Modelling, simulation and optimisation of port system ...

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Int. J. Agile Systems and Management, Vol. 2, No. 1, 2007

Modelling, simulation and optimisation of port system management Keshav Dahal* School of Informatics, University of Bradford, Bradford, BD7 1DP, UK E-mail: [email protected] *Corresponding author

Stuart Galloway Institute of Energy and Environment, University of Strathclyde, 204 George Street, Glasgow, G1 1XW, UK E-mail: [email protected]

Ian Hopkins Rolls Royce plc., PO Box 31, Derby, DE24 8BJ, UK E-mail: [email protected] Abstract: The effective management of port systems forms a significant economic and operational challenge for the port operators. Essentially, these ports receive, store, process and dispatch a variety of bulk commodities. This paper details the modelling, simulation and optimisation of port operations such that an effective operational management is obtained. This has to be achieved through a reduction in financial costs and improving utilisation of the equipment. Through the explicit characterisation of port components, a tool was developed that permits the construction of port simulation models. A Genetic Algorithm-based approach has been integrated with the port system model to optimise the operation of the port. Two case studies based on real world port systems are discussed. It is demonstrated that through the action of the GA on the port system model, the design and operation of the port can be significantly improved. And more than this, the architecture developed demonstrates a flexible and powerful mechanism for combining a process simulation tool with an optimisation capability. Keywords: Genetic Algorithm; GA; modelling; optimisation; port systems; simulation. Reference to this paper should be made as follows: Dahal, K., Galloway, S. and Hopkins, I. (2007) ‘Modelling, simulation and optimisation of port system management’, Int. J. Agile Systems and Management, Vol. 2, No. 1, pp.92–108.

Copyright © 2007 Inderscience Enterprises Ltd.

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Biographical notes: Keshav Dahal is a Senior Lecturer and a founding member of the Modelling, Optimisation, Scheduling and Intelligent Control (MOSAIC) Research Centre in the School of Informatics at the University of Bradford, UK. He also worked as a Research Fellow in the Institute for Energy and Environment at the University of Strathclyde in Glasgow, UK. He obtained his PhD and an MSc from the University of Strathclyde. His research interests lie in the areas of evolutionary algorithm, artificial intelligence, modelling, scheduling and optimisation. Stuart Galloway is a Rolls-Royce Senior Research Fellow in the Institute for Energy and Environment at the University of Strathclyde in Glasgow, UK. He obtained his PhD in Mathematics from the University of Edinburgh with research on the numerical modelling of Stefan problems. He has been working in the field of electrical power engineering for the last seven years and has been involved in a number of research projects funded by both industries, EPSRC and the EU. His research interests include electricity markets, intelligent scheduling, power system optimisation and simulation. He has published over 30 refereed journal and conference papers. Ian Hopkins is a Team Leader for Methods at Rolls-Royce Control Systems, Derby, UK. He has over 10 years of experience as a Software Engineer and a Project Manager for RR Industrial Business (includes Materials Handling and Control Systems). His interests lie in control, software engineering, system analysis and modelling.

1

Introduction

Optimisation problems, such as resource allocation, job-shop scheduling, equipment utilisation, and process scheduling occur in a broad range of industries including chemical processing, batch processing, oil refinery and water treatment facilities. Solving these problems is important for the economic operation of facilities and has been studied in the literature. Example problems include inventory management of a refinery (Lee et al., 1996), scheduling of multiproduct plants consisting of a sequence of stages (Pinto and Grossman, 1994), optimisation of crude oil supply to a refinery (Shah, 1996), operational optimisation in shipping yard (Lai, Lam and Chan, 1995) and scheduling of pumping pipelines (Sasikumar et al., 1997). For many real world resource management problems, the material flow process yields to the application of many traditional solution techniques (Pinto and Grossman, 1994; Lee et al., 1996; Shah, 1996). Other such applications have seen the use of considered heuristic methods in an attempt to tackle domain specific constraints (Lai, Lam and Chan, 1995; Sasikumar et al., 1997; Jozefowska et al., 2002). Significantly, the dynamics of the system are ignored and as such some of the operational subtleties are lost. Other authors have described similar stochastic and unpredictable problems through the use of simulation. A real-time interactive simulation model of bulk shipping terminals was constructed in Weiss, Thomet and Mostoufi (1999). Some of the characteristic features associated with simulation model development were described in Geuder (1995) and Debuse, Rayward-Smith and Smith (1999). Furthermore, several authors have coupled simulation models with optimisation components in an attempt to improve solution quality (Debuse, Rayward-Smith and Smith, 1999; Hart et al., 1998).

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In recent years, the Genetic Algorithm (GA) has become an increasingly popular and successful approach to the optimising complex real world problems (Glover and Kochenberger, 2003). The GA is an iterative search procedure which is adaptive and is based on the genetic processes of biological organisms. By attempting to emulate these processes, GAs can ‘evolve’ solutions to suitably encode theoretical and real world problems. GAs have been used for optimising simulation models (Paul and Chanev, 1997; Hart et al., 1998; Dahal et al., 2003). This paper extends this work by focusing on the development of a modelling, simulation and optimisation tool; and reports the use of operation heuristics rules within the GA optimisation process. It is intended to capture some of the operational features of port operation, whose omission would result in a less comprehensive model that is incapable of considering dynamic operational constraints. These have been successfully incorporated through the modelling of port components and systems within a discrete event simulation environment. This characterisation attempts to emulate the operation of a bulk material port processing system through an explicit characterisation of the individual component of a port (e.g. berth and conveyor). The main drivers for this work from software prospective are the development of representative structures that are reusable, robust and flexible such that further functionality may be included as required. The optimisation capability coupled to the simulation tool was provided through the use of a GA and heuristics for port operation. This paper discusses the effective management of bulk material port processing systems and details the approach taken for the development of a tool for modelling, simulation and optimisation of port system operations. The design and accommodation of an integrated optimisation component represents one of the main aspects of this work. The use of the model is highlighted and established as an effective means of supporting the design and development of new and existing port facilities. A description of a GA developed for operation with a simulation model is given and the resulting port facility optimisation shown with the results from the two realistic case studies.

2

Modelling, simulation and optimisation

2.1 Outline of port systems An overview of the bulk handling port facilities with the relationships among their components is shown in Figure 1. During port operation, various materials, such as coal, coke, iron ore or iron pellets are imported (supplied) to or exported (demanded) from the bulk facility. Following the arrival of a vessel carrying materials (supply), it is placed on a queue until an appropriate berth and units for the berth become available. Unloaders (running on track) are used to unload material from the vessel. The unloaders transfer the material to an importing conveyor system. A transfer station connects different conveyer systems to provide different routes. The material is either collected from a conveyor by a stacker and stored in a stockpile or fed to a direct demand through buffers. Likewise, materials not supplying a direct demand are taken away by the exporting vessels (demand). Following the arrival of an exporting vessel at the port system, it similarly joins a queue until an appropriate berth and units for the berth become available. Ship loaders are used to load material to the vessels. These components take material from an exporting conveyor which in turn obtains the material from a stockpile through a reclaimer. The control room manages the overall operation of the system.

Modelling, simulation and optimisation of port system management Figure 1

Overview of bulk handling port facility and allowed relationship among the port components

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Essentially, a port system receives, stores, processes and dispatches materials using port components, such as unloader, loader, conveyor, transfer station, stacker, reclaimer, etc. Ports act as buffers between the incoming and outgoing vessel traffics. The arrival and departure of vessels from a port define the physical inputs and outputs of the facility, while material may be fed to further facilities like steelworks. Typical requirements associated with port management and operations are to obtain efficient utilisation of equipment and systems, and maintenance and operating costs. For example, if vessels have a waiting time longer than a defined unloading or loading time, the facility owner must pay demurrage costs to the vessel operators. However, often this is challenging due to optimisation difficulties. Typically, these problems involve the need to consider a variety of different scenarios with respect to port operation and management. For example, by bringing in a few large vessels or many small vessels, the same amount of material may be entered into the port system. The question may be asked, what are the economic and operational impacts of these two scenarios? Do the existing berthing facilities have enough capacity to accommodate the larger vessels? Perhaps, small vessels can be unloaded in parallel, whereas larger vessels must be unloaded in series? Other scenarios may take account of plant failures or maintenance outages. The nature of the port facilities is such that no two ports will be operated or managed in the same way resulting in a unique set of operational and economical conditions for each port. Regardless of this, uncertainty in arrival patterns presents scheduling and optimisation challenges on a regular basis.

2.2 Port system modelling The dynamics of port systems, uncertainty in the arrival pattern of the vessels coupled with the random failures of port components makes the mathematical modelling of such facilities difficult. Furthermore, there is a high interaction among port components in the port facility as generically depicted in Figure 1. Any mathematical models of a port facility have to take account of the numerous operational constraints and nuances of the port system itself. And consequently, the development time for a specific model can be significant. For this reason, port simulation software was developed which permits the construction of specific port models from generic component models. In order to provide a generic port modelling capability, a library of object models for bulk handling equipment and activities (see Figure 1) was produced as shown in Figure 2. The object models are designed for a limited number of contexts but with the flexibility to work in multiple port models. Each port object characterises both the healthy and failed behaviour of equipment of that type, the maintenance requirements for each associated component, and the influences of each of these aspects of object behaviour have on its possible neighbours. It is the generic characterisation of these aspects of behaviour and influence, together with the restrictions (context) placed upon the connectivity of these objects, which makes for a powerful and flexible modelling resource. A structured software methodology, waterfall like approach, was adopted for the development of the port system simulation and optimisation software, primarily because the access to domain experts on port systems was restricted. We used a systematic and sequential model development to provide transparency among development stages to allow any future expansion of its functionality (Pressman, 2001). The key requirements and data features for port models and systems were identified. In order to capture the necessary specialist domain knowledge associated with port system operation and

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practice, a structured approach was employed for the capture of this knowledge. This was supported through technical meetings with port system experts, port strategists, design engineers, and operation and maintenance engineers, and was based on the knowledge capture methodologies (Moyes et al., 1996). Importantly, this knowledge capture was not merely focused on particular port facilities, but was for an agreed set of contexts that were deemed sufficient to represent a reasonable number of facilities. Figure 2

Port model library and example port system model

Thus, the port object models were designed based on the information obtained to define the key functionality of the port system components and activities that characterise their corresponding generic models and details of the system data structure and exchange. The port simulation software was realised using an object-oriented discrete event simulation method (Geuder, 1995).

2.3 Port system simulation The port simulation software provides a generic tool for building and running simulation models for supporting the operations and design of new and existing port facilities as shown in Figure 2. The port simulation software facilitates the construction of a simulation model by dragging, dropping, networking and parameterising the port objects. The activities and operation of the constructed port model can then be simulated over a specified time frame. This then gives an indication of the performance of the actual, redeveloped or hypothetical port to which the model relates. Figure 2 shows an example of a port model as seen on the modelling palette of the port simulation software – this port is employed for the case study considered in Section 4. The simulation of the port system operation produces a diverse array of performancerelated results. These results fall into two categories, namely, performance measures and logged data. The performance measures include the utilisation and availability of equipment, monetary costs incurred, operational and maintenance data. The logged data forms a detailed record of all the operational details including arrival and departure information for vessels, loading and unloading details of the vessels, start and stop information for component maintenance/failures/operation, and periodic storage levels of

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stockpiles. Through these performance indices, various forms of assessment both economic and operational can be determined.

2.4 Port system optimisation The port simulation software as designed does not inherently provide any optimisation capability. Instead, it provides the facility for adequate design and operation of bulk material facilities through scenario playing. Therefore, in order to provide an optimisation capability to the port simulation software, an optimisation component (optimiser) has been developed separately and integrated with the port simulation software as shown in Figure 3. Figure 3

Integrated port simulation and optimisation software

Several deterministic mathematical methods and heuristic techniques are reported in the literature for modelling and solving scheduling problems (Lee et al., 1996; Shah, 1996; Dumitrescu and Stutzle, 2003). Often the mathematical modelling and solution techniques in these papers are based on classical methods, such as integer and linear programming, network flow, branch-and-bound and dynamic programming. However, these methods are generally unsuitable for non-linear objectives and constraints in their standard form. Heuristic methods can be adopted which have the potential to reduce the computational time significantly (Sasikumar et al., 1997), however, this often requires a significant operator input and may even fail to find feasible solutions (Dumitrescu and Stutzle, 2003). In order to overcome some of the limitations associated with classical or heuristic methods for optimisation metaheuristic approaches, such as GA, simulated annealing and tabu search have been introduced to solve optimisation problems relating to complex real world problems (Glover and Kochenberger, 2003). The port optimiser shown in Figure 3 consists of three modules: optimisation processing module, optimisation engine and result display. The optimisation processing module acts as an interface between port models and the optimisation engine. It collects details from the port simulation model and constructs an optimisation problem to solve. It also provides the user access to select and specify key aspects of the port model for

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optimisation. The optimisation processing module also processes and screens the port model parameters using port operation heuristic rules. The port model simulates the operation of the port system with the supplied parameters and returns performance measures to the optimisation processing module. The optimisation engine uses a GAbased optimisation technique as described in Section 3. The result displays the module dynamically and processes the results of the optimisation process for display to the user.

3

GA optimisation engine

3.1 Introduction GAs are techniques based on natural genetic and evolutionary mechanisms. GAs are iterative procedures which work with a population of candidate solutions. Candidate solutions are encoded using a suitable representation and an evaluation function is used to assign a quality (evaluation) value to every solution produced. First, GAs generate an initial population of candidate solutions randomly or by some other means. The population is then evolved by creating new solutions from those in the current population through the use of GA operators, such as selection, crossover and mutation. Selection is the operation by which individuals in the population pool are chosen for mating (to become parents) according to their fitness (evaluation) values. Consequently, population members that have a high evaluation value have a higher probability of being selected for breeding. Once the two parent strings have been selected for breeding, they are then subjected to ‘crossover’ by exchanging substrings among them. This is done with some chosen probability; otherwise, the parent strings remain unchanged. A single resulting ‘child’ string is then produced and is subsequently subjected to ‘mutation’, whereby the value at each position in the string is changed with some probability. The iterative algorithm is stopped when a defined stopping criteria is reached. GA-based approaches have been attempted to solve industrial optimisation problems, such as in agriculture (Hart et al., 1998), port facility (Dahal et al., 2003), steelworks (Paul and Chanev, 1997), and water treatment (Dahal et al., 2001). GAs capable of dealing with dynamic changes in the problem environment has been developed coupling with simulation models (Paul and Chanev, 1997; Hart et al., 1998; Dahal et al., 2003) and combining with heuristic (Dahal et al., 2001). This work also selects a GA approach as in Dahal et al. (2003) and combines port operational heuristic as in Dahal et al. (2001) to provide an improved optimisation capability to the port simulation tool. This GA-based optimisation engine readily accommodates the generic construction of the underlying problem.

3.2 Problem construction and encoding Once a port simulation model is constructed, the optimisation processing module, as shown in Figure 3, collects all controlling factors, physical variables and decision variables in the port system considered and presents for user selection. The controlling factors of the port facilities may be the sequence and route in which the materials are to be moved, selection of the component modes of operation and throughput levels of plant. Physical variables correspond with the sizing of port system components. Decision

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variables on the other hand account for choices or selections from lists of strategic alternatives for port operations that are characterised in the simulation process. For example, vessels arriving at the port may be queued according to different queuing strategies including first-in-first-out and order according to demurrage potential. During optimisation, selections are made from all available strategies to act as operating regimes for the port model. The physical and decision variables of the port system can be mapped to a set of integers to form a GA chromosome as D1, D2, D3, }, Dn. The gene in the chromosome (Di) relates to either a strategic decision variable of the problem (this type of variable is encoded using a symbolic representation) or corresponds to the physical variables for the port system components. Once the user defines problem (makes selection of variables), the chromosome retains a fixed length through out the duration of the optimisation. Through the direct use of the integer representation, the different ranges of the physical variables are encoded (and decoded using an inverse mapping). The range for each of the different variables is predefined by a suitable mapping from the physical variables of the problem.

3.3 Construction of evaluation function The goodness (evaluation value) of a trial solution is calculated by using an evaluation function, which is constructed using port system performance measures. Again, the optimisation processing module collects all the available performance measuring criteria from the port model being optimised, and presents for user selection. Most of the problem constraints, such as the arrival times of vessels and initial conditions of the facility are specified and subsequently managed by the port simulation model. Similarly, the operating rules of equipment and physical (hard) constraints of the port system are also embedded explicitly in the port simulation model. The upper and lower limits for equipment capacities are configurable during the specification of the optimisation problem. A number of less rigid constraints can also be selected and utilised explicitly in the optimisation problem through inclusion as penalty elements in the evaluation function. For example, the breakings of maximum and minimum stockpile levels are not embedded in the model; instead they are included as penalty factors. The selected performance measuring criteria and penalty factors make up the evaluation function. The effective range for each criterion is bounded by a minimum and maximum value. In this work, the range-dependence of competing criteria is scaled out of the problem. A normalisation and scaling scheme is introduced which eliminates the range-dependence and allows the solution to converge on an acceptable subset of solutions. The evaluation function is the weighted sum of the penalty values for each constraint violation and the normalised objective function itself. The evaluation function, Ev, is given by Ev =

§ Fi min · ¸+ Fi ¸¹

¦ Z ¨¨© i

i

¦Z j

j

§ F jmax ¨1  ¨ F j ©

· ¸ ¸ ¹

¦Z P

k k

(1)

k

where Fi min is the ith objective for minimisation; F jmax is the jth objective for ~ maximisation; Fi and F j are normalising values to scale their respective objectives in

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proportion to their extrema; Pk is the penalty value for breaking the kth constraint of the problem; and Zi, Zj and Zk are preference weightings. The structure of the normalisation functions are such that for the global optimisation of the evaluation function, Ev, conflicting objectives are treated equally with neither of the normalised terms being able to dominate the solution space. The normalising values Fi and F j are the estimated maximum values. One problem with this formulation is how an a priori estimate is obtained for the extrema Fi and F j . Given that a port model is flexible and subject to the dynamics of port operation, information from an initial problem is used to tailor the evaluation function to suit the particular search space. This is achieved in the first simulation by seeding an individual in the initial population of solutions with extreme (upper or lower) values of the variables for the given port. For example, in the case studies below, a solution that utilises the smallest sizing variables for a port operation gives the longest processing times for material movement. Hence, the highest demurrage cost) will be obtained which can be used for scaling for Equation (2) below.

3.4 GA operators, heuristics and filtering process After constructing an optimisation problem for the port model being considered, the optimisation processing module generates trial sets of controlling factors, physical and decision variables (candidate solutions) to inoculate the GA initial population pool. This is done using a number of heuristics depending upon the selected variables and performance measures, which include ‘use shortest route’, ‘unload as early as possible’, ‘supply demand uniformly’, ‘select stockpile with largest empty space’. The model then returns performance measures obtained from the simulation. An evaluation value is constructed from these performance measures for the trial solution. The optimisation processing module filters the trial solution and repairs it to remove any obvious violation of constraints using some operational rules extracted from the port model. For example, these repairs include making valid connections of different conveyors to provide a valid route for a material transfer. The repaired candidate solution is then passed to the port model for evaluation. The filtering process extracts port specific knowledge from the port model and assigns an approximate evaluation measure for obviously bad candidate solutions. It also blocks previously evaluated solutions from being simulated by the port model in order to improve the efficiency of the process. The GA performance is generally dependent upon the particular GA structure, operators and parameters used. A range of GA operators/parameters are provided for user selection, they include: steady state and generational population update approaches; roulette wheel, ranking, tournament selection and replacement; n-point crossover; random and repair mutation; population size, tournament size, selection bias, and crossover and mutation probabilities. The implemented stopping criterion for the solution process is twofold. Firstly, a maximum iteration number is specified above which the number of iterations will not exceed. Secondly, if no improvement in the solution quality is observed ones, a specified number of iterations the algorithm is stopped.

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Test results and discussion

The simulation and optimisation of two case studies, based on the operation of real-world port facilities, are presented and discussed in this section. The first case study is a simple scheme with a single and linear route. A detailed analysis of results is presented to demonstrate the capabilities of the integrated port simulation and optimisation tool. The second case study presents a more complicated port facility with multiple routes for material transfer and hence, many operational decisions to be made. Section 4.1 describes the optimisation problem considered in this paper before presenting the test results for two case studies in the subsequent sections.

4.1 Optimisation problem description Optimisation of port facilities can take many forms. A variety of optimisation and scheduling problems exist. In this paper, we are specifically interested in the optimisation of the operational design of bulk handling port facilities. Given the configuration of the facility as well as the vessel arrival patterns, the contents of ships and the plant capacity limitations, the problem becomes one of the best determining operational strategies and equipment sizes in order to minimise total facility operating costs, especially demurrage costs (charges for any delays of loading and unloading of vessels). This requires minimising delays to vessels, maximising utilisation of equipment, ensuring continuous and steady supply of materials as demanded by subsequent facilities. The solution must satisfy the physical and operating constraints of the facility. The key aspects (controlling factors) of the operations of port facilitates for optimisation include the vessel queuing strategy, selection of conveyer routes, unloading/loading capacities, up- and down-stream route capacities. We can include two performance measures in the evaluation of a trial solution to this problem. The first performance measure is related to the overall financial performance of the port facility and mainly includes the demurrage costs. The demurrage costs associated with the ith vessel are calculated using the following formula,

Div

­§ « t d  t a  D w » · c i i °¨ « i »  1¸¸ Di , 24 ®©¨ ¬« ¼» ¹ ° ¯0

if tid  tia t Diw

for i 1, 2,! , N v ,

(2)

otherwise

where ¬˜¼ is the floor function, Div is the demurrage cost (£) of the ith vessel, t ia is the arrival time of the ith vessel (hours), t id is the departure time of the ith vessel (hours), Nv is the number of vessels, Diw is the agreed loading/unloading time of the ith vessel (hours), and Dic is the demurrage rate of the ith vessel (£). The second performance measure to be included in the evaluation of a trial solution to this problem is maximisation of the utilisation of equipment which represents a need to reduce redundancy in existing systems and justify investments in new or upgraded equipment. The utilisation measure, Uj, incurred by the jth equipment can be calculated using

Modelling, simulation and optimisation of port system management Uj

1 T

Nt ( j )

¦ 't

j ,k

for j 1, 2,! N e

103 (3)

k 1

where the time T is the length of the complete simulation period; Nt(j) is the number of tasks in a complete simulation period for the jth equipment; 't j ,k is defined as the difference between the start and finish times of the kth task for the jth equipment, and Ne is the number of equipments. In summary, these two objective functions can be expressed as: Nv

Minimise

v i

¦D ,

(4)

i 1 Ne

Maximise

¦U . j

(5)

j 1

4.2 Case study 1 4.2.1 Port facility and optimisation The model representation of the first example port system as contained in the port simulation software tool is shown in Figure 2. The port system consists of supply and demand sides. The supply side consists of port, berth, track, two conveyors, a transfer station and stacker components. Two vessels bringing two different material types arrive at the port. First is a 40-kton vessel with a cargo of coal which arrives on the first day. This vessel has an arrival frequency of 7 r 2 days. Second is a 20-kton vessel with a cargo of coke which arrives on the second day. This vessel has an arrival frequency of 7 r 2 days. The 40-kton vessel has a demurrage window of 26 hours and a demurrage rate of £10,000/day. The 20-kton vessel has a demurrage window of 13 hours and a demurrage rate of £5,000/day. The two different material types carried by the vessels cannot be mixed and consequently, they must be stored in separate stockpiles. Both stockpiles have a maximum capacity of 100 ktons. The initial tonnage of the coal stockpile is 50 ktons and the coke stockpile has an initial tonnage of 30 ktons. Incoming material types can be transported across the supply side of the port at a maximum rate of 1,500 tons hour1. The demand side of the port consists of reclaimer, three conveyors, a transfer station, coal buffer and coke buffer port components. The outgoing materials are being used to feed two separate constant demands, one for each material type. The coal demand is in operation for 12 hours day1 drawing 500 tons hour1. The coke demand is in operation for 8 hours day1 also drawing 500 tons hour1. Equipment is put through a cleaning process prior to the changing over among different material types which takes an hour. Each of these port features are defined with appropriate attributes of the example port model. Furthermore, in order to include the impact of equipment failure, the conveyors, unloaders, stacker and reclaimer models are subjected to a random failure, which is characterised by equipment-specific mean time between failure and mean time to repair. The objectives for the optimisation problem are to minimise total operating costs and maximise the utilisation of equipment over a simulation period of ninety days such that the stockpile limits are not exceeded. The effect of varying the vessel queuing strategy,

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selection of conveyer routes, unloader capacities, up- and down-stream conveyor capacities, stacker capacity and stacker split rate are considered when attempting to meet these objectives. In the reported case study, the operation of equipment terms, the second component of Equation (4), was not selected for the objective function due to the difficulty in obtaining reliable values for the running cost functions for the port component. The evaluation function (1) for this case study uses the demurrage costs (2) and utilisation measure (5) as Fimin and F jmax , respectively. The weighted sum of the normalised values of these objective function and the penalty values for each constraint violation gives the evaluation measure of a trial solution. This optimisation problem is stochastic in nature and is characterised by the random arrival of vessels and the random failures of the equipments.

4.2.2 Port simulation A single simulation of the port model shown in Figure 4 over a 90-day horizon was performed. Table 1 contains the physical and decision parameters utilised for the port system model (labelled ‘Original’). Some of the performance indices resulting from the three-month simulation of the port model are presented in Table 2 (labelled ‘Original’). These results represent what might be considered a reasonable solution considered by a design engineer. During this simulation run, the stockpile limits were not exceeded. Although the average utilisation of equipment might seem rather low, it primarily reflects the fact that the vessels arrive at the port only two days in seven. Finally, the total demurrage costs incurred are due to the over-lapping of vessel presence at the port since sufficient time is provided by the demurrage windows for each vessel to be unloaded. One way to improve the results obtained from the port system model is to execute a number of different scenarios. This requires by redefining the required parameters in the model and repeating the simulation. However, often such a trial and error approach can result in an unfocused search through the possible alternatives and consequently, the solution that yields the best improvement is often missed. Through the use of the optimisation approach, a more focused and ‘unbiased’ method can be used to determine a ‘best’ solution for the port system.

4.2.3 Optimisation run The GA design which gives the best performance for solving this optimisation problem has been identified after a process of experimentation. The GA in this paper has been designed using the steady state population updating approach, ranking selection operator, two-point crossovers, random mutation operator and the elitist approach. On the basis of experimentation, the GA parameters employed in this application are: a mutation probability of 0.08, a crossover probability of 0.60 and a population size of 25. The maximum number of iterations was set equal to 1,000. Ten GA runs have performed with different initial populations. Part of these initial population pool have been generated using heuristics ‘unload as early as possible’, ‘select stockpile with largest empty space’, and randomly to provide diverse solutions.

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Modelling, simulation and optimisation of port system management Figure 4

Table 1

Model representation for case study 2

Port model parameters for original and ‘optimised’ located solution Decision parameter Queuing strategy

Original

FIFO

Optimised

FIFO

Table 2

Sizing parameters (capacity in tons hour1) Unloaders 1

2

Conveyors 1

2

3

4

5

750 750 3,000 3,000 1,500 1,500 1,000 1,000 750 1,750 1,750

750

750

750

Stacker Reclai Capacity Split rate mer 3,000

1,500

1,000

1,750

750

750

Performance measures of the original simulation and the optimised solution Number of vessels

Average utilisation (%)

Total demurrage cost

Stockpile average level (tons)

40 k

20 k

Original

13

13

34

£54,593

Coal 58,038

Iron ore 32,199

Optimised

13

13

33

£33,871

58,566

32,545

4.2.4 Comparison of results The port specification (the sizing and decision parameters) and performance measures identified by the GA run which gave in the best evaluation measure are included in Tables 1 and 2 (labelled ‘Optimised’). Table 2 shows the ‘Optimised’ solution has reduced the total demurrage costs by 38% at the expense of a 1% reduction in utilisation with respect to the ‘Original’ solution, while there is no significant change in the average

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stockpile levels for both the coal and coke stockpiles. Analysing these ‘Optimised’ port parameters and the ‘Original’ port specification in Table 1, a variety of improvements to the design can be seen. Firstly, the combined unloader capacities have been increased from 1,500 to 1,750 tons hour1. There was enough redundancy in the incoming conveyors in the original specification (3,000 tons hour1) to accommodate this rise. However, the ‘Optimised’ solution obtained through the optimisation process has considerably reduced the capacities of the incoming conveyors, although they are still able to accommodate the increased input. The stacker capacity has also been reduced considerably. On the demand side of the port model, there has also been a reduction in capacities. The demand side in the ‘Optimised’ solution has a route capacity of 750 tons hour1 which is able to meet the demand on each of the material types. By increasing the throughput of material on the supply side of the port (1,500– 1,750 tons hour1), a reduction in demurrage costs has been achieved. These costs are incurred through vessels waiting in the port model beyond their demurrage window. Hence, unloading the vessels more rapidly has less of an infringement on the window. The utilisation measure on the other hand could be increased by unloading vessels slowly. The resulting ‘Optimised’ solution to the optimisation problem has a compromise in both the demurrage costs and utilisation of equipment measures. Decreasing the route capacity of the demand side of the port model to 750 tons hour1 increases the utilisation for demand side equipment and consequently, the utilisation measure as a whole. The route capacity of the demand side of the port model has no direct influence on the demurrage costs of the system, however; the route must be enough at least to meet the material demand.

4.3 Case study 2 The model representation of the second case study considered is shown in Figure 4. Again this model was built using the port simulation software. The port facility processes and stores three types of materials. The two incoming berths can unload any of these materials. A network of three incoming conveyor systems, through a transfer station, provides a route for these materials from an incoming berth to an appropriate stockpile. The materials are also taken away by outgoing vessels through an appropriate route. The port also feeds a further facility with a constant demand. This port facility clearly presents a more complicated operational challenge than that seen in the first port scenario. Here, the arrival of vessels are more frequent, alternative berths are available for unloading vessels and an appropriate route for loading and unloading should be identified for transferring materials. A single simulation run of this facility was carried out with existing sizing and typical decision parameters for 28 days. The total operating costs and average utilisation of the port resources were £38,580 and 0.49, respectively. The optimisation process was set for maximum 1,000 iterations with the same GA parameters as in the previous case study. The best solution found by the optimisation tool over the ten runs had total operating costs and average utilisation of £24,479 and 0.62, respectively. The detailed results returned by the optimisation tool showed that this significant improvement was primarily a result of selecting effective routes for loading and unloading material in addition to using more appropriate equipment sizes and vessel queuing strategies. The best performing GA run found the best solution after 145 iterations. The use of port operational heuristics to generate the initial candidate solutions and the use of filtering

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mechanism improved the computation time by reducing the number of iterations (simulation runs) required for the optimisation process. This case study demonstrates that the port system simulation facility can give valuable insight into the operation of more complex port systems and can indicate scheme improvements where operational problems can be minimised.

5

Conclusions

A practical account of port management and operation problems have been discussed. A brief summary of the structured development process involved in producing port modelling, simulation and optimisation facility was provided. This software characterises the individual components of ports and their interaction so as to admit the generic construction of port models. A GA-based approach with port heuristics and operational rules has been integrated with the port simulation tool to optimise port model design and operation. The GA-based approach generates trial sets of parameters for the physical and decision variables which are employed by the port simulation model. A selection of the resulting performance indices are normalised to remove range-dependence and are employed to construct an evaluation value for each trial solution attempted. This GA and simulation model interaction results in an optimisation capability which can be applied generically to different problems, be they at different ports or relating to a port facing different uncertainties. Two case studies based on real world port systems have been presented and a significant improvement is demonstrated in the operational and economic performance as a result of the GA and simulation model interaction. The optimisation of this type, once initiated, requires repeated communication between the port model and the optimisation component. Consequently, the simulation model will need to be executed a number of times in order to assess the quality of different solutions for the GA. This is because each re-parameterised model’s quality or goodness requires assessment by way of the simulation. Clearly, this can result in lengthy computation times for the optimisation process where, typically, several months of port operations are assessed. However, this computation time is not considered problematic for the design and planning problems for which the simulation facility is suited.

References Dahal, K.P., Burt, G.M., McDonald, J.R. and Moyes, A. (2001) ‘A case study of scheduling storage tanks using a hybrid genetic algorithm’, IEEE Transactions on Evolutionary Computation, Vol. 5, pp.283–294. Dahal, K.P., Galloway, S.J., Burt, G.M., McDonald, J.R. and Hopkins, J.R. (2003) ‘A port system simulation facility with an optimisation capability’, Int. J. Computational Intelligence and Applications (IJCIA), Vol. 3, pp.395–410. Debuse, J.C.W., Rayward-Smith, V.J. and Smith, G.D. (1999) ‘Parameter optimization for a discrete event simulator’, Computers and Industrial Engineering, Vol. 37, pp.181–184. Dumitrescu, I. and Stutzle, T. (2003) ‘Combinations of local search and exact algorithms’, in G.R. Raidl et al. (Eds.). Applications of Evolutionary Computing: EvoWorkshops (Vol. 2611, pp.212–224), LNCS, Berlin, Germany: Springer Verlag.

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Geuder, D.F. (1995) ‘Object oriented modeling with simple++’, Paper presented in the Proceedings of the 1995 Winter Simulation Conference, pp.534–540. Glover, F. and Kochenberger, G. (Eds.) (2003) Handbook of Meta-Heuristics. Boston, MA: Kluwer. Hart, R.P.S., Larcombe, M.T., Sherlock, R.A. and Smith, L.A. (1998) ‘Optimisation techniques for a computer simulation of a pastoral dairy farm’, Computers Electronics in Agriculture, Vol. 19, pp.129–153. Jozefowska, J., Mika, M., Rozycki, R., Waligora, G. and Weglarz, J. (2002) ‘A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan’, Journal of Scheduling, Vol. 5, pp.487–499. Lai, K.K., Lam, K. and Chan, W.K. (1995) ‘Shipping container logistics and allocation’, Journal of operational research society, Vol. 46, pp.689–697. Lee, H., Pinto, J.M., Grossmann, I.E. and Park, S. (1996) ‘Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management’, Industrial & Engineering Chemistry Research, Vol. 35, pp.1630–1641. Moyes, A., Burt, G.M., McDonald, J.R., Capener, J.R., Dray, J.N. and Goodfellow, R. (1996) ‘Combining design and operational knowledge to enhance generator plant diagnostics’, IEE Proceedings Generation Transmission and Distribution, Vol. 143, pp.300–304. Paul, R.J. and Chanev, T.S. (1997) ‘Optimizing a complex discrete event simulation model using a genetic algorithm’, Neural Computing and Applications, Vol. 6, pp.229–237. Pinto, J.M. and Grossmann, I.E. (1994) ‘Optimal cyclic scheduling of multistage continuous multiproduct plants’, Computers and Chemical Engineering, Vol. 18, pp.797–816. Pressman, R.S. (2001) Software Engineering: A Practitioners Approach. New York, NY: McGrawHill. Sasikumar, M., et al. (1997) ‘PIPES: a heuristic search model for pipeline schedule generation’, Knowledge-Based Systems, Vol. 10, pp.169–175. Shah, N. (1996) ‘Mathematical programming techniques for crude oil scheduling’, Computers and Chemical Engineering, Vol. 20, pp.1227–1232. Weiss, M., Thomet, M. and Mostoufi, F. (1999) ‘Interactive simulation model for bulk shipping terminals’, Bulk Solids Handling, Vol. 19, pp.95–98.