# Route Selection Travelling From Southampton To Croydon Tourism Essay

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## Introduction

A problem as determining a route for travelling from Southampton to Croydon has been chosen as a result of the requirement of enrolling biometrics for visa extension.

The main approach to solve the problem was Multi-criteria Decision Analysis and four criteria for decision were determined as arrival time, total cost, transfer times and walking time. Transportation information was mostly collected from some reliable websites.

## Route selection

A preliminary route map was drawn based on the combination of the information, and it developed by removing some unavailable alternatives. To describe explicitly, a form was used to represent the features of each optional route.

Each criterion was given a weighting coefficient and utilities were assigned to evaluate the performance of the alternatives under the determined criteria. Afterwards, utilities were calibrated and summed up to estimate the alternatives. By calculation, the optimal route was selected under the given conditions. The route is travelling to London Waterloo by Mega train and then transferring twice by trains to West Croydon probably at 12:40. The total ticket price will be ¿¡21.30. There will be 3 transfers and at least 7 minutes will be spent on walking between stations.

## Methodology specification

Management Scientists use models to help decision-making after defining problems and implement the models by practicing. One of the most common MS methods is Decision Analysis (DA), which determines optimal choice under conditions of uncertainty by assessing probabilities and values. Generally the first step is formulating the problem, and then building the decision tree companied with determined probabilities and values. Finally, an optimal choice can be figured out by solving the decision tree.

According to different situations, distinct DA approaches can be adopted. One of those is Multi-criteria Decision Analysis (MCDA), which is utilised when decision-makers are faced with making numerous and conflicting evaluations. Measurements in MCDA are subjective and a form is normally applied to represent strategies and criteria. Techniques to MCDA are also various.

On the other hand, problems may often ill-structured. In this case, problem structuring methods are available. Moreover, multi-methodology is helpful for MS practitioners in maintaining both the analytical view and the real-world view in mind simultaneously, which is essential for MS.

## Recommendation

The recommended alternative is route A (travelling to London Waterloo by Mega train and then transferring to West Croydon by trains).

Under different situations different MS approaches can be adopted and multi-methodology may improve the analysis and the result.

## Problem formulation

A valid UK student visa is essential for an international student to study in the UK. Overseas students who wish to remain in the UK after the expiry of their visas will be required to apply for another visa. According to information given by the UK Border Agency, "Foreign nationals from outside the European Economic Area making certain applications to the UK Border Agency have to enrol their biometrics" (Identity Cards for Foreign Nationals - Biometric Enrolment Process, 2009).

AS a Chinese student studying in University of Southampton in England with a 50-day visa, I am one of those that need to extend the visa and I received a letter from UK Broader Agency asking me to provide my biometric data within 15 working days. If I fail to do so, my application may be refused as invalid and I will not be able to say in UK to continue my master course. Therefore, I booked an appointment for the enrolment at 14:15 on Wednesday the 28th November at Croydon Biometric Enrolment Centre, which lies in Croydon, London. My friend, who will go to Croydon with me for the same purpose, has a class on Wednesday morning, so we cannot set off until 9:45 when the class is over from Southampton Uni Interchange station. On the other hand, we need to arrive at the office half an hour before the allocated appointment time in order to have enough time to go through the security and reception areas. In another word, we should arrive before 13:45 because my friend's appointment is later than mine. Otherwise, the appointment may be unavailable. Yet, it does not matter how early to arrive because we can queue up for the enrolment once we arrive.

Since we have never been to Croydon, we had better to plan for the route for travelling from Southampton to Croydon beforehand. A fast, convenience and low-priced itinerary to Croydon can help us enrol biometrics, as part of the visa application, easily. Conversely, we may waste time and money and even fail to provide biometrics, which may lead to the rejection of visa extension, if we have chosen an inappropriate route.

## Methodology

In this article, the main approach used to solve the problem is Multiple-criteria decision analysis (MCDA), because more than one condition needs to be considered.

After gathering useful information, a route map is created to show optional routes compared with each other by some criteria.

Each criterion is given a weighting coefficient to express how important it is for the decision-making. For instance, the weighing coefficient for criterion arrival time is 0.30 and that for criterion walking time is 0.16. It means the later one is worth less consideration.

Then utilities are defined to measure the situation in a certain criterion. Assigned utility of 1 is for the best and 0 is for the worst. The intermediate situations are measured by linear programming. Take arrival time for example, considering all routes, the earliest arrival time is 12:40 and the latest is 13:44, with a difference of 64 minutes, so utility for 12:40 is 1 and for 13:44 is 0. The arrival time of route A is 13:29, 49 minutes later than 12:40, thus utility is 0.2 (see figure 1.1).

## (13:29, 0.2)

Figure 1.1 An example of utility assigning

As criteria have different weighting coefficient, utilities need to be calibrated (formula 1.1).

Calibrated utility = Original utility Ã- Relative weighting coefficient (1.1)

It is known that the weighting coefficient for criterion arrival time is 0.30 and the original utility for arrival time of route A is 0.2, so the calibrated utility for arrival time of route A is 0.06 (0.30Ã-0.2).

After all, the final score of a route is the summation of the calibrated utilities for all criteria of this route. The alternative with the highest score is the recommended choice.

## Information collection

Most transportation information was gained online from some reliable websites. Firstly, maps of Croydon and London can be searched on "Google Maps" website (http://maps.google.co.uk). Secondly, "Journey Planner" found on "Transport for London" home page (http://www.tfl.gov.uk/) can be used as a tool to organise routes based on different demand, such as starting and destination, transport modes, and routes of the fastest or with the fewest changes or with the least walking between stops. Besides, information of ticket fares and vehicle timetable are offered on some websites, which are "National Rail Enquiries" (http://www.nationalrail.co.uk/), for trains, "National Express" (http://www.nationalexpress.com/) for coaches, "Uni-Link" (http://www.unilinkbus.co.uk/) for uni-link buses of Southampton, and TfL (http://www.tfl.gov.uk/) for London buses, trams and tube. Furthermore, cheaper tickets may be available from websites: "Megatrain" (http://www.megatrain.com/uk/) and "First Trans Pennine Express" (FTPE) (http://www.tpexpress.co.uk/). Something else worth to mention is that we have 16-25 Railcards, which can save 1/3 off rail fares across Britain, and Oyster cards, which offers the cheapest way to make journeys by buses, trams and tube in London.

The required information is relied on the following clues:

The fastest routes from Southampton Uni Interchange to Croydon Biometric Enrolment Centre (CBEC).

Coach from Southampton to London. That is because tickets of coaches are usually cheaper than those of trains, but extra ways to CBEC should be found from Heathrow Airport or Victoria Coach Station.

Routes from London Waterloo Station to CBEC. Although Mega trains are quite cheap, passengers cannot get on or off at intermediate stations apart from the starting station and the terminus, which are Southampton Central Station and London Waterloo Station in this case.

Routes suggested by FTPE. Some cheap tickets are offered on this website for students who have 16-25 Railcards.

Ticket price and transport timetable.

## Information selection and combination

Criteria that optional routes will be measured by are as follows:

The most possible arrival time.

Total cost including return journey.

Transfer times during a journey.

Walking time (regardless the time spent on transferring in the same station).

Since most information, except for the ticket price, of return journey is out of consideration, it is sensible to buy round-trip ticket, which normally costs much less than two one-way tickets bought separately. With combination of gathered information, a preliminary route map can be showed as figure 2.1.

## * ** *** ****

W

R

12:42-12:50;¿¡3.71

R

7min

13:00-13:22

CJ WC 13:29; ¿¡15.21; 4; 7min

W

W

R

12:43-13:02;¿¡3.71

R: Mega

10:55-12:34;¿¡9

17min

5min

LW LWE EC 13:19; ¿¡15.21; 4; 22min

12:42-12:50;¿¡3.2

12:41-12:54;¿¡3.71

W

R

T

17min

LB EC 13:11; ¿¡18.41; 4; 17min

## âˆ¥

B:468

B:1/168/172

W

12:45(± 7)-12:49; 12:50(±10)-12:54;

12:44(± 8)-12:49; ¿¡2

3min

12:55(±8)-13:47;

¿¡2

E&C WG 13:50; ¿¡15.50; 4; 3min

(+20min, if traffic jam)

9:57-10:33; ¿¡2.5

B: U1C

11:13-13:27;¿¡3.71

R

W

17min

SCe EC 13:44; ¿¡16.25; 2; 17min

R

W

10:30-11:58;¿¡18.85

R

7min

12:11-12:33

SUI CJ WC 12:40; ¿¡21.30; 3; 7min

## âˆ¥

W

12:22-13:59; ¿¡3.2

B:X26

10:30-12:15;¿¡10

C

9:57-10:14; ¿¡2.5

B:U1C

3min

HA WG 14:02; ¿¡15.75; 3; 3min

W

13:33-14:03; ¿¡3.71

R

SCo (+30min, if traffic jam)

W

10:30-13:10;¿¡10

C

7min

15min

VC VR WC 14:10; ¿¡16.21; 4; 22min

(+30min, if traffic jam)

Figure 2.1 Preliminary route map

* arrival time, ** total cost including return journey, *** transfer times during a journey, **** time spent on walking

12:45(± 7)-12:49: every 7 minutes per bus¼Œ (+20min, if traffic jam): if the traffic condition is bad, it will take extra 20 minutes for maximum

Stations:

CJ: Clapham Junction Station

EC: East Croydon Station

E&C: Elephant & Castle Station

HA: Heathrow Airport

LB: London Bridge Rail Station

LW: London Waterloo Station

LWE: London Waterloo East Station

SCe: Southampton Central Station

SCo: Southampton Coach Station

SUI: Southampton Uni Interchange

WC: West Croydon Station

VC: Victoria Coach Station

VR: Victoria Rail Station

Transport modes: B: bus, R: railway, T: tube, C: coach, W: walk

## Model simplify

Features that will affect decision for each route are showed in figure 2.1. As mentioned, 13:45 is the deadline for arrival. As a result, some routes can be vetoed before in-depth analysis (see figure 2.2).

## * ** *** ****

W

7min

R

R

CJ WC 13:29; ¿¡15.21; 4; 7min

R

R

W

17min

W

5min

LW LWE EC 13:19; ¿¡15.21; 4; 22min

W

17min

R

T

LB EC 13:11; ¿¡18.41; 4; 17min

R

W

17min

B

SUI SCe EC 13:44; ¿¡16.25; 2; 17min

R

R

W

7min9:57

CJ WC 12:40; ¿¡21.30; 3; 7min

Figure 2.2 Route map

* arrival time, ** total cost including return journey, *** transfer times during a journey,

**** time spent on walking; Transport modes: B: Bus, R: railway, T: tube, W: walk

Stations:

CJ: Clapham Junction Station

EC: East Croydon Station

LB: London Bridge Rail Station

LW: London Waterloo Station

LWE: London Waterloo East Station

SCe: Southampton Central Station

SUI: Southampton Uni Interchange

WC: West Croydon Station

To describe more simply and explicitly, letters A to E are used to represent the routes (see table 2.1).

Table 2.1 Features of alternative routes

Route

Arrival time

Total cost (¿¡)

Transfer times

Walking time (min)

A

13:29

15.21

4

7

B

13:19

15.21

4

22

C

13:11

18.41

4

17

D

13:44

16.25

2

17

E

12:40

21.30

3

7

## Importance weighting determination

The first step is to determine weighting coefficient to the main criteria to show to what extent each criterion will affect the decision (see table. 2.2).

Afterwards, it is time to weight the importance of features. Within each criterion, utility of 1 is assigned to the best and utility of 0 to the worst (see table 2.3 to 2.6).

Table 2.2 Weighting coefficient for the main criteria

Criteria

Arrival time

Total cost

Transfer times

Walking time

Weighting coefficient

0.30

0.32

0.22

0.16

Table 2.3 Importance weighting for arrival time

Arrival time

12:40

13:11

13:19

13:29

13:44

Utility

1

0.5

0.4

0.2

0

Table 2.4 Importance weighting for total cost

Total cost (¿¡)

15.21

16.25

18.41

21.30

Utility

1

0.8

0.5

0

Table 2.5 Importance weighting for transfer times

Transfer times

0

2

3

4

Utility

1

0.5

0.25

0

Table 2.6 Importance weighting for walking time

Walking time

0

7

17

22

Utility

1

0.7

0.2

0

Accordingly, importance weighting for features can be specified into the alternative routes as table 2.7.

Table 2.7 Original importance weighting for features of optional routes

Route

Arrival time

Total cost

Transfer times

Walking time

A

0.2

1

0

0.7

B

0.4

1

0

0

C

0.5

0.5

0

0.2

D

0

0.8

0.5

0.2

E

1

0

0.25

0.7

## Importance weighting calculation

The final step is to calibrate the utilities with weighting coefficient to calculate the importance weighting for each alternative (see table 2.8).

Table 2.8 Calibrated importance weighting for routes

Route

Arrival time

Total cost

Transfer times

Walking time

Score

A

0.06

0.32

0

0.112

0.492

B

0.12

0.32

0

0

0.44

C

0.15

0.16

0

0.032

0.342

D

0

0.256

0.11

0.032

0.398

E

0.3

0

0.055

0.112

0.467

## Result

As table 2.8 shown, route A owns the highest score. That is to say, it is the optimal choice for travelling from Southampton to Croydon to enrol biometrics according to the designed requirement. Therefore, the recommended route is as figure 2.3.

W

R

R

R

B* ** *** ****

SUI â†’ SCe â†’ LW â†’ CJ â†’ WC â†’ CBEC 12:40; ¿¡21.30; 3; 7min

Figure 2.3 Final choice

* arrival time, ** total cost including return journey, *** transfer times during a journey,

**** time spent on walking

Stations:

CBEC: Croydon Biometric Enrolment Centre

CJ: Clapham Junction Station

SCe: Southampton Central Station

SUI: Southampton Uni Interchange

WC: West Croydon Station

Transport modes: B: Bus, R: railway, W: walk

Back-checking the result into reality, it is a sensitive route for travelling from Southampton to Croydon.

## Management Science

Management Science (MS) "uses a panoply of analytical methods to better understand those decisions or situations in order to help those decision-makers" (Williams, 2008). It uses various scientific research-based principles, strategies, and analytical methods to find out the optimal decision.

Usually, practitioners may carry out Management Science following these steps (Chapman, Cooper and Page, 1987):

Define the problem.

Construct a model.

Calculate the solution.

Test the model.

Implement the solution.

## Decision Analysis

Decision Analysis (DA) is an approach used for making decision under conditions of uncertainty in order to determine the optimal decision around relevant alternatives by estimating the probabilities and values of certain events and outcomes that will occur. As a set of many procedures, methods and techniques for identifying, interpreting, and evaluating the considerable aspects of a decision situation, DA is one of the favourite approaches that practising Management Scientists may adopt to carry out their professional activities.

## Scope

A decision analytic approach is applicable to problem can be formulated as:

A choice between a set of alternatives.

With each alternative is associated a set of possible outcomes along with a probability of occurrence.

With each outcome can be associated a value.

## General procedures

Formulate the decision problem. List all of the objectives and all of the uncertain events followed by their possible outcomes.

Combine the information into the basic constructed decision tree by placing the nods of decision and event logically (like figure 2.1 and figure 2.2).

Determine the probabilities or values of the possible outcomes of each uncertain event (like table 2.2-2.7).

Solve the decision tree (table 2.8).

(Keeney, 1982)

## "Taxonomy" of methods

There are lots of decision analytic approaches and different situations have different requirement of methods. The following are some methods used commonly (Keeney, 1982):

Deterministic methods: making decision under certainty. Each alternative is associated with only one outcome.

Stochastic methods: making decision under risk. Each alternative is associated with more than one outcome and each outcome is associated with a certain probability of occurrence.

Uncertainty decision analysis. Each alternative is associated with more than one outcome but the occurrence probability of each outcome is not certain.

Multi-criteria decision analysis. Each alternative is associated with many outcomes, which possess different attributes or objectives.

Group decision analysis. Decisions are made by groups consisting of multiple entities that have pluralistic purposes.

## Multi-criteria decision analysis

Multi-criteria decision analysis (MCDA) is one of the Decision Analysis approaches and it aims at supporting decision-makers faced with making numerous and conflicting evaluations. Measurements in MCDA are derived or interpreted subjectively and the outcome depends on the preferences of the decision-makers.

## General form

Analysts practicing MCDA usually use a form (like table2.7 and table 2.8) to represent a number of strategies, alternatives or actions, and a number of criteria, aspects or dimensions (see table 3.1).

Table 3.1 A general form for MCDA

Criterion 1 (f1)

Criterion 2

Criterion 3

Criterion n

Strategy 1 (S1)

Strategy 2

Strategy 3

Strategy n

fn(Sn)

## MCDA approach

Again, there are many approaches to MCDA, including:

Analytic hierarchy process (AHP). Paired comparisons are used to weight criteria and score alternatives.

Multi-attribute utility theory (MAVT). Separate utility functions are developed to represent each criterion and the functions are combined to evaluate the alternatives.

Goal programming. Each objective is given a value of anticipation. The optimal choice is the one achieves target values most.

Superiority and inferiority ranking method.

Outranking approaches. The demand of score options can be eliminate.

## Problem structuring methods

Decision analysis methods are utilized to deal with more structured situations whose parameters are difficult to quantify. However, problems are difficult to define not only because decision-makers and analysts may have diverse understanding and aspirations of the problems, but also because there may be complicated problem-situations that lead to difficult to structure the problems. Problem structuring methods are helpful in structuring ill-structured problems to enable them to be amenable to analysis. Some available methods are: Soft Systems Methodology (SSM), Scenario analysis and Strategic choice (Williams, 2008).

## Multi-methodology

Management Scientists need to regard the real world critically and construct and solve the model analytically simultaneously, though different paradigms underlie these activities. Therefore, combination of different methods and paradigms is necessary for MS practitioners to maintain both the analytical view and the real-world view in mind simultaneously so that it can enable these two views to develop and support each other. This apparent contradiction, or antinomy, is an essential element of good Management Science (Williams, 2008).

## Route selection

According to the analysis, route A (travelling to London Waterloo by Mega train and then transferring twice by trains to West Croydon) got the highest score. It means that comprehensively taking account of all criteria that affect the decision, route A is the recommended choice for this problem under determined conditions. The probable arrival time will be 12:40 and it will cost ¿¡21.30 for tickets. Three transfers will be taken and at least 7 minutes will be spent on walking between stations.

## Management Science Approach

Modelling is one the most important tools for Management Science practicing, so an appropriate model is essential for solving problem. What a model will be depends on what the problem is.

Usually, a problem is not easy to formulate. That because problem-situations may be complicated and the understanding and aspiration by decision-makers and analysts may different. Different methods are suitable according to different situations.

Problems under conditions of uncertainty can be tackled by Decision Analysis.

Problems whose parameters are difficult to quantify may require Multi-criteria Decision Analysis.

Problems that are ill-structured may need to be structured by problem structuring method.

Additionally, Management Scientists can use multi-methodology to solve problems in order to ensure the MS procedures and results are practical.