A port system simulation facility with an ... - Semantic Scholar

A port system simulation facility with an optimisation capability Keshav P. Dahal1, Stuart J. Galloway2, Graeme M. Burt 2, Jim R. McDonald 2 and Ian Hopkins3 1

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School of Informatics, University of Bradford, Richmond Road, Bradford, BD7 1DP Institute for Energy and Environment, University of Strathclyde, 204 George Street, Glasgow, UK, G1 1XW. 3 Rolls-Royce plc, PO Box 31, Derby, UK, DE24 8BJ.

Abstract This paper details the optimisation of bulk material port handling systems through the use of a metaheuristic based approach. The effective management of port systems requires effective solutions for the design, operation and maintenance of these facilities. This has to be achieved through a reduction in financial costs, and an increase in the utilisation of equipment and other resources. The operation of a port system is complex and difficult to model mathematically. Consequently, through the explicit characterisation of port components, a port modelling tool was developed that permits the generic construction of port simulation models. An evolutionary approach based on a genetic algorithm was developed to provide an optimisation capability to the port simulation tool. Two case studies based on real world port systems are presented and the results are discussed. Through the action of the genetic algorithm on the port system model, the operation of the port can be significantly improved - this includes equipment replacement and operational scheduling. A significant improvement is demonstrated in both the operational and economic performance as a result of the GA/model interaction. Keywords: Descrete event simulation; evolutionary optimisation; genetic algorithm; bulk handling port system.

1. Introduction Bulk material handling port facilities receive, store, process and dispatch a variety of commodities or materials. The management of these port systems requires effective solutions for the design, operation and maintenance of these facilities. The authors undertook a research & development project on modelling and optimisation of port systems in conjunction with Rolls -Royce Materials Handling. A port modelling tool was developed that permits the generic construction of port simulation models. A generic optimisation engine based on an evolutionary optimisation approach, namely genetic algorithms (GA), was developed and integrated with the modelling tool. This paper details the research context and the approach taken for the development of this generic modelling and optimisation tool. The use of the tool is highlighted and established as an effective means of supporting the design and development of new and existing port facilities. The issues with integration of the modelling and optimisation capabilities are discussed along with the process implemented for constructing an optimisation problem for a port scenario. A description of the GA technique is given in the context of the port facility optimisation. The results from two case studies are presented and discussed.

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Corrsponding author: email: [email protected]; tel: +44 1274 23 4019; fax: +44 1274 23 3920.

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Unloader/Loader

jetty

Conveyor

Berth

Stockpile

Stacker/Reclaimer Transfer station

Conveyor Reclaimer

jetty Unloader/Loader

Conveyor Conveyor Buffer

Berth jetty

Feeder

Steelworks jetty

Fig. 1: Bulk handling port facility.

1.1. Commercial drivers The effective management of processing facilities, both economically and operationally, forms a significant problem for facility operators. A typical layout of a simplified bulk handling port facility is shown in Fig. 1. During port operation various materials, such as coal, iron ore, iron pellets, are imported to or exported from the bulk facility. Essentially, these materials are received, stored, processed and dispatched using port components such as unloader, loader, conveyor, transfer station, stacker, reclaimer etc. The ports act as buffers between the incoming and outgoing vessel traffic. The arrival and departure of vessels from a port are the physical inputs and outputs of the facility. The material may be fed to further facilities such as steelworks. In design and operational settings there are many problems faced by port designers and managers. Typically these problems involve the need to consider a variety of different scenarios with respect to port operation and management. The management prospective may be driven by the economics of a tendering requirement. The port operators and designers on the other hand are faced with the operational objectives of a port system as well as the economic drivers that come from management. Furthermore, the nature of 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. There is therefore, a need of a generic port system modelling capability for the port operators and designers such that different operational and design aspects of port systems can be analysed. Typical requirements associated with port management and operation are to obtain efficient utilisation of equipment and systems, and minimise maintenance and operating costs - the latter are often due to scheduling difficulties.

1.2. Research context The material flow process yields to the application of many traditional techniques for many real world resource management problems [9,13]. Other such applications have considered heuristic methods in an attempt to tackle domain specific constraints as in [8, 15]. A generic mathematical model of port system operation would be extremely complex and difficult to model. This is primarily because there is uncertainty with the dynamics of port operation, arrival patterns of vessels and random failures of port components. Any mathematical model of a port system would have to be able to take account of the numerous operational constraints and nuances of the port system itself. 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 [17]. The simulation model itself does not have any optimisation capability. Several authors have coupled simulation models with optimisation components in an attempt to improve solution quality [4, 6, 12]. Several deterministic mathematical methods and heuristic techniques are reported in the literature for optimisation of material flow problems [6] and [16]. Often the mathematical optimisation techniques in these papers are based on classical methods such as integer and linear programming, network flow, branch-and-bound, and dynamic programming. These methods however, are generally unsuitable for the non-linear objectives and constraints in their standard form.

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Heuristic methods can be adopted which reduce the computational time significantly [15]. This can however, often require significant operator input and may even fail to find feasible solutions [11]. In order to overcome some of the limitations associated with classical or heuristic methods for optimisation, metaheuristic techniques such as genetic algorithms (GAs), simulated annealing (SA), tabu search (TS), have been used very successfully to solve optimisation problems relating to operation and design of complex real world problems [4, 6, 12, 14]. In this work a generic port modelling tool for simulating the port system operation has been developed in order to minimise mathematical complexity. The generic nature of the port modelling tool requires an equally flexible approach to optimisation. A GA -based technique, the most widely used evolutionary approach, has been selected to provide optimisation capability to the simulation tool. Given that other metaheuristic methods operate by the principle of identifying solutions and assessing them through performance measures, the integration approach described herein can likewise be extended to these approaches. This paper will demonstrate that an evolutionary (a metaheuristic) approach coupled with a simulation model can provide an effective and flexible modelling and optimisation environment.

2. Software tool 2.1. Port modelling tool A generic port modelling tool was developed using the discrete event simulation modelling approach. In order to provide generic port modelling capability a library of models of bulk handling equipments and activities (library of port

Results display

Optimisation component

Optimisation engine (GA) Optimisation processing module

Port modelling tool

Port Model

Library of port components

Fig. 2: Framework of the integrated port simulation and optimisation tool.

objects) were produced, for example, models for berth, conveyor, control room etc (see Fig. 2). These component models are designed for a limited number of contexts but with the flexibility to work in multiple port models. The relevant operating rules and the physical constraints of these components are included in the models. This is achieved by capturing the specialist domain knowledge associated with port system operation and practice. A structured approach was employed in the capture of this knowledge based on [10]. In this way explicit characterisation of uncertainty in constructed port equipments and activities can be captured. Furthermore, port component models also allow the characterisation of both the healthy and faulty behaviour of equipment, as well as the maintenance requirements for each component. The software development was performed in three main phases; requirement gathering, design and imp lementation. In the requirement gathering stage, the key requirements and data features for port models and systems were identified. The functional, system test and design specifications were developed from the information thus

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obtained. Finally the softwa re was realised using a discrete event simulation package called Simple++ [7]. A significant review process was conducted at each of these three stages. The port simulator interface facilitates the construction of a simulation model by dragging, dropping, networking and parameterising defined port objects. A 'sanity check' function tests the layout of the network of objects against the limited set of legitimate contexts for each object. 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 it relates. In this way a greater understanding of the operation and management of such facilities can be obtained. The simulation of port system operation produces a diverse array of performance related results. Typically 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 operational details including arrival and departure information for vessels, loading and unloading details of vessels, start and stop information for component maintenance/failures/operation, and periodic storage levels of stockpiles. Through these performance indices various forms of assessment both economic and operational can be determined. As well as user-driven the resulting port model can be driven by an optimisation system to assess the impact of any design and operational decisions.

2.2. Optimisation component In order to solve optimisation problems of port systems an optimisation component was developed and integrated with the port modelling tool. The framework of the integrated port simulation and optimisation software is shown in Fig. 2. Through the use of simulation the related constraints and operational practices can be, in general, accommodated explicitly within this fra mework. This software yields to the construction of generic problem modelling of ports and consequently, any optimisation technique employed must have similar generic features. Furthermore, in practice these problems include many uncertainties and flexibilities, for example, material arrival pattern, failure of equipment and manpower availability. Although different metaheuristic approaches, such as GA, SA and TS, can be employed as an optimisation engine, a GA-based technique was selected for port optimisation. The applications of GA -based approaches are widely reported for different industrial problems [1,2,12,14] and it was considered that they could be readily utilised in a generic fashion for this problem. GAs are search and optimisation methods based on a model of evolutionary adaptation in nature [14]. Unlike traditional ‘hill-climbing’ methods involving iterative changes to a single solution, GAs work with a population of solutions, which is ‘evolved’ in a manner analogous to natural selection. Candidate solutions to an optimisation problem are represented by chromosomes, which usually encode the solution parameters as a numeric string. The ‘fitness’ of each solution is calculated using an evaluation function which measures its worth with respect to the objective and constraints of the optimisation problem. A new population is created by stochastic operators - typically ‘crossover’, which swaps parts of solution strings (chromosomes), and ‘mutation’, which changes random bits in the strings. Relatively ‘fit’ solutions survive, ‘unfit’ solutions tend to be discarded. Successive iterations yield fitter solutions, which approach the optimal solution to the problem. The principle of this application involves the GA optimisation engine generating a trial solution and the port model simulating the operation of the port system with the parameters of the trial solution. The model then returns performance measures, for example demurrage cost and utilisation figures, obtained from the simulation. An evaluation value is constructed from these performance measures for the trial solution. The optimisation processing module screens the trial solution and repairs it to remove any obvious violation of constraints using some operational rules extracted from the port model. These repairs, for example, 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 screening 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 optimisation of port system models, once initiated, requires repeated communication between the port model and the optimisation component. This is because each re -parameterised model’s quality or goodness requires assessment by way of the simulation. This clearly can result in lengthy computation times for the optimisation process where, typically, several months of port operations are assessed. This computation time is however not considered problematic for the design and planning problems for which the simulation facility is suited. The subsequent sections present the application of the port modelling and optimisation tool to solve a port system optimisation problem, and demonstrates that the GA and discrete event model based approach is appropriate for process industry problems.

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3. Port system optimisation 3.1. Optimisation problem description Optimisation of processing facilities can take many forms, for example, a variety of scheduling problems exist such as the scheduling of manpower or tasks. Similarly , the effective economic management is also required in operational side of facilities. This has to be achieved through the utilisation of equipment, effective staffing levels and other resources. In this paper we are specifically interested in the optimis ation of the design and scheduling of operations of bulk handling port facilities. This optimisation problem aims to find a sequence of operationally feasible daily activities for the plant and material-movement systems of these facilities such that the overall production targets are met. The controlling factors of the port facilities may be the sequence & route in which the materials are to be moved, selection of the component modes of operation and throughput levels of plant. Given the configuration of the facility as well as the vessel arrival patterns, the contents of vessels and the port component capacity limitations, the problem becomes one of determining the best operational strategies and equipment sizes in order to minimise total facility operating costs. This requires minimising delays to vessels, maximising utilisation of equipment, ensuring continuous and steady supply of materials demand to subsequent facilities. The solution must further satisfy the physical and operating constraints of the facility. This problem represents a complex constrained combinatorial optimisation problem.

3.2. Optimisation problem formulation As with many real-world problems the desired solutions often involve optimising more than one criterion, sometimes with conflicting objectives. Two objectives have been identified for the optimisation problem described above: minimise total operating cost of the facility and maximise utilisation of resources available. The total operating cost of the facility is constituted of two costing terms. The first costing term is related to the overall financial performance of the port facility and mainly includes the demurrage costs, i.e. charges for any delays of loading and unloading of vessels. The demurrage costs associated with the i-th vessel are calculated using the following formula,

  t d −t a − D w   i c d a w  i i +1 Di , if t i −t i ≥Di 24    0 otherwise

  Div =  

for i = 1,2 ,K , N v ,

where ⋅ is the floor function, Div is the demurrage cost (£) of the i-th vessel, t ia is the arrival time of the i-th vessel (hours), t id is the departure time of the i-th vessel (hours), N v is the number of vessels, Diw is the agreed loading/unloading time of the i-th vessel (hours), and Dic is the demurrage rate of the i-th vessel (£). Cost terms of the second type are associated with the operation of equipment and are a combination of start up costs, running costs and shut down costs. Formally, this can be represented by the following equation,

(

N e N t ( j)

on off ∑ ∑ S j + R j, k ∆t j,k +S j

j=1 k=1

),

where Ne is the number of equipments, Sjon and Sjoff are start up and shutdown costs (fixed) for the j-th equipment respectively. The function Nt (j) is the number of tasks in a complete simulation period for the j-th equipment. The function Rj,k is rate of the running costs for the j-th equipment tackling task k and ∆t j ,k is defined as the difference between the start and finish times of the k -th task for the j-th equipment. The second objective, maximisation of the utilisation of equipment represents a need to reduce redundancy in existing systems and justify investments in new or upgraded equipment. The utilisation measure, Uj , incurred by the j-th equipment can be calculated as given by 1 Nt ( j ) U j= ∑ ∆t j,k , for j=1,2,…N e , T k =1 where the time T is the length of the complete planning period. In summary these two objective functions can be expressed as:

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(

Nv

N e N t ( j)

i =1

j=1 k=1

)

off Minimise ∑ Div + ∑ ∑ Son , j + R j, k ∆t j,k +S j

Ne

Maximise ∑ U j . j =1

In addition, the optimisation problem has the following constraints: Arrival times of vessels, initial conditions of facility, demand of materials from facility, operating rules and physical constraints of individual equipment of the facility, and equipment capacity limitation.

4. GA implementation 4.1. Problem encoding The encoding of solutions using an appropriate representation is a crucial aspect of the implementation of a GA for solving an optimisation problem [14]. Two types of optimisation variables have been identified for the problem described in the previous section, namely, sizing and decision variables. Sizing variables correspond directly with the sizing of port system components, such as, the maximum capacity of a conveyor. Dec ision variables on the other hand account for choices or selections from lists of strategic alternatives adapted - port operations and 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.

α 1 α 2 ϕ1 ϕ2 ϕ3 ϕ4 ϕ5

β

γ

χ

λ 1 λ2

Fig. 3: Typical chromosome structure.

The sizing and decision variables of the port system can be mapped to a set of integers. Through the direct use of the integer representation the different ranges of the physical variables can be easily encoded (and decoded using an inverse transform) to a chromosome of fixed length. The integer representation is employed exclusively within the GA, while the port simulation model operates with the physical variables. Fig. 3 shows a typical chromosome which once the problem is defined, retains a constant length throughout the duration of the optimisation. The genes, (α1 , α2 ..) in the chromosome relate to strategic decision variables of the problem, such as, the different queuing strategies available, connection decision of conveyors for a route. The remaining genes correspond to the sizing variables for the port system components (for example, ϕ1… ϕ5 relate to 5 conveyor belts). The integer range for each of the different variables is predefined by a suitable mapping from the physical variables of the problem.

4.2. Evaluation function The evaluation value is calculated by using port system performance measures. The operating rules of equipment and the physical 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. Penalty functions are used to penalise solutions, which violate these specified constraints in proportion to the amount by which the constraints are violated. The optimisation problem described above represents a multiple objective problem with two conflicting criteria: minimise total operating cost and maximise component utilisation. An approach, such as multi-objective genetic algorithm (MOGA) with Pareto ranking [5], could be applied to solve this multi criterion problem. However, in order to pro vide a generic optimisation capability to solve a user defined port optimisation problem, a weighting coefficient approach has been employed to combine multiple objectives into a single function. A common difficulty encountered with this approach in many multiple objective problems is range-dependant dominance in the solution space [3, 5]. In multiple objective problems each of the different criteria that make up the objective function return values within a particular range. In this work the range dependence of competing objectives is scaled out of the problem. A normalisation and

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scaling scheme is introduced which eliminates the range dependence and allows the solution to converge on an acceptable subset of solutions. The evaluation function, Ev, which is to be minimised, is given by  Ne   Nv  Ev =ω 1Γ  ∑ Div +ω2Ψ  ∑ U j  +∑ω l Pl .  i =1   j =1  l where the functions Nv

 Nv

∑ Div

 Γ  ∑ Div  = i=1~ v  i=1  D

, and

Ne

∑U j  Ne  j=1 Ψ  ∑ U j  =1− ~ U  j=1  are appropriate normalisation functions for each of the terms in the objective function. The parameters ω1 , ω2 and ωl act as preference weightings in the evaluation function. Pl is the penalty value for violation of the l-th constraint. The two normalisation functions, Γ (.) and Ψ (.) , scale their respective arguments in proportion to their extremals, and map the ~ ~ resulting argument into an appropriate range. The denominators D v and U of the normalisation functions are the estimated maximum values of total cost and total utilisation respectively. These values are estimated after obtaining the first simulation results of the port model with minimum values of sizing parameters. Candidate solutions with low evaluation measures have high fitness values while solutions with high evaluation measures take low fitness values. In summary, the genetic algorithm generates trial sets of parameters for the sizing and decision variables which are checked and repaired before passing to the port model. These parameters are then employed by the port simulation model. A selection of the resulting performance indices are scaled to remove range-dependence and are employed to construct an evaluation value for each trial solution attempted. The evaluation function is the weighted sum of the penalty values for each constraint violation and the normalised objective function itself.

4.3. GA architecture The performance of a GA is generally dependent on the particular GA structure, operators and parameters used. The particular GA design which gives the best performance is typically identified after a process of experimentation. After a number of experiments and from the authors' previous experience with GAs applied to other problems, see [1, 2], the GA in this paper has been designed using the steady state population updating approach, ranking selection operator, two point crossover, random mutation operator and the elitist approach. An adaptive crossover and mutation operator can be employed to reduce the amount of experimentation required to find the favourable GA parameters [14]. However, in this application they were fixed on the basis of experimentation and previous experience. The GA generates the initial population pool of candidate solutions by sampling the search space at random. During each iteration step, a ranking selection operator is used to choose parent solutions from the current population. The ranking selection method picks two solutions from the population with probability based upon the measured goodness of the solutions. The selected solutions are then subjected to crossover with a defined crossover probability. A standard two-point crossover operator has been employed which exchanges sections between these two selected solutions with the defined crossover probability. One of the resulting solutions is then chosen to undergo mutation. A standard random mutation operator has been used to change the integer at each position in the solution within the allowed range with a defined mutation probability. The steady state genetic algorithm directly inserts a new solution into the population pool replacing a less fit individual, this being adopted here using a ranking replacement operator similar to the ranking selection operator. The elitist approach, which ensures that the best individual in the population pool is never replaced, has also been applied. The algorithm is terminated when a defined stopping criterion is reached. The stopping criteria chosen here is either a specified maximum iteration number has elapsed or no improvement in the solution quality detected after a specified number of iterations.

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5. Case studies In this section two case studies of port optimisation are presented both are based on the operation of real-world port facilities. 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. Both of these problems described here include only the water route of the facility, the modelling and optimisation framework, however, can incorporate road routes and rail routes.

Fig. 4: Model representation of port scenario 1 in port simulator.

5.1. Port system scenario 1 The schematic representation of this port model is shown in Fig. 4, and includes both supply and demand sides. This figure shows the actual model representation resulting from the use of the port simulator interface. The supply side consists of two unloaders (Unloader 1 and 2), two conveyors (Conveyer 1 and 2) and a stacker. Two types of vessels bringing two different material types arrive at the port model on a regular basis - with a degree of uncertainty. The first is a 40 kilo-ton vessel with a cargo of coal which has an arrival frequency of 7 days +/- 2 days, unloading time of 26 hours and a demurrage rate of £10,000/day. The second is a 20-kiloton vessel with a cargo of iron ore which has an arrival frequency of 7 days +/- 2 days, unloading time of 13 hours and a demurrage rate of £5000/day. The two different material types carried by the vessels cannot be mixed and consequently, they must be stored in separate stockpiles, each of which has a maximum capacity of 100 kilotons. The initial tonnage of the coal stockpile is 50 kilotons and the iron ore stockpile has an initial tonnage of 30 kilotons. Incoming material types can be transported across the supply side of the port model at a rate of 1500 tons/hour. The demand side of the port model consists of a reclaimer and three conveyors (Conveyer 3, 4, and 5). The outgoing materials are being used to feed two separate demands, one for each material type. The coal demand is in operation for 12 hours/day drawing 500 tons/hour, while the iron ore demand is in operation for 8 hours/day also drawing 500 tons/hour. Equipment is put through a cleaning process prior to changing over between different material types. This, together with all of the above features, have been implemented into the port model using the port simulator interface. 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 objective for the optimisation problem is to minimise total demurrage costs incurred and maximise the utilisation of equipment such that the stockpile limits are not exceeded. Start up, shut down and equipment running costs

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have not been included in the objective function for this particular application. The effect of varying the queuing strategy, unloader capacities, upstream and downstream conveyor capacities, stacker capacity and stacker split rate is considered when attempting to meet this objective. This optimisation problem is stochastic in nature, and is characterised by the random arrival of vessels and the random failures of the equipments. A 90 day (3 month) simulation period was considered appropriate for this problem. All these elements of the optimisation problem have been implemented and configured using the optimisation processing module interface. 5.1.1. Port model results A single simulation run of this port model was carried out with the sizing and decision parameters shown in the first row of Table 1, labelled as 'Original solution'. Some of the performance indices resulting from this three month simulation are presented in the corresponding row of Table 2. These results represent what might be considered a reasonable solution by a design engineer. During this simulation run the tonnage of the both stockpiles did not exceed their limits. Furthermore, although the average utilisation of equipment might seem rather low, it primarily reflects the Table 1: Port model sizing and decision parameters for original and “optimised” located solution Decision parameter Queuing

Sizing parameters (capacity in tons/hour) Unloaders

Strategy

1

Original solution

FIFO

750

Optimised solution

FIFO

2

Conveyors 1

2

3

Stacker 4

5

750 3000 3000 1500 1500 1000

1000 750 1750 1750 750 750

750

Reclaimer

capacity split rate 3000

1500

1000

1750

750

750

Table 2: Performance meas ures obtained from the original simulation and the optimised solution. Number of vessels

Average utilisation

40 kilo

20 kilo

Original solution

13

13

34%

Optimised solution

13

13

33%

Total demurrage cost Stockpile average level (tons) Coal

Iron ore

£54,593

58,038

32,199

£33,871

58,566

32,545

fact that vessels arrive at the port only two days in seven. Finally, the total demurrage costs incurred are due to the overlapping of vessel arrivals and failures of equipments, although an enough time is provided in the demurrage windows for each vessel to be unloaded. One way of identifying bottlenecks of the port system in order to improve the results obtained from the port system model is to execute a number of different scenarios. If the demurrage costs incurred are considered to be unacceptably high the overall throughput of the port model may be increased by raising the capacities of the unloaders. 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 genetic algorithm approach described in the previous section a more focused and “unbiased” method can be used to determine an “optimum” solution for the port system model 5.1.2. Optimisation results On the basis of experimentation and experience 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 120 and furthermore, the algorithm will be stopped if no improvement is observed in the solution quality for 75 iterations. The initial population (first 25 trial solutions) is generated randomly. This is reflected in the variability in the evaluation value evident for these 25 iterations shown in Fig. 5. This figure shows the scaled total demurrage costs

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incurred, the scaled utilisation of equipment and the scaled evaluation value for each trial solution attempted, plotted against the iteration number. The “optimised” solutions are located towards the end of the iterative process where there is an increase in utilisation and a decrease in demurrage costs. The improvement exhibited in the solution quality is a consequence of the genetic operators. The small peaks observed in the evaluation value are a consequence of the mutation operator of the genetic algorithm altering “gene” values in the corresponding trial solutions. The row labelled as 'Optimised solution' of Table 1 contains the sizing and decision parameters utilised in one of many solutions identified by the GA which result in the “best” evaluation measure. The 'Optimised solution' solution gave the performance indices presented in the row labelled as 'Optimised solution' of Table 2 with that for the preliminary simulation. Comparing the GA identified port parameters and the 'Original solution' presented in Table 1 a variety of improvements to the design can be identified. Firstly, the combined unloader capacities have been increased from 1500 tons/hour to 1750 tons/hour. There was enough redundancy in the incoming conveyors in the original specification (3000 tons/hour) 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 between the 'Optimised solution' and the 'Original solution'. The demand side now has a route capacity of 750 tons/hour which is able to meet the demand on each of the material types. 1.10 1.00 0.90 0.80 Scaled Utiliasation

Scaled Utilisation Scaled Total Demurrage Cost Scaled Total Demurrage Cost Evalauation Value Evaluation Value

Scaled Performance Indices

0.70 0.60 0.50 0.40 0.30 0.20 0.10

85

82

79

76

73

70

67

64

61

58

55

52

49

46

40

37

34

31

28

25

22

19

16

13

7

10

43

-0.10

4

1

0.00

Interation Number

Fig. 5: Plot of scaled utilisation, scaled total demurrage costs and the scaled evaluation value against iteration number. By increasing the throughput of material on the supply side of the port (1500 tons/hour to 1750 tons/hour) a reduction in demurrage costs will be observed. This is because these costs are incurred through vessels waiting in the port model beyond their unloading time. Hence by unloading the vessels more rapidly less of an infringement on the unloading time will be observed. The utilisation measure on the other hand could be increased by unloading vessels slowly using an unloader with a small capacity. Hence the resulting solution to the optimisation will be 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/hour 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 however, has no direct influence on the demurrage costs of the system, the route must be at least enough to meet the material demand. The results given by the 'Optimised solution' solution represent an improvement over results obtained for the 'Original solution' as shown in Table 2. The total demurrage costs have been reduced by 38 % at the expense of a 1% reduction in utilisation, while there is no significant change in the average stockpile levels for both the coal and iron ore stockpiles.

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5.2. Port scenario 2 The model representation of the second case study considered is shown in Fig. 6. Again this model was built using the port simulator interface. 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 unloadin g should be identified for transferring materials.

Fig. 6: Model representation for port scenario 2 in port simulator.

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 subsequently run for 170 iterations with the same GA parameters as in the previous case study. The best solution found by the optimisation tool returned total operating costs and average utilisation of £24,479 and 0.62 respectively. The detailed results returned by the simulation facility 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. 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.

6. Conclusions This paper presented the use of a GA-based metaheuristic approach integrated with a discrete event simulation model to solve design and operational problems in a bulk handling port facility. A generic port modelling tool was developed through an explicit characterisation of individual components of port facilities. The port modelling tool characterises the complex interaction of the port objects, and therefore a complex mathematical model need not be developed for optimisation purposes. Instead, the simulation model is used as part of the GA evaluation 'function'. The simulation model provides performance indices for the given scenario, which are combined to form an evaluation measure. Furthermore, the optimisation problem encoding is simpler than otherwise as a result of the explicit characterisation of many constraints and operational practices within the simulation model.

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Multiple objective fitness functions can cause problems within GAs because the separate objectives have unequal effective ranges. Within the optimisation problem formulation the separate objectives are treated in such a way as to eliminate the range dependence from the evaluation function. 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 were presented and a significant improvement is demonstrated in both cases in the operational and economic performance as a result of the GA and simulation model interaction. The GA as described has been shown to provide an effective means of optimising the design and operation of port system models.

7. Acknowledge ments The work was supported by the engineers and design staff at Rolls -Royce.

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