This chapter rst reviewed research on the FSP in ESTTs. ESTTs are industrial settings with a number of PDPs where goods are transported repeatedly between these points by a eet of vehicles. Each PDP is usually equipped with a machine to process goods. Next to each machine there can be a buer for transition of goods between vehicles and machines to decrease their waiting time. Examples of ESTTs are manufacturing shop oors, warehouses and container terminals. The FSP in ESTTs is a very important tactical problem that needs to be addressed carefully. Having too few vehicles is not e cient and may impair the performance of the system whereas using too many vehicles is very expensive and can increase the possibility of deadlocks and collisions in the system. In the literature, this problem was addressed using various techniques: calculus-based approaches, queuing theory, simulation, exact optimisation and meta-heuristics. In ESTTs there exist some sources of uncertainties that might have a signi cant impact on the optimal eet size such as changes in the travel time of vehicles due to any disruption such as breakdowns, deadlocks and collisions. The existing approaches, however, did not consider the uncertainty in the environment properly. This leaves an important gap in the current research. In addition, despite the supposed importance of buers on the performance of ESTTs, the impact of buers on the optimal eet size was hardly investigated. This thesis will attempt to bridge this gap by developing an EA combined with the Monte Carlo simulation to identify the optimal number of vehicles that is robust to the changes due to uncertainties. These eorts are presented in Chapters 3 and 4.
In addition, the simulation research in container terminals was reviewed in this chapter (Section 2.4).This chapter rst explained the existing simulation software and programming libraries used in the literature to develop simulation models. In addition,
it reviewed simulation software packages that were developed speci cally for container terminals. It then reviewed dierent simulation studies in container terminals on various applications. The applications of simulation in container terminals are mainly to identify the optimal settings and number of cranes/vehicles in the terminals and also evaluating the performance of container terminals with dierent scenarios and strategies. A table summarising the major simulation research in container terminals was then provided. Despite the existing simulation tools that can be used for the simulation of container terminals, there is a clear lack of a exible simulation tool speci cally developed for container terminals. Chapter 6 will attempt to close this gap by developing a exible simulation framework for simulation of container terminals based on the FlexSim CT software.
Evolutionary Fleet Sizing in Static
and Uncertain ESTTs
3.1 Introduction
This chapter proposes an EA to identify the optimal number of vehicles in ESTTs. The ESTTs are industrial settings where goods are transferred repeatedly between multiple PDPsby a eet of vehicles. At each PDP there is a machine to process the goods. Once goods have been processed, they will be picked up by vehicles and be transferred to another machine for further processing. Next to each machine, there might be a buer, which is a limited space designed to temporarily store goods in a queue. The purpose of the buer is to reduce the waiting time. Vehicles can drop o goods in the buer without having to wait for the machines to be available. Machines can also place the goods in the buer for vehicles to collect later. ESTTs are very common in industrial applications. Typical examples are manufacturing factories, warehouses, container
terminals and distribution centres (Vis, 2006).
One very important problem in an ESTT is the FSP - identifying the optimal number of vehicles to transfer goods. Having too few vehicles may decrease perfor- mance while having too many vehicles is expensive and may introduce deadlocks1.
This problem is not trivial. In real-world cases, it is highly complex and the optimal eet size depends on many factors such as the uncertainty in travel time of vehicles; the dynamics of machines' process time; and the size of the buer. These factors, however, have not been previously fully considered, leaving an important gap in the current research. This chapter attempts to close this gap by proposing an EA to solve the FSP by considering the above factors. The proposed algorithm will be tested on two case studies of container ports2.
Speci cally, the outcome of this chapter will help answering the following questions for the rst time: 1) How to determine the optimal/robust number of vehicles in static/uncertain ESTTs, especially container terminals? 2) How to analyse the impact of uncertainties on the optimal number of vehicles? 3) What is the impact of the buer size on the optimal/robust eet size?
The novelty of this chapter can be summarised as follows: First, an EA is proposed to solve the FSP in this context, with better performance than existing state-of-the-art methods. Second, a new formulation for the FSP is developed so that EA components can be built upon. Third, for the proposed EA, the following elements are developed: a representation, a local search, two operators and an adaptive learning mechanism. Fourth, the uncertainties in the FSP in container terminals are taken into account and solved. Two high delity simulation models (with dierent scenarios) were also
1A deadlock is a situation in which one or more involved vehicles cannot move. There are dierent
reasons for deadlocks, such as a lack of competent tra c control schemes or using too many vehicles etc.
2These two container ports have committed to consider the result of this research to improve their
developed to serve as the benchmark for the EA in the uncertain cases. Finally, a set of test cases is developed using realistic data from real European container terminals to resolve the issue of lacking benchmarks in this problem.
The rest of this chapter is structured as follows. Section 3.2 describes the FSP in container ports. Section 3.4 describes the proposed EA for the static case and its dierent components are explained in detail. In Section 3.5, a combination of the proposed EA with Monte Carlo simulation to determine the robust number of vehicles under uncertainties is described. The general approach to generate the test cases is given in Section 3.6. The experimental results of the static case including comparison results with the CPLEX solver are presented in Section 3.7. Experiments to study the eectiveness of this robust optimisation approach are described in Section 3.8. Finally, the conclusion is provided in Section 4.4.