition) coupled with uncertainty both in the inherit system and surrounding pose a challenge for decision makers (Sterman, 1994). It is essential to understand and to analyze these complexities, when planning for the long-term life-cycle of strategic assets (Turan, Elsawah, Moallemi, Ryan et al., 2018). Thus, we develop a hybrid simulation model by combining a systems dynamics (SD) and discrete event simulation (DES) to cope with these challenges and to simulate the dynamic behavior of naval vessel systems under uncertainty (Elsawah et al., 2018). This simulation model enables us to explore the effect of different acquisition and retirement plans-among other decisions-on the system’s performance through construction and simulation of feedback interactions, delays, and their reinforcing and balancing effects in vessel systems. Further, the stock-and-flow structure of the SD model perfectly aligns with the resource-based view of strategies (Warren, 2005), where stocks represent assets and resources at different stages in their life-cycle, and flows represent the processes which cause these resources to change their state. It also fits well with the idea of life-cycle analysis by taking a longer view of

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H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

Fig. 6. The hierarchical model design (Red box denotes the input from the optimization module and brown boxes denote inputs from the user).

Fig. 7. The hybrid simulation model for the fleet management at the aggregated level. Colors show the information exchange among modules.

the asset at different states, and considering possible delayed consequences (Onat, Kucukvar, Tatari, & Egilmez, 2016). Moreover, we take advantage of DES to model short-term tactical elements in the life-cycle of vessels such as maintenance policies. The simulation model has a hierarchical and object-oriented design (See Fig. 6), where the hierarchy is constructed by considering the processes or activities that the asset undertakes through its life-cycle. The high-level of the hierarchy corresponds to abstract concepts (i.e. asset life-cycle), and the low-level corresponds to the physical elements of the system (i.e. flow rates in the SD model). These flow rates are determined by the decision makers (or might be optimized). Activities consume input (resources and rules) to generate effects. Rules include both decision rules (i.e., the rule by which a resource is allocated to activities) as well as the physical or hard system constraints (e.g., stock cannot go below zero).

The hierarchical view of the asset is aligned with how designers of the naval vessel support system conceptualize the system. It is also aligned with SD as a top-down analysis approach which starts with a focus on those elements and behaviors that are most significant for strategy performance, and branches down to the factors and relationships that influence their change (Coyle, 1992). Fig. 7 provides an aggregate view of the simulation model structure. For example, for the maintenance sub-module, the vessel starts waiting in the queue (depending on availability of resources). Then, the required resources to perform maintenance are allocated by using dock capacity and workforce capacity modules and seized by the vessel as illustrated in Fig. 7. The vessel is sized for the duration of “expected lead time for maintenance” and released after the elapse of this duration. Afterward, vessel enters into licensing stage in its life-cycle, and the licensing sub-module simulates this

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Table 1 Description of the sub-modules in the simulation model. Sub-modules

Function

Main stocks

Input variables

Output variables

Service Entry Service Exit

Sets the vessels entry rate Calculates the number of vessels to exit service Calculates the number of vessels waiting to start licensing, and their resource requirements

Vessels in retirement

Asset Service Schedule Asset Service Schedule

Vessels entry rate Vessels in retirement

Vessels waiting to start licensing, Vessels in licensing

Vessel waiting to start licensing

Maintenance

Calculates the number of vessels waiting to start maintenance, and their resource requirements

Vessels waiting to start maintenance, Vessels in maintenance

Operations

Calculates the number of vessels in operations, and the achieved rate of effort (measured as the number of sea weeks) at class and vessel levels. Generates the workforce capacity across the three career stages (recruits, trainees, trained crew) Assigns resources to activities based on requirements and capacity.

Vessels waiting to start operations, Vessels in operations, total number of sea-weeks (per class, per vessel) Recruits, trainees, trained crew

Vessels exiting maintenance, expected duration for licensing, allocated crew, allocated docking capacity Vessels exiting maintenance, expected duration for maintenance, allocated workforce, allocated docking capacity Maintenance triggers, expected duration for maintenance

Vessels exiting operations, Capacity for Offshore trainees generating rate

Capacity of off-shore training

-

-

Capacity allocation rules

-

Licensing

Workforce (uniform) capacity Capacity allocation

stage in the figure. Table 1 describes the rest of the sub-modules in the simulation model. 5. Computational experiments In this section, several computational experiments are performed to investigate the performance of the developed simulatedbased algorithm and to derive useful managerial insights under different settings. Sensitivity and scenario discovery analysis are also conducted in Section 5.1 to study the effects of varying the parameters on the fleet availability, waiting times and utilization of important resources. We present a hypothetical case study that might be considered as a modernization attempt for a naval vessel fleet. In this context, eight problem instances are generated with different numbers of new fleet size |J| (6, 12 and 18 vessels), transition period length L (4, 8 and 10 years), transition start time tstart (early, late and random), and objective function type (maximization of number of vessel available and minimization of capability gap). The early transition start time indicates that the first acquisition has to occur within the first 10 years of the planning period; i.e., t min ∈ [0, 10]. j For the late transition start time, the acquisitions have to start after the completion of the first 10 years; i.e., tj > 10 ∀j ∈ J. And, random transition start time basically indicates that acquisition can happen anytime within the planning horizon; i.e., tj ∈ [0, T] ∀j ∈ J. Table 2 shows the definition of each case in the testbed. We assume the old fleet size |I| is six vessels and the planning period length T is 47 years (the equivalent of 2453 weeks). We replicate the simulation runs independently from each other for 30 times

Vessel waiting to start maintenance

for each fleet-transition schedule S produced by the optimization module. In the meantime, we use the same sequence of random numbers during the simulation of different schedules so that an unbiased comparison between different fleet-transition schedules are achieved. We run the simulation model with weekly time steps and calculate outputs (performance indicators) as weekly averages if otherwise indicated. The user input parameters required to set-up and run the simulation module (see Fig. 3) are populated with values given in Table 3. In our hypothetical cases, we assume there exist three regions and two fleets, and resources in these regions are docks (with different features to accommodate different maintenance types), manpower (required for maintenance activities), crew (uniform and non-uniform required to operate the vessel), and shore-based facility. There exist two types of resource in the simulation model: (i) deterministic resources (e.g., docks, manpower and uniform crew). That is, their capacities and availability do not depend on a probability distribution, and (ii) stochastic resources (e.g., nonuniform crew and shore-based facility) where availability of the resource is a function of a random variable. For example, when there is a request for a non-uniform crew, the request will be met with 0.9 probability. We use deterministic parameters to model the fleet properties such as required time to complete maintenance activities and the maximum amount of time that a vessel can stay on operational status. We use two methods to show and compare the validity of the proposed simulation-optimization approach. In the first method, we simplify the problem by ignoring resource uncertainties to

Table 2 The definition of testbed instances. Case ID

New fleet size

Transition length

Transition start time

Objective function type

1 2 3 4 5 6 7 8

12 12 12 12 6 18 12 12

10 years 10 years 10 years 10 years 10 years 10 years 4 years 8 years

Random Early Late Random Random Random Random Random

Max. availability Max. availability Max. availability Min. capability Max. availability Max. availability Max. availability Max. availability

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H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158 Table 3 The input parameter values for the simulation module. Fleet properties and resource requirements Operations

Maintenance type (duration week/Manpower required/trigger)

Fleet

Max. operations week

Operational crew requirement

intermediate maintenance

intermediate docking

Mid-cycle docking

Full-cycle docking

OLD NEW

60 52

60 60

8/50/24 6/40/26

26/100/24 20/80/26

52/200/24 45/160/26

104/400/24 90/320/26

Mid-cycle Docking

Full-cycle Docking

1 1 0 0

0 0 1 2

Deterministic resources and capacities

Resource

Region

Dock

Region 1 Region 2 Region 3

Resource

Region

Manpower

Region 1 Region 2 Region 3

Resource

Region

Crew

Region 1 Region 2 Region 3

Construction Year

Intermediate Maintenance

32 0 0 36

2 2 0 0

Capacity (# Docks) Intermediate Docking 1 1 0 0

Becomes Available at Year

Capacity (# Person)

36 0 4

200 250 400

Initial Crew Available

Initial # of Trainees

Minimum Crew Level

Separation Fraction (per week)

Recruitment Rate (per week)

Trainee to Trained Delay (week)

300 300 0

0 50 0

300 0 0

0 0.0002 0

0 2 1

12 0 0

Resource

Region

Shore-based Facility

Region 1 Region 2 Region 3

Stochastic resources and capacities Resource

Region

Non-Uniform Crew

Region 1 Region 2 Region 3

Probability of availability 0.9 0.9 0.9

find upper bounds. That is, we assume stochastic resources and capacities in Table 3 have probability of availability values equal to one. We solve the obtained deterministic model with the developed GA and use SD-DES as fitness evaluation function by setting the simulation replication number to one. The optimized objective function value of the first method is denoted as GA upper-bound. In the second method, we solve the same simplified model as in the first method. In this method, we use a simulated annealing (SA) algorithm -as a benchmark model- rather than the developed GA. SA algorithm is one of the most popular and robust meta-heuristic algorithms that enables the solution of many hard combinatorial optimization problems (Suman & Kumar, 2006). SA uses a stochastic search strategy to find an optimal solution. In particular, the algorithm starts with a randomly generated initial solution. At each iteration, SA generates a neighborhood solution of the current one. If the objective function (i.e., operational availability or capability gap) value of the new solution is better than the current one, SA chooses the neighborhood solution as a new solution. Otherwise, SA accepts the neighborhood solution with a small probability. In the SA algorithm, we use the same solution representation and the same initial solution generation technique as discussed in Section 4.1.1. As the cooling schedule, we adopt a dynamic temperature decrease function introduced by Atiqullah (2004). We set initial and final temperatures to 10,0 0 0 and 1, respectively. SA is equipped with two neighborhood solution generation functions that are similar to the first and second mutation operators explained in Section 4.1.3. Further, the same simulation model (SDDES) is used for the fitness evaluation as in the first method. The

Probability of availability 0.9 0.9 0.9

optimized objective function value of the second method is denoted as SA upper-bound. All algorithms are coded in Python programming language and the simulation model is developed in AnyLogic 8TM simulation software. We implement and run all problem instances on a standard desktop computer with 12 cores 2.70 GHz CPU. Fig. 8 indicates that simulation-optimization approach is on average 7% worse than the GA upper-bound regarding fleet availability when all cases are considered. On the other hand, it yields on average 32% higher fleet availability compared to the SA upper bound. Fig. 8 also presents how the population of solutions S evolves with respect to the objective of maximizing the expected number of operational vessels as functions of both runtime and generation number. We plot the best (i.e., the maximum expected operational availability) and worst fleet-transition schedules found in each generation, and we also record the average performance of all solutions in every generation for each case. We observe that the new fleet size |J| is the most important factor affecting the algorithm runtime. That is, on the average the runtime increase from 4.50 × 105 to 4.73 × 105 and from 4.73 × 105 to 5.73 × 105 cpu seconds when the new fleet size changes from six to 12 and from 12 to 16, respectively. The proposed algorithm generally converges to the optimized solutions in the earlier generations with the exception of case 8 in which the best solution is found in generation 32. When the operational availabilities obtained by different fleet size are compared, a doubled increase from six to 12 new vessel leads to 13.61% improvement in expected operational availability. Further, an additional six more vessels; i.e., increasing new fleet size from 12 to 18, results

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Fig. 8. Evolution of population’s characteristics to maximize the expected number of operational vessels for each test case.

in only a 11.59% rise in the availability. This intuitive result shows that increasing fleet size without dynamic adjustment of resource capacities produces a diminishing return in the operational fleet availability. We set γ t as four vessels ∀t ∈ [0, T] as capability threshold for all experiments. Fig. 9 presents how expected capability gap alters throughout the algorithm run for the chosen threshold value. Similar to the previous conclusions, the lowest expected capability gap value 106.73 is observed under the largest new fleet size of 18, which indicates on average there will be less than four vessels in 106.73 weeks out of the next 2453 weeks in the planning period. The amount of improvement in the capability gap is around 74% when the new fleet size increases from six to 18 vessels. After finding the optimized solutions for each case via simulation-optimization approach: we simulate each optimized fleet-transition schedule S for additional 200 replications, (i) to test the robustness (the objective function gap between the worse and best scenario performances) of each schedule, (ii) to investigate the effect of factors such as transition length (TL) and transition start time (TS) on performance for cases where the new fleet size (NFS) is equal (i.e., cases with 12 vessels), and (iii) to collect additional statistics in order to compare optimized schedules with respect to the secondary performance metrics such as resource utilizations and waiting times.

In this direction, Fig. 10a and 10b show the distributions of the expected operational availability and capability gap for each case, respectively. Firstly, all schedules obtained at the end of simulation-optimization procure are robust, even the worstperforming schedule (case 5) has only 6.7% gap in terms of the fleet availability, which proves the applicability of the proposed approach. Next, we infer that the larger fleets are more robust compared to small fleets (i.e., NFS value of six). Further, for the equal NFS, we observe that the late TS (case 3) provides inferior availability in contrast to early (case 2) and random TS (case 1, 4, 7 and 8). When TL values are compared, 10 years of TL reaches a higher average operational availability as in case 2, nevertheless, a decision maker with risk-averse behavior may choose the schedule obtained with 4 years of TL as in case 7 due to the tight gap achieved and robust behavior of the solution. In addition, Fig. 10b points out that schedule with 8 years TL (case 8) outperforms 10 years TL regarding capability gap, which has to be also taken account by the decision maker. Fig. 11 present the distributions of the collected output statistics regarding secondary performance indicators; e.g. utilization of docks, manpower and crew and waiting time for activities, for each optimized fleet-transition schedule during the additional 200 replications.

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Fig. 9. Evolution of population’s expected capability gap for each test case.

Fig. 11 also helps the decision maker to identify scare (or abundant) resources leading to the poor fleet performance. To illustrate, the system produces a sufficient number of uniform crew to operate vessels with the input values (e.g., recruitment rate and delay to train trainees) listed in Table 3. We observe less than 18% average crew utilization even in the largest fleet size (case 6). Moreover, the initial capacity planning strategy for docks proposed in Table 3 is also considered ample due to the average dock utilizations fluctuating between 30% and 38%. We notice an interesting insight regarding the shore-based facility. That is, none of the input factors (NFS, TL and TS) affect the average waiting time for this resource. Because availability of this resource at a particular time t only depends on a probability distribution as stated earlier. The decision maker may be interested in fleet performance at a particular time point t ∈ [0, T] or performance progress throughout the planning period [0, T] to figure out vulnerable time frames for fleet rather than an aggregate level analysis. In this context, Fig. 12 and Fig. 13 present the variation of the number of available vessel and the probability of satisfying capability threshold requirement as functions of time, respectively. Confidence interval (CI) plots for the number of operational vessels (at each time point t) are shown in Fig. 12 for each eight optimized schedules found from case 1 to case 8. The average number of operational vessels at time t (i.e., dark gray solid lines in the Figures) for given the fleet-transition schedule S is denoted as μS (t), and calculated by averaging the number of operational vessels at

time t obtained from 200 simulation replications. Then, the 95% CI ranges (i.e., gray shaded areas in the Figures) for schedules are found as follows:

95% CI at time t



=

σS (t ) σS (t ) , μS (t ) + ηR−1,(1−.95)/2 √ μS (t ) − ηR−1,(1−.95)/2 √ R



R

∀t ∈ [0, T ] where, σ S (t) is the standard deviation for the number of operational vessels at time t for schedule S calculated by R simulation replication, and ηR−1,.95 denotes the t-distribution value corresponding R − 1 degree of freedom. We observe a tight CI range at the beginning of the planning period (until around week 500) since the state (e.g., amount and availability) of the resources in the future is less predictable compared to the near future. Besides, for the small fleet size (case 5), the average number of vessels and the fluctuations in the CI settle down faster compared to other fleet-transition schedules due to the completion of fleet renewal process relatively earlier. Another interesting insight, we realize that both optimized flee-schedules for case 6 and 8 behave almost similar regarding staying the above of capability threshold value γ of four operational vessels. Thus, the decision maker may prefer acquiring six fewer vessels and complete the renewal process in 8 years rather than commissioning 18 vessels and completing the renewal in 10 years.

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Fig. 10. The distribution of performance metrics for each optimized fleet-transition schedule.

To complement of the previous analysis, we derive a probability approximation and its confidence range to measure the success probability of each fleet-transition schedule in terms of accomplishing the capability needs. First, we define an indicator variable Ir {S} as follows:

 I r {S } =

1, if Or (t |S ) ≥ γ 0, otherwise





σ pS (t )

= maximum 0, pS (t ) − ηR−1,(1−.95)/2 √ R

t = 1, . . . , T

r=1

(13)



 σ pS (t ) 

minimum 1, pS (t ) + ηR−1,(1−.95)/2 √ R

where Or (t|S) denotes the number of operational vessel at time t in the rth simulation replication when the fleet-transition schedule S is employed. Now, we can calculate the probability of satisfying capability requirements at time t with schedule S, PS (#operational at time t ≥ γ ), for the given capability threshold value γ by using the approximation in Eq. (13). R 1 I r {S } R

95% CI at time t



t = 0, . . . , T and r = 1, . . . , R

PS (#operational at time t ≥ γ ) 

And, 95% confidence interval for the approximated probability can be constructed as follows:

, t = 1, . . . , T

where, pS (t) is the short notation for PS (#operational at time t ≥ γ ), and σ pS (t ) is the standard deviation for the approximated probability values. Notice that, we truncate the interval in order to keep probability values between zero and one. Based on Fig. 13, we observe several sharp fluctuations in the chance of meeting capability needs during the first 500 weeks with the exceptions of case 6 and 8. Hence, the decision maker has to pay special attention to the fleet in the first 10 years of the planning period to prevent underutilization of vessels. This analysis also reveals that time frames that require special attention. For example, when a fleet renewal strategy with short transition length (case 7) is chosen, there is a high probability that capability

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Fig. 11. The secondary performance measure distributions for each optimized fleet schedule.

Fig. 12. The confidence interval (95%) progress for the number of operational vessels as a function of time.

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Fig. 13. The 95% confidence interval progress for the probability of meeting capability requirement.

Table 4 The uncertainty space used for scenario discovery analysis. Parameter

Uncertainty range

Sampling method

NEW fleet max. operations week OLD fleet max. operations week Separation fraction per week Recruitment rate per week Trainee to trained delay (week) Maintenance duration multiplier Dock capacity Manpower capacity multiplier

[44, 60] [54, 66] [0, 3 × 10−4 ] [0, 4] [0, 18] [0.5, 1.2] [-1, 2] [0.5, 1.5]

Uniform Uniform Uniform Uniform Uniform Uniform Uniform Uniform

Integer Integer Float Float Integer Float Integer Float

needs will not be satisfied around weeks from 1300 to 1500 (i.e., vulnerability period). When a large fleet size is employed (case 6), the vulnerability time frame shifts to earlier weeks between 800 and 900. 5.1. Sensitivity and scenario discovery analysis In the previous section, we assumed only two resources; i.e., non-uniform crew and shore-based facility, have stochastic behavior throughout the planning horizon and optimized fleet-transition schedules by ignoring the stochastic behavior of the other input parameters. However, in the real-life cases, all assets and resources are subject to uncertainty. Therefore, in this subsection, we perform an extensive sensitivity and scenario discovery analysis to examine the impact of uncertainties associated with several parameters as well as non-uniform crew and shore-based facility. Table 4 shows the parameters that we consider uncertain in this subsection together with their uncertainty ranges modeled as uniform probability distributions. To illustrate, NEW fleet maxi-

mum operations week can be any integer value between 44 and 60 weeks with equal probability. Maintenance duration and manpower capacity multiplier express the increase or decrease ratio compared to the initial settings in the Table 3. For example, when the maintenance duration multiplier takes the value of 0.5, all types of maintenance durations are reduced by 50% for both of the fleets. Lastly, negative values in the dock capacity uncertainty range imply a reduction in the planned dock capacity at all regions for all dock types. First, we sample 10 0 0 independent points from each parameter in Table 4. Afterward, we run each eight optimized schedule found in Section 5 with these sampled values. Thus, a total of 80 0 0 different simulation experiments are performed by the stand-alone use of the simulation module. Fig. 14 presents a set of parallel coordinate plots to summarize our findings and point out some interesting observations1 Fig. 14a shows the mapping between input space (input factors), realized values of uncertainties and output space (performance indicators) for all simulation experiments. In this plot (i) axes corresponding to input space are: new fleet size (NFS), transition period length (TL) and transition start time (TS), (ii) axes corresponding to the realization of uncertainties are: NEW fleet maximum operations week (NFO), OLD fleet maximum operation week (OFO), maintenance duration multiplier (EMD), manpower capacity multiplier (MR) and dock capacity (DC), (iii) axes corresponding to output space are: average maintenance waiting (AMW), average

1 This interactive plot is available online at https://plot.ly/∼hasan1/37.embed. We suggest that readers perform additional scenario discovery analysis to obtain further insight.

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Fig. 14. Scenario discovery analysis.

manpower waiting (AMPW), average waiting for a dock (ADW), average dock utilization (ADU), average manpower utilization (AMU), average crew utilization (ACU), total time in operations (TOT), average number of operational vessels (AA), average percentage of operational vessels (PA) and capability gap (GAP). The values on output space axes are calculated after each simulation run. We use a heat-map coloring scheme based on GAP values. From Fig. 14b to Fig. 14e, we perform some illustrative scenario discovery analysis. That is, the decision maker chooses one or more performance indicators and set them to desired values based on his/her preferences, and determines the input parameter values and the scenarios (realization of uncertainties) leading to desired performance. For example, when the decision maker is interested in input factors and scenarios leading to the highest operational availability as in Fig. 14b, it is essential to have a larger new fleet with 18 vessels and a slow renewal period of 10 years. While doing this, the decision maker should be aware of the fact that this fleet tran-

sition setting would require almost 50% faster maintenance operations (see the EMD axes) coupled with 10% more manpower. Further, NEW and OLD fleet vessels have to spent around 15% and 10% longer time at sea to achieve this performance, respectively (see NFO and OFO axes). Another interesting observation based on Fig. 14c, is that the highest PA is not achieved with a large fleet; instead, to keep six or 12 vessels in the fleet is enough to maintain high PA values. The decision maker may also be interested in some extreme scenarios that may happen in reality. In this direction, Fig. 14d reveals a scenario, in which a six vessel fleet performs as-well-as a fleet with 18 vessels without any investment on additional dock capacity. In another extreme setting, a large fleet with 18 vessels may perform poorly when NFO values drop down under 48 weeks as shown in Fig. 14e. Fig. 15 shows how the recruitment rate and the training delay of crew affect the PA values at each region as heat-map contour plots. We obtain a counter-intuitive result that low recruitment

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Fig. 15. The effect of recruitment and training delay on fleet availability.

Fig. 16. Effect of dock capacity decisions on fleet availability.

rates, together with long training delays do not necessarily lead to a poor fleet performance. The capacity decisions regarding docks are costly and have long-term effects on local environments. Thus, we perform a deeper investigation if the additional investment in dock capacity is required. Fig. 16 shows the averaged results of 80 0 0 simulation runs performed in this subsection with respect to expected operational number of vessels. We conclude that additional investment in dock capacity does not have a significant effect on the fleet availability independent of the fleet size. 6. Conclusions and future research directions The fleet renewal problem poses several challenges for decision makers due to its multi-dimensional and complex structure, including a vast amount of interacting variables that influence the fleet’s operational performance. This paper presents a solution approach which coupling a hybrid simulation model and an enhanced genetic algorithm to identify efficient fleet renewal strategies. The developed approach leverages the power of simulation modeling and an optimization algorithm. The simulation model acts as a macro-level strategy evaluation tool, and the optimization algorithm provides microlevel analysis by searching several different strategies without the need for a trial-error method in a lower runtime. Further, the developed approach is also capable of solving renewal problems that expand over several decades and contain resource uncertainties, which is not possible with traditional optimization algorithms. The extensive numerical experiments show that the proposed approach not only finds good and robust renewal strategies but

also points out resources causing vulnerability for the fleet. The main results and conclusions based on our numerical experiments include: (i) We observe several sharp fluctuations in the chance of meeting capability needs during the first 500 weeks. Hence, the decision maker has to pay special attention to the fleet in the first 10 years of the planning period to prevent underutilization of vessels. (ii) We conclude that the workforce planning system is sufficient in producing uniform crew to operate vessels. We also conclude that the initial capacity planning strategy for docks proposed is ample due to the low average dock utilization. (iii) The approach points out some extreme scenarios in which a small fleet performs as-good-as a much larger fleet without any resource investment. This study can be extended in many ways. As future research, the fleet properties (such as required time to complete maintenance activities and the maximum amount of time that a vessel can stay on operational status) might be modeled as random variables. This can be readily achieved by adding random parameters based on selected probability distributions to the simulation module. This would enable the decision maker to model and analyze more realistic cases such as resource and fleet failures leading to unplanned maintenance activities. Another interesting future research direction would be adding more details and granularity to simulation sub-modules such as workforce capacity module that simulates crew life-cycle as shown in Fig. 7. This module assumes there is only one type of workforce (crew) in the system. However, to operate a vessel usually requires different types of

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H.H. Turan, S. Elsawah and M.J. Ryan / Expert Systems With Applications 145 (2020) 113158

workforce (e.g., officers and sailors) with different expertise levels (e.g., ranks). Adding a workforce sub-module with a career structure for each type of workforce would be a valuable improvement in the model. From the methodological point of view, an integrating of machine learning techniques such as the reinforcement learning with simulation-optimization framework would be a novel methodological contribution to find optimized dynamic policies (regarding e.g., fleet renewal, workforce amount and maintenance decisions) rather than static policies that we studied in this manuscript. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.eswa.2019.113158. Credit authorship contribution statement Hasan Hüseyin Turan: Conceptualization, Methodology, Software, Formal analysis, Data curation, Writing - original draft. Sondoss Elsawah: Software, Data curation, Validation, Writing review & editing. Michael J. Ryan: Resources, Writing - review & editing, Project administration. References Adamides, E., Stamboulis, Y., & Varelis, A. (2004). Model-based assessment of military aircraft engine maintenance systems. Journal of the Operational Research Society, 55(9), 957–967. Ahram, T. Z., Karwowski, W., Sala-Diakanda, S., & Jiang, H. (2017). Modeling decision flow dynamics for the reliable assessment of human performance, crew size and total ownership cost. In Advances in applied digital human modeling and simulation (pp. 117–129). Springer. Aladeemy, M., Tutun, S., & Khasawneh, M. T. (2017). A new hybrid approach for feature selection and support vector machine model selection based on self-adaptive cohort intelligence. Expert Systems with Applications, 88, 118–131. Atiqullah, M. M. (2004). An efficient simple cooling schedule for simulated annealing. In A. Laganá, M. L. Gavrilova, V. Kumar, Y. Mun, C. J. K. Tan, & O. Gervasi (Eds.), Computational science and its applications – iccsa 2004 (pp. 396–404). Berlin, Heidelberg: Springer Berlin Heidelberg. Bivona, E., & Montemaggiore, G. B. (2010). Understanding short-and long-term implications of ”myopic” fleet maintenance policies: A system dynamics application to a city bus company. System dynamics review, 26(3), 195–215. Bräysy, O., Porkka, P. P., Dullaert, W., Repoussis, P. P., & Tarantilis, C. D. (2009). A well-scalable metaheuristic for the fleet size and mix vehicle routing problem with time windows. Expert Systems with Applications, 36(4), 8460–8475. Caicedo, S., & Diaz, F. (2009). Too early, too quickly: Impact of short-term decisions in fleet renewal programs. Too Quickly: Impact of Short-Term Decisions in Fleet Renewal Programs (July 30, 2009). Coyle, R., & Gardiner, P. A. (1991). A system dynamics model of submarine operations and maintenance schedules. Journal of the Operational Research Society, 42(6), 453–462. Coyle, R. G. (1992). A system dynamics model of aircraft carrier survivability. System Dynamics Review, 8(3), 193–212. Du, J. Y., Brunner, J. O., & Kolisch, R. (2016). Obtaining the optimal fleet mix: A case study about towing tractors at airports. Omega, 64, 102–114. Elsawah, S., Ryan, M. J., Gordon, L., & Harris, R. (2018). Model-based assessment of the submarine support system. In Incose international symposium: 28 (pp. 392–406). Wiley Online Library.

Fagerholt, K., Christiansen, M., Hvattum, L. M., Johnsen, T. A., & Vabø, T. J. (2010). A decision support methodology for strategic planning in maritime transportation. Omega, 38(6), 465–474. Fagerholt, K., & Lindstad, H. (20 0 0). Optimal policies for maintaining a supply service in the norwegian sea. Omega, 28(3), 269–275. Gavranis, A., & Kozanidis, G. (2015). An exact solution algorithm for maximizing the fleet availability of a unit of aircraft subject to flight and maintenance requirements. European Journal of Operational Research, 242(2), 631–643. Goldberg, D. E., & Holland, J. H. (1988). Genetic algorithms and machine learning. Machine learning, 3(2), 95–99. Größler, A., Bivona, E., Fuzhuang, L., & Größler, A. (2015). Evaluation of asset replacement strategies considering economic cycles: Lessons from the machinery rental business. International Journal of Modelling in Operations Management, 5(1), 52–71. Jiang, J., Ng, K. M., Poh, K. L., & Teo, K. M. (2014). Vehicle routing problem with a heterogeneous fleet and time windows. Expert Systems with Applications, 41(8), 3748–3760. Krishnasamy, G., Kulkarni, A. J., & Paramesran, R. (2014). A hybrid approach for data clustering based on modified cohort intelligence and k-means. Expert Systems with Applications, 41(13), 6009–6016. Kunc, M. H., & Morecroft, J. D. (2009). Resource-based strategies and problem structuring: using resource maps to manage resource systems. Journal of the Operational Research Society, 60(2), 191–199. Li, X., Leung, S. C., & Tian, P. (2012). A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Systems with Applications, 39(1), 365–374. Lin, R.-C., Sir, M. Y., & Pasupathy, K. S. (2013). Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services. Omega, 41(5), 881–892. Loxton, R., Lin, Q., & Teo, K. L. (2012). A stochastic fleet composition problem. Computers & Operations Research, 39(12), 3177–3184. Mahdavi, I., Paydar, M. M., Solimanpur, M., & Heidarzade, A. (2009). Genetic algorithm approach for solving a cell formation problem in cellular manufacturing. Expert Systems with Applications, 36(3), 6598–6604. Mardin, F., & Arai, T. (2011). A system dynamics model for replacement and overhaul policies on capital asset subject to technological change. The 29th international conference of the system dynamics society. Mathew, T. V., Khasnabis, S., & Mishra, S. (2010). Optimal resource allocation among transit agencies for fleet management. Transportation Research Part A: Policy and Practice, 44(6), 418–432. McLucas, A., Lyell, D., & Rose, B. (2006). Defence capability management: Introduction into service of multi-role helicopters. 24th international conference of the systems dynamic society. Monnerat, F., Dias, J., & Alves, M. J. (2019). Fleet management: A vehicle and driver assignment model. European Journal of Operational Research, 278(1), 64–75. Onat, N. C., Kucukvar, M., Tatari, O., & Egilmez, G. (2016). Integration of system dynamics approach toward deepening and broadening the life cycle sustainability assessment framework: a case for electric vehicles. The International Journal of Life Cycle Assessment, 21(7), 1009–1034. Owais, M., & Osman, M. K. (2018). Complete hierarchical multi-objective genetic algorithm for transit network design problem. Expert Systems with Applications, 114, 143–154. Simeonova, L., Wassan, N., Salhi, S., & Nagy, G. (2018). The heterogeneous fleet vehicle routing problem with light loads and overtime: Formulation and population variable neighbourhood search with adaptive memory. Expert Systems with Applications, 114, 183–195. Sterman, J. D. (1994). Learning in and about complex systems. System Dynamics Review, 10(2–3), 291–330. Suman, B., & Kumar, P. (2006). A survey of simulated annealing as a tool for single and multiobjective optimization. Journal of the Operational Research Society, 57(10), 1143–1160. Turan, H. H., Elsawah, S., Moallemi, E. A., Ryan, M. J., et al. (2018). Optimizing acquisition strategies for high-value assets via simulation-based genetic algorithm. In Systems evaluation test and evaluation conference 2018: Unlocking the future through systems engineering: Sete 2018 (p. 301). Engineers Australia. Warren, K. (2005). Improving strategic management with the fundamental principles of system dynamics. System Dynamics Review: The Journal of the System Dynamics Society, 21(4), 329–350. Yuan, F.-C. (2009). Simulation–optimization mechanism for expansion strategy using real option theory. Expert Systems with Applications, 36(1), 829–837. Zheng, S., & Chen, S. (2018). Fleet replacement decisions under demand and fuel price uncertainties. Transportation Research Part D: Transport and Environment, 60, 153–173.