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City University of Hong Kong
Department of Computer Science
Dissertation
Rostering System for aircraft service industry
Lam Chi Wo
50447402
2004-2005
Supervisor: Dr. Andy Chun
Master of Science
in
Computing
Lam Chi Wo MSC 50447402
TABLE OF CONTENT
1.
INTRODUCTION............................................................................................................................... 5
1.1.
BACKGROUND .............................................................................................................................. 5
1.1.1.
Aircraft Services industry ....................................................................................................... 5
1.1.2.
Needs for better scheduling .................................................................................................... 6
1.1.3.
Rostering in Aircraft Services Industry................................................................................... 7
2.
PROJECT AIM & OBJECTIVES .................................................................................................... 8
3.
PROBLEM DESCRIPTION.............................................................................................................. 9
3.1.1.
Problem analysis .................................................................................................................... 9
3.1.1.1. Labour Demand.................................................................................................................... 10
3.1.1.2. Engineer Supply.................................................................................................................... 10
3.1.1.3. Constrains............................................................................................................................. 11
3.1.1.4. Roster.................................................................................................................................... 12
3.1.2.
4.
5.
Evaluation criteria................................................................................................................ 12
LITERATURE REVIEW................................................................................................................. 14
4.1.
RESEARCH ON ROSTERING ......................................................................................................... 14
4.2.
APPROACHES AND ALGORITHMS ................................................................................................ 16
ALGORITHM DESIGN................................................................................................................... 18
5.1.
THE PROBLEM ............................................................................................................................ 18
5.2.
ALGORITHM OBJECTIVES ............................................................................................................ 19
5.3.
PROBLEM SOLVING APPROACH ................................................................................................... 19
5.4.
ROW FORMING ........................................................................................................................... 20
5.4.1.
Constrains in row forming.................................................................................................... 20
5.4.2.
Preparing possible row combinations .................................................................................. 21
5.5.
ROSTER FORMING ....................................................................................................................... 25
5.5.1.
Constrains in roster forming ................................................................................................ 25
5.5.2.
Demand................................................................................................................................. 26
5.5.3.
Sampling strategy ................................................................................................................. 27
5.5.4.
Linear Forward Search ........................................................................................................ 27
5.5.4.1. Solution naming.................................................................................................................... 28
5.5.5.
Multi-directions Search ........................................................................................................ 32
5.5.6.
Genetic Algorithm................................................................................................................. 32
5.6.
EVALUATION .............................................................................................................................. 35
5.6.1.
Shift distribution ................................................................................................................... 35
5.6.2.
The fitness function............................................................................................................... 36
5.6.3.
Case base.............................................................................................................................. 37
5.6.4.
Problem signature ................................................................................................................ 37
Lam Chi Wo MSC 50447402
5.7.
6.
7.
THE OVERALL ALGORITHM ......................................................................................................... 39
SYSTEM ANALYSIS ....................................................................................................................... 40
6.1.
BASIC SYSTEM REQUIREMENT .................................................................................................... 40
6.2.
FUNCTIONAL SPECIFICATION ...................................................................................................... 40
6.3.
USE CASES ANALYSIS ................................................................................................................ 43
6.4.
USE-CASE SCENARIO .................................................................................................................. 45
6.5.
CONCEPTUAL CLASS DIAGRAM .................................................................................................. 46
SYSTEM DESIGN............................................................................................................................ 47
7.1.
DESIGN CLASS DIAGRAM ........................................................................................................... 47
7.1.1.
Presentation Layer ............................................................................................................... 47
7.1.2.
Domain Layer ....................................................................................................................... 47
7.2.
SEQUENCE DIAGRAM ................................................................................................................. 48
DATABASE DESIGN................................................................................................................................... 50
7.2.1.
ER diagram........................................................................................................................... 50
7.2.2.
Table listing .......................................................................................................................... 51
7.2.3.
Table Details ........................................................................................................................ 51
7.3.
8.
INTERFACE DESIGN..................................................................................................................... 54
SYSTEM IMPLEMENTATION ..................................................................................................... 60
8.1.
PROGRAMMING LANGUAGE ........................................................................................................ 60
8.2.
DATABASE SYSTEM ................................................................................................................... 62
8.2.1.
System Architecture .............................................................................................................. 63
8.3.
SYSTEM TESTING ....................................................................................................................... 63
8.4.
SYSTEM EVALUATION ................................................................................................................ 65
8.4.1.
Performance Evaluation....................................................................................................... 65
8.4.2.
The Gene Hunter .................................................................................................................. 65
8.4.3.
Simple GA model .................................................................................................................. 65
8.4.4.
Evaluation Scenario ............................................................................................................. 67
8.4.5.
Result .................................................................................................................................... 69
8.4.5.1. RosterBuilder Vs GeneHunter .............................................................................................. 69
8.4.5.2. Result Analysis...................................................................................................................... 70
8.4.5.3. Observations from the results ............................................................................................... 71
9.
8.4.6.
Sampling Strategies in RosterBuilder................................................................................... 72
8.4.7.
Results................................................................................................................................... 72
8.4.8.
Observations from the results ............................................................................................... 73
CONCLUSION ................................................................................................................................. 75
9.1.
ACHIEVEMENTS ......................................................................................................................... 75
9.2.
FURTHER DEVELOPMENT............................................................................................................ 76
Lam Chi Wo MSC 50447402
REFERENCES ........................................................................................................................................... 78
10.
APPENDIX ................................................................................................................................... 80
10.1.
PROJECT SCHEDULE ................................................................................................................... 80
10.2.
ATTACHMENT CD CONTENT ...................................................................................................... 80
10.3.
SYSTEM REQUIREMENTS ............................................................................................................ 80
10.4.
INSTALLATION GUIDE ................................................................................................................ 81
Lam Chi Wo MSC 50447402
1. Introduction
1.1.
Background
1.1.1. Aircraft Services industry
Aircraft Services, in a broader sense, is referring all services
providing to the aircraft that is landed and parked in the airport. These
include cabin cleaning, ground services (drainage, power supply, push
back service) and maintenance service. Aircraft maintenance services
include periodic inspection (the A, B, C, D checks) and lines
maintenance which maintains aircrafts that are actively in service.
Since the operation mode of periodic inspection and line maintenance
are totally different, in this study, we will focus on the line
maintenance section of aircraft services industry. As the operation
mode of cabin cleaning and ground service sections is just a simpler
version of line maintenance section, we assume that the result of the
study on line maintenance case can be applied to other sections without
difficulties.
In Hong Kong, there are 3 government approved Aircraft
Services Companies operating in the Hong Kong Chak Lap Kok
International airport.
Lam Chi Wo MSC 50447402
1.1.2. Needs for better scheduling
Unlike other ground transportation industry that having their
own depot for the maintenance and servicing of their rolling stock, it is
a norm for airline operator to contract out the maintenance and
servicing of their aircraft to aircraft servicing company. This, of course,
due to the extremely heavy cost burden of airlines to operate
maintenance facilities in all airports they will reach. And this also
provides the opportunities for the aircraft services company to survive.
Aircraft services companies operating in an international airport, like
Hong Kong Chak Lap Kok International airport, will serve aircrafts
coming from different airlines and country. To comply with the strict
aviation requirement of different authorizations and customers, the
maintenance engineers of the aircraft services companies have to
possess different licenses and approvals according to the requirement
of the regulations set by the aviation authority and airline customers.
The diversification of license requirements of the aircraft being served
makes the manpower cost to be one of the major operation cost of
Aircraft Services company.
To increase the profit margin, the company wants to hire as few
engineers as possible. However, to maintain the services level, the
company has to maintain enough number of engineers having different
license and skill sets that can fulfil the requirements from airlines
customers. In view of such, the better utilization of the manpower
becomes one of the key factors for the company to succeed. It has been
seen in the literature that a good personnel schedule can reduce the
number of labour needed significantly.
Thus a better way of
scheduling engineer is needed and is vital to the company.
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1.1.3. Rostering in Aircraft Services Industry
Rostering, which is the preparation of roster for available staff,
in aircraft services industry is known to be a complex and difficult task.
The complexity of the problem is a result of constrains set by the
government regulations, airworthiness requirements, airlines (customer)
requirements, international standard, company policy, flight schedule
and the human factors.
Since there is not much rostering software specially designed
for aircraft services industry, there are two common ways of preparing
roster in aircraft services industry. The first one is to prepare the roster
manually. The responsible staff prepares the roster using general
office-use software like spreadsheet and text editor. The staff prepares
the roster by his/her experience and knowledge. The computer
software is only used to help counting and printing of the roster. The
quality of the roster is solely depends on the experience and knowledge
of the responsible staff. Since the resulting rosters are normally stored
in the computers in a document or spreadsheet format, the summary
information can be provided is limited. And, obviously, the process of
making roster manually is fairly slow.
Another way commonly used is to adopt the personnel
scheduling software developed for other similar industry, like airlines.
However, as the operation model of airlines crews is different from
that of aircraft maintenance industry, a lot of customizations and/or
modifications are needed before the system can be adopted
successfully.
Lam Chi Wo MSC 50447402
2. Project Aim & Objectives
This project aims to research an Artificial Intelligence
methodology suitable for solving rostering problem in aircraft service
industry. Design and develop a prototype system for testing the
methodology.
The objective of the project is to study and analyze the
requirement and characteristic of rostering problem in aircraft service
industry. Research and review the Artificial Intelligence methodology
used in rostering problem. Design and Program a prototype system.
Evaluate the performance of the methodology using the prototype
system.
Lam Chi Wo MSC 50447402
3. Problem description
3.1.1. Problem analysis
In this study, we are going to build a rostering system for
aircraft maintenance industry. The output of the system is a monthly
roster showing the work shift of all maintenance engineers for the next
month. The block diagram of the proposed system is show as Figure 1.
Figure 1: Block diagram of Rostering System
The information of demand and available supply are fed into
the system as input. Using the defined methodology, a roster is
generated subject to constrain imposed. The details of each block will
be described in following section.
Lam Chi Wo MSC 50447402
3.1.1.1. Labour Demand
Labour demand is a set of numbers showing how many
engineers of which type is needed in which work shift for which day.
Work shift is a list of predefined working period. From another
point of view, work shift is a grouping of working hours in a day. The
whole working periods are grouped into a number of shifts. In our case,
we assume there are 3 shifts pre-defined:
Shift Code
Shift Description
Start time
End Time
D
Day Shift
07:30
16:30
A
Afternoon Shift
14:30
23:30
N
Night Shift
23:00
08:00
(next day)
Off
Day off
The labour demand is listed in terms of work shift, instead of
hours.
3.1.1.2. Engineer Supply
Engineer supply is a list of engineer that can be assigned to fill
the labour demand. Each engineer has his/her own list of skill-set, that
is the licenses or approval that he/she is bearing. When assigning
engineer to fill the labour demand, the skill-set of the engineer must
match the skill set requirement of the labour demand. In our case, we
assume engineer skill set is classified by its grade.
Lam Chi Wo MSC 50447402
3.1.1.3. Constrains
Constrains here refers to everything that restricts, guide and
limit the assignment of supply to the demand. Specifically, constrains
are the rules, regulations, policies, criteria or preferences that the
resulting roster has to meet. Constrains are the main factors that makes
rostering so difficult.
There are many types of constrains in rostering, and the
constrains for different industries, departments, or even seasons are
different. Constrains can be categorises into two types – the hard
constrain and soft constrain. Hard constrains are the rules or regulation
that must be follow and it cannot be violated in any case. For example,
there is a rule set by the authority that engineers performing aircraft
maintenance must have enough rest. So, the roster must ensure that
there is no more than 7 consecutive working days for every engineer,
there must be a rest day after 7 consecutive working days.
In contrast, soft constrains are the guideline or normal practice
that nice to have. For example, the company policy stated that night
shift should be evenly distributed. That is every engineer should have
equal chance of assigning night shift. And the number of days between
two night shift weeks should be maximised. Since this is just a soft
constrain, it can be released in the case that the supply is not enough to
fill up the demand.
Typical hard constrain in aircraft maintenance includes:
1. At least 12 hours rest time between every consecutive shifts
2. At least 1 rest day after 7 consecutive working days.
3. Continuous working time should not exceed 10 hours
Typical soft constrain in aircraft maintenance includes:
Lam Chi Wo MSC 50447402
1. Night shifts are evenly distributed, days between night shift periods
should be maximised.
2. There should be fixed pattern of day off, or the length of working
period should be fixed.
There is another type of constrains that we called
“Background” constrain. Background constrains is the “background”
information that will affect the preparation of current roster. One of the
examples is the roster of pervious month. Since the first day of the
current roster is the consecutive days of the last day of the previous
roster. Hence, previous roster must also be considered.
3.1.1.4. Roster
Roster in the output stream of the system should be a table
showing the assignment of the supply to the demand. However, as the
resulting roster is read by human being. The table is not grouped by
demand; it is grouped by supply, i.e. name of the engineer, with the
demand filled. (see the table below)
Jan 1
Jan 2 Jan 3
Engineer A
D
D
Off
Engineer B
A
Off
D
Engineer C
N
Off
D
……
…….
3.1.2. Evaluation criteria
Since there may be more than one feasible roster in the solution
domain, and we want to choose the best one among, we need some
means to know the quality of a roster. We must define some measures
Lam Chi Wo MSC 50447402
to weight different rosters that may be generated. In our case, a penalty
system will be used to mark the roster generated.
The marking scheme is a measure of the violation of constrains.
So it is the summation of penalties for each type of constrains:
Demand penalty
Penalty will be given if any of the
demand cannot be filled.
Hard Constrain penalty
Penalty will be given if any of the
hard constrain is violated
Soft Constrain penalty
Penalty will be given if any of the
soft constrain is violated
Background Constrain penalty
Penalty will be given if any of the
background constrain is violated
Obviously, the weight of the 4 penalties types would be
different. For example, the penalty for hard constrain will be much
higher than that of soft constrain. So the resulting solution will be
biased to those only having soft constrain violation. Roster solutions
will be compared by the corresponding total penalty calculated.
Lam Chi Wo MSC 50447402
4. Literature Review
4.1.
Research on Rostering
Reviewing the literature about rostering, it has been an active
research subject since 1950’s. ERNST et al [6] have done an extensive
review on the researches that have been done to try solving the
problem. ERNST summarised and categorised the paper that have been
published concerning rostering by their proposed approach and the
types of problem that going to solve.
Table 1: Categorisation of papers by solution method. [6]
Table 2: Categorisation of papers by application [6]
Based on the result presented by ERNST, there are only a few
papers focused on the rostering of Aircraft Maintenance Industry.
Dijkstra et al [10] presented the problem of planning a multi-skilled
workforce of engineers required to carry out aircraft maintenance. In
Lam Chi Wo MSC 50447402
this paper, the planning of aircraft maintenance personnel is solved
using a Lagrangean relaxation approach and a constructive heuristic
which can obtain an approximate solution quickly. Alfares [9]
presented a case study describing the generation of a weekly roster for
aircraft maintenance staff of Saudi Aramco. Simple IP models are used
to determine the minimum number of staff required and the optimal
assignment of days off and shifts.
Besides the studies focused on Aircraft Maintenance Industry,
there are some studies focused on similar industries that are worth
noted. Usher [4] presented a preliminary review of scheduling
problems in airlines. KOHL et al [5] has discussed in details the
solution method employed in a commercial crew rostering system for
airlines.
The number of studies being done in so many different
approaches and application areas hint that there is no “one-fits-all”
solution available. Certain degree of adoption and customization is
needed for different situations and applications.
Lam Chi Wo MSC 50447402
4.2.
Approaches and algorithms
Within the around 70 references reviewed, ERNST identified
28 different methods have been used to solve rostering problem in
different areas. Among those 28 identified methods, we can see that
there are two main streams of approaches that most researchers are
working on. They are the mathematical programming and Heuristic
approach.
Mathematical programming method, including its special cases
and variation, like linear programming, integer linear programming,
and many network flow problems, models the rostering as an
optimization problem and seek to minimise or maximise an objective
subject to a set of constraints by mathematic methods. Recent
publications using mathematical programming like Azmat et al [7], and
Eitzen et al [8] that used Integer programming. The strength of
mathematical programming methods is that they can give out solution
in comparative shorter time and in most of the case, the optimum
solution can be found if it exists. However, as constrains of roster have
to be transformed into mathematical form before the problem can be
solved by the optimizer, it is less flexible to cope with the situation that
constrains of the problem will be changed frequently. Furthermore, the
number of constrains can be “considered” is limited by the capability
of the mathematical solver being used.
Heuristic approach has been used extensively in research to
tackle difficult combinatorial problems for a long time. And another
term, “meta- heuristic” was defined to describe the heuristic methods
that are based on local search improvement and applying complex
techniques to explore and guide neighbourhood searches. Examples of
meta-heuristics include simulated annealing, tabu search, evolutionary
algorithms, genetic algorithms, iterated randomised construction,
GRASP, ant colony optimization and problem space search methods.
Lam Chi Wo MSC 50447402
Heuristic approach can due with complex problem with many and
frequently changing constrains. Instead of taking the problem as a
mathematical optimization problem, heuristic approach treats the
problem as a searching problem. They search for good answer in the
solution space. Ideally, the optimum answer can be found if the whole
solution space has been searched. However, as the size of the solution
space grows rapidly with the input of the problem, the solution space is
simply too large and it is too costly to visit all solutions in order to find
the optimum solution. So, different techniques are applied to reduce
the time and storage cost of finding the solution. The ?? is to change
the target to local optimum instead of optimum. That means the
solution obtained may not be the best one, it is only a feasible one with
certain quality. Since these algorithms having shorter calculation time
are comparatively easier to implement and the sub-optimum solution
obtained is already good enough in most of the case, they are preferred
in real and practical rostering situation.
Lam Chi Wo MSC 50447402
5. Algorithm Design
5.1.
The problem
In this paper, rostering problem is treated as a searching problem. The
input of the problem is the dimension forming the roster. These include the
number of shift, number staff, number of days, number of demand, the
rules/constrains has to be complied and the evaluation criteria which judge the
good/bad of a roster. The space being searched is the combinations of different
days, shifts and staff.
As shown in the figure above, a roster is a table formed by rows and
columns. Row in the roster form represents the shifts assigned to one staff.
Column in the roster form represents the shifts assigned for one day. Roster
generation actually is the task of filling the blanks on the rostering form with a
predefined shift code. There is always a short list of shift codes defining what
can be put into the blank.
In general, there is a list of possible shift S with m elements
S = {S1 , S 2 ,......S m }, m ≥ 1
and a roster can be viewed as a collection of n rows, where n=number of staff,
RTi = {R1 , R2 ,......Rn } , n ≥ 1
Lam Chi Wo MSC 50447402
and each row i has d elements where d = number of days
Ri = {ri1 , ri 2 ......rid } , d ≥ 1
where rij ∈ S
Thus, with different combination of the elements rij , there are C r
possible rows for row r
Cr = m d
and with different combinations of rows Ri , there are C RT possible
roster.
C RT = C r = (m d ) , C RT ≥ 1 ----------------------------------(1)
n
n
Therefore, the problem is to search for a solution roster RTsol ∈ RT
{
RT = RT1 , RT2 ,......RTCRT
5.2.
}
Algorithm objectives
So, the objective of the desire algorithm is:
“To find a feasible solution which complies with all constrains
(at least all hard constrain) and, if possible, fulfil all demands without
excess in reasonable time.”
5.3.
Problem solving approach
It is obvious from equation (1) that the search space to be
searched will grow rapidly if either number of staff, shift or day is
increased. So, it is not practical or realistic to tackle the problem
directly. One of the ways to reduce the size or complexity of problem
being solved is to divide it into several sub-problems and tackle them
individually.
As discussed in previous section, a roster is formed by a
combination of rows, and each row is formed by a combination of cells.
We also know that the cell combination, which forming the row, is
limited by horizontal constrains; while the row combination, which
forming the roster, is limited by vertical constrains. So, our approach is
to divide the rostering problem into the problem of row forming and
Lam Chi Wo MSC 50447402
roster forming. The block diagram below shows the flow of the
approach.
5.4.
Row forming
5.4.1. Constrains in row forming
Constrains affecting row forming is the shift pattern that is not
allowed or to be blocked. These patterns are defined by user and can be
used to account for the minimum working time requirement.
Shift
Shift Description
Start time
End time
D
Day Shift
07:30
16:30
A
Afternoon Shift
14:30
23:30
N
Night Shift
23:00
08:00
Code
For example, if we have 3 shifts as shown in the table above,
and there is a constrains that, for every two consecutive shift
assignments, there must be at least 12 hours between the end time of
the former shift and the start time of the later shift. So, for the shifts
listed below, the shift pattern shown below must be blocked.
Shift pattern
Time between
AD
6.5 hours
ND
Overlap
NA
6.5 hours
Lam Chi Wo MSC 50447402
It is obvious that any solution containing these shift patterns are
not “legal” solution and can be discarded. So, these patterns will be
used to reduce the number of possible cell combinations.
Another typical horizontal constrain is the number of
consecutive working days and night shifts. According to the labour
regulation from the government, there must be one holiday within 7
consecutive working days. In other words, the maximum number of
consecutive working day is 6. And following the policy of the
company, there should not be more than 3 consecutive night shifts for
each engineer.
So any rows containing over 6 consecutive working days and
over 3 consecutive night shifts will be ignored.
5.4.2. Preparing possible row combinations
Engineer A
Jan 1
Jan 2
Jan 3
Jan 4
D
Î D?
Î D?
…
Î A?
Î N?
Î O?
Î A?
Î D?
Î A?
Î N?
Î O?
Î N?
Î D?
Î A?
Î N?
Î O?
Î O?
Î D?
Î A?
Î N?
Î O?
Lam Chi Wo MSC 50447402
The figure above shows the process of filling a row of
roster. Say, if a “D” is filled in the 1st cell, when filling the 2nd cell,
there are 4 possible choices (Assume there are four shifts defined), for
each choice in the 2nd cell, there are another 4 choices for the 3rd row,
and so on.
However, if we consider the shift constrains, an “A”
shift can not be followed by a “D” shift, and “N” shift cannot be
followed by “D” or “A” shift. So, the possible combination will be
reduced, and the table will become:
Engineer A
Jan 1
Jan 2
Jan 3
Jan 4
D
Î D?
Î D?
…
Î A?
Î N?
Î O?
Î A?
Î A?
Î N?
Î O?
Î N?
Î N?
Î O?
Î O?
Î D?
Î A?
Î N?
Î O?
So, our task in this stage is to find out all possible cell
combinations which can form a “legal” row. It is obvious that this can
be solved by tree-search using backtracking method.
Lam Chi Wo MSC 50447402
We define a n level tree that represents a single row in a roster
having n-1 day. Each node in the tree represents a possible shift
assignment. Each level represents one column in the row. The tree
below shows a 3 level tree representing a row for 3 days.
Backtracking method is applied in tree building process, so that
any path having “illegal” pattern, having too many consecutive work
or night shift is marked as “dead-end” (nodes with red cross) , and no
more path will be grown from that node.
After building the tree, all possible rows can be obtained by a
depth first search. Since all paths with “illegal” pattern are ignored and
killed from the tree, all rows obtained in the depth first search comply
with horizontal constrains. In other words, the search space of the
roster is reduced with only legal rows.
The tree below is a sample tree of a 3 days row. The number of
possible path is reduced to 41 from a total of 64 according to the shiftconstrains.
Lam Chi Wo MSC 50447402
If, for demonstration purpose, we set the maximum number of
consecutive working days and maximum number of consecutive night shift
to 2 and 1 respectively, the number of possible rows will be further reduced
to 29.
The same constrains are applied on different number of days to
see the effect on reducing the number of possible row and the result is
shown as below:
No.
day
2
of No. of possible row
without constrain
applied
16
No. of possible row
with constrains applied
% of
reduction
13
18.8%
3
64
29
54.7%
4
256
85
66.8%
5
1024
232
77.3%
6
4096
632
84.6%
7
16384
1753
89.3%
8
65536
4809
92.7%
9
262144
13228
95%
10
1048576
36420
96.5%
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5.5.
Roster forming
5.5.1. Constrains in roster forming
Now we have a list of possible rows for each staff. To form the
roster, we need to combine the rows picked from each staff.
Name
Staff A
Possible row
Î DDD ?
Î DDA ?
Î DDN ?
Î DDO ?
…….
Staff B
Î DDD ?
Î DDA ?
Î DDN ?
Î DDO ?
…….
Staff C
Î DDD ?
Î DDA ?
Î DDN ?
Î DDO ?
…….
Staff D
Î DDD ?
Î DDA ?
Î DDN ?
Î DDO ?
…….
Lam Chi Wo MSC 50447402
5.5.2. Demand
The criteria for picking the rows to form the roster is that the
combination of rows have to comply with vertical constrains defined
for the roster. As discussed in previous section, one of the main
vertical constrains is the demand of the day. Below is a table of
demand.
Shift Day 1
Day 2
Day 3
D
1
1
1
A
1
1
1
N
1
1
1
….
….
Demand specified how many staff required for a shift. That
means, for any column of a roster, the number of staff assigned to
specific shift must be equal or greater than the number demanded in
the demand table. In the other way round, we don’t want to have overassignment of staff, i.e. the number of staffs assigned to a shift is more
than the number required. So, we always want to have a roster that can
meet the demand with minimum over-assignment. As we assume that
the number of staff required in the demand definition is the minimum,
any roster that cannot meet demand will be considered as “illegal” and
will be filtered.
Lam Chi Wo MSC 50447402
5.5.3. Sampling strategy
Although the number of possible row for each staff is reduced
in the row forming stage, the number of possible roster formed by
combining those possible rows is still very huge. That means a lot of
time and cost have to be spent to search for a good solution. In order to
get a balance between the time spent and solution quality, we relax the
condition that we can accept sub-optimum solution. Adopting the idea
of randomness and continuous improvement from Genetic Algorithm,
instead of checking every possible solution to look for the true
optimum, we pick samples randomly from the solution space, and
choose the best one in the sample set to be the solution.
Since the sampling strategy will affect the quality of the
solution and the performance of the system, three sampling strategies
are used. They are namely, “Linear Forward Search”, “Multi-direction
Search” and “Genetic Algorithm”
5.5.4. Linear Forward Search
Assuming we have K solutions in the solution space and k is
very large. The simplest method to pick samples from the solution
space is using a random number generator to generate a random
number from 1 to K. However, this method arise a problem of
repeatability and evenness. If we draw J random numbers,
where J ≤ K , from the space 1 to K, the J numbers drawn may not be
unique and evenly distributed over the space. If there are repeated
numbers in the numbers drawn, it will be a waste of processing time as
we might evaluate the same sample more than one time, and it will
reduce the chance of picking the optimum solution. And if the numbers
drawn are not evenly distributed, the final solution will be biased the
chance of getting the optimum will also be reduced. To overcome the
Lam Chi Wo MSC 50447402
problems, Linear Forward search picks samples in one direction with a
random step size. The steps of Linear Forward search is shown as
below:
1. Sort the solutions linearly to certain order.
2. Set the sample index j 0 = 0
3. Define a maximum step size T, 0 < T ≤ K and generate a
random number r, 0 < r ≤ T
4. Pick sample at j n = j n −1 + r
5. Repeat step 3 and 4 until j n ≥ K
This method provides assurance on the uniqueness and
evenness of samples. It also provides flexibility that we can control the
sample size by the step size T. Step size T can be interpreted as “one
sample will be picked per T solutions”. The figure below demonstrates
how the samples are picked using the customized sampling method.
5.5.4.1. Solution naming
To use Linear forward search and for the convenient of storing
and describing the solution, we need to name the solutions in number
and sort them in certain order. As the solutions we are now working on
in this stage is a combination of row of each staff and there is no
explicit ordering among the solutions, we have to define a way to name
and order the solutions. The table below shows an example of the
possible solution.
Lam Chi Wo MSC 50447402
Name
Possible row
Staff A
1. DDD
2. DDA
3. DDN
4. DDO
Staff B
1. DDD
2. DDA
3. DDN
Staff C
1. DDD
2. DDA
3. DDN
4. DDO
For we have 3 staffs and the number of possible row is 4, 3 and 4
respectively, there are 48 possible solutions for the roster. They are
listed in the table below:
Sol.
#
Sol.
A
B
C
#
A
B
C
1
1
1
1
25
3
1
1
2
1
1
2
26
3
1
2
3
1
1
3
27
3
1
3
4
1
1
4
28
3
1
4
5
1
2
1
29
3
2
1
6
1
2
2
30
3
2
2
7
1
2
3
31
3
2
3
8
1
2
4
32
3
2
4
9
1
3
1
33
3
3
1
10
1
3
2
34
3
3
2
11
1
3
3
35
3
3
3
12
1
3
4
36
3
3
4
13
2
1
1
37
4
1
1
14
2
1
2
38
4
1
2
15
2
1
3
39
4
1
3
16
2
1
4
40
4
1
4
17
2
2
1
41
4
2
1
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18
2
2
2
42
4
2
2
19
2
2
3
43
4
2
3
20
2
2
4
44
4
2
4
21
2
3
1
45
4
3
1
22
2
3
2
46
4
3
2
23
2
3
3
47
4
3
3
24
2
3
4
48
4
3
4
Obviously, the simplest method is to make a table like the one
above which list out all possible solutions and give every one a
solution number. However, this will consume huge among of memory
if the number of possible solution is very large. So, a naming method
that does not require explicit listing is needed. Examining the solution
listed in the table carefully, we found that there is one way to name the
solution without listing them explicitly. The solutions in the table
above are listed in a convention that the right-most column is increased
first. The 2nd right-most column will be increased until the right-most
column reaches its max. In general, except the right-most column,
every column will be increased until the column in its right side
reached maximum. Using this listing convention, all solutions are
already implicitly numbered. Given any number within the solution
space, the corresponding number in each column can be retrieved
using the following algorithm.
Let,
M be the total number of solution, M>0
j be the solution number, 0 ≤ j < M
Cij be the corresponding number in column i for solution j
Tmaxi be the corresponding maximum number for column i
Function gd(i) = gd(i-1) x Tmaxi,
= Tmaxi ,
for i=1 ;
=1,
for i=0
a mod b = the remainder of
if
for i>1 ;
a
b
( j mod gd(i) > 0 )
Lam Chi Wo MSC 50447402
then
⎡ j mod gd (i ) ⎤
C ij = ⎢
⎥
⎢ gd (i − 1) ⎥
else
C ij = T max i
For demonstration purpose, we take one solution number
arbitrarily from the solution table above.
For j=33, M=48, Tmax1 =4, Tmax2 =3, Tmax3 =4
gd (0) = 1
,
gd (1) = T max i = 4
,
gd (2) = 4 × 3 = 12
,
gd (3) = 12 × 4 = 48
Q j mod gd (1) = 33 mod 4 = 1 >0
⎡1⎤
∴C1,33 = ⎢ ⎥ = 1
⎢1⎥
Q j mod gd (2) = 33 mod12 = 9 >0
⎡9⎤
∴C 2,33 = ⎢ ⎥ = 3
⎢4⎥
Q j mod gd (3) = 33 mod 48 = 33 >0
⎡ 33 ⎤
∴C 3,33 = ⎢ ⎥ = 3
⎢12 ⎥
So, the corresponding column values for solution 33 is {3,3,1} which
matches the value in the table.
Lam Chi Wo MSC 50447402
5.5.5. Multi-directions Search
There is one obvious draw back in the Linear Forward search. If the
solutions are gathered near the end of the list, it will need a very long time to
obtain the solution because, by design, it has to start searching from the first
solution in the list. For such occasion, a Multi-directions search may shorten
the searching time.
Instead of listing the solutions (combinations of rows) linearly, Multidirections search pick samples randomly by randomly choosing row for each
staff and combine them to form the solution.
Staff A
Rand(1, Amax)?
Staff A
1
Staff B
Rand(1, Bmax)?
Staff B
3
Staff C
Rand(1, Cmax)?
Staff C
4
Staff D
Rand(1, Dmax)?
Staff D
2
=>
Using such method, every sample picked is independent and does
not affect the next sample to be picked. Thus the sampling point is
“jumping” in the solution space. This may improve the performance of
discovering solutions that gathered in the one part of the solution space.
5.5.6. Genetic Algorithm
Although Multi-directions method may shorten the time for
discovering solution, there may be the chance that the time is increased. It
is because Multi-directions search is work on a totally random basis. There
is no guidance on which direction to go. If we are lucky, we can find
solution in the first iteration. But if we are not lucky, there will be no
solutions found even it iterated for millions of times. So, we want a
method which can provides randomness with certain degree of direction.
Genetic algorithm simulates the nature’s evolution process.
Individual in the nature produce offspring by mating with another
Lam Chi Wo MSC 50447402
individual. The chromosome of the produced offspring is created by
“crossovering” the chromosome of its parents. That means some genes of
the offspring are obtained from one of its parents and the other genes are
obtained from another parent. This is why, in the nature, offspring are
usually having some similarity but not equal to their parents. And if the
chromosome of the offspring makes itself able to survive in the world, the
offspring will be able to mate with another individual to produce another
offspring. This process keeps good genes alive in the world. However, if
offspring has some bad genes, the offspring will not be able to survive and
hence without chance to produce offspring. This will destroy the bad genes.
By continue the process many times, the quality of chromosome will be
keep improving and only individuals having good chromosome will be left
in this world. Genetic algorithm applies this idea into problem solving. By
defining the genes with problem variables, continuously producing
offspring by mating individual solution, and kill those bad solution, after
certain generations, all individual left will be good answer to the problem.
To use Genetic Algorithm in our problem, we define the gene as below:
Gene 1
Row selection for staff A
Gene 2
Row selection for staff B
Gene 3
Row selection for staff C
……
……
The length of the chromosome is defined as the number of staff in
the roster. Each gene in the chromosome represents a row selection for the
corresponding staff. So, each chromosome is representing one combination
of rows, or we can say it is representing one roster.
Lam Chi Wo MSC 50447402
With the Gene definition decided, we have to define some
parameters for the problem.
Parameter
Explanation
Typical value
Population Size
The number of individuals created for 50
each iteration
Cross over rate
The chance that the chromosome will
0.9
be cross-over with another individual in
a generation. These probabilities range
from 0 to 1.
Generation Gap
The fraction of individuals that do not 0.98
go into the next generation. It is
specified as a fraction from 0.0 to 1.0
The steps of the operation are listed as below:
1. Create a generation randomly
2. Evaluate and sort the individuals by demand fulfilment
3. Good individuals are left for producing offspring.
4. Form a new generation by combining the offspring produced and the
individual left in last generation.
5. Repeat step 2 until iteration criteria fails.
Analyzing the Genetic Algorithms, it is a random approach as the populations
are generated randomly. However, as part of the population is generated by
crossovering good solutions, the search using GA is not totally random. It
searches over the solution space randomly and at the same time looking
around the space near the good solution found.
Lam Chi Wo MSC 50447402
5.6.
Evaluation
After obtaining a list of “legal” roster that complies with the
demand requirement, we have to choose the best one to be our final
answer. To evaluate the “good” or “bad” of a roster, the soft constrain
is used.
5.6.1. Shift distribution
Within the space of “legal” roster solutions that met the
demand constrains, there exist some solutions that the distributions of
shifts are not even. Below is one of the examples.
Day 1
Day 2
Day 3
Staff A
D
D
D
Staff B
Off
Off
Off
1
1
Demand 1
….
for D
It is obvious that the roster above is not a good one, although it
can meet the requirements of demand. The shifts are unevenly
distributed as staff A has to work consecutively for 3 days, while staff
B no needs to work in this 3 days. Therefore, we have to consider the
shift distribution when looking for good roster solution. Beside the
distribution of off day, the distribution of special shift has to be
considered too. Night shift is one of special shift that we have to
consider.
Lam Chi Wo MSC 50447402
5.6.2. The fitness function
Since the vertical constrains in our case is quantitative, a fitness
function will be used to judge or evaluate the resulting roster. In our
case, there are three vertical constraints to meet:
1. Demand constrain (Meet demand with minimum over-assignment)
2. Off day distribution
3. Night shift distribution
So we use three indexes to cater for the three constrains. They are
Demand fulfilment DF
= Total number of shift that the number
of staff assigned is not equal to the
number of staff required.
Off day deviation OD
= Summation of standard deviation of
the count of off day for each staff
Night shift deviation ND
= Summation of standard deviation of
the count of night shift for each staff
In order to reflect the importance of these three indexes, weight
factors are assigned as below:
Index
Weight
Demand Fulfilment, DF
2
Off day deviation, OD
1
Night shift deviation, ND
3
So, the fitness function is defined as below, and it will be used
to judge whether a roster solution is good or not.
F fitness = 3 × ND + 2 × DF + OD ----------------------------------------(2)
Lam Chi Wo MSC 50447402
5.6.3. Case base
As randomised approach is used, there may be the case that if
we run the algorithm for 3 times, the qualities of the “best rosters”
being found in 3 runs are not the same, and may even decreasing. This
is due to the randomized sampling method. The samples picked for
evaluation in each time are not the same, so the “best” solution in the
first run, may not be the best one in another run. To overcome this
repeatability problem, the idea of case base is adopted. For every run,
the solution number of the best solution will be stored into the database
with a signature of the problem. For any future run, the database will
be queried to see if there is any record saved having the same problem
signature. If yes, that solution will be retrieved, and it will be
compared with the best solution found in the sampled solutions to
obtain the best among them. If the best solution in the sampled set is
better than the retrieved one, the database record will be updated with
this better solution number. Using such case base comparison, the
quality of the “best” solution can be retained in different runs, and it
ensures the quality of the result will only be the same or improving, if
we repeat the procedure again and again.
5.6.4. Problem signature
Like other case base problem, one of the important issues is the
definition of problem signature. How do we know the problem we
currently dealing with is the same as the one stored in database? To
define the signature of the problem, we have to get balance between
the size and the amount of information stored in the signature. Since
the signature will be used as the key for searching, it should be kept
small and simple to facilitate efficiency searching.
Lam Chi Wo MSC 50447402
Recalling the analysis of the problem in previous section, the
( )
n
total number of possible solution is m d , where m is the number of
shift, d is number of day, and n is the number of staff. So, if these
numbers of two problems are the same, that two problems will have
the same number of total possible solutions. And that is the upper
bound of the size of the search space. However, as we apply backtracking in the row forming stage to reduce the search space, the actual
total number of possible solution is not only affected by these three
numbers. Constrains will also affect the problem size. However, it
would be too complex and lengthy to store all constrains in the
problem ID. In order to get a balance between space and accuracy, the
outcome of constrains is being used. In the row forming stage, the shift
constrains are used to filter out the solution having illegal shift patterns
and this operation reduced the number of possible rows for each staff.
We then make an assumption that, if two problems A and B, having
the same number of shift, staff and day, and the number of filtered
solutions for all staffs of problem A is the same as the number of
filtered solutions for all staff of problem B, we assume that there are
high chances that both problem A and B are using the same set of
constrain.
Thus, we define the problem ID as follow:
ProblemID= [Number of days]
+ [Number of Shift]
+ [Number of possible rows per staff]
Lam Chi Wo MSC 50447402
5.7.
The overall algorithm
The following flow chart summarized the proposed algorithm.
Lam Chi Wo MSC 50447402
6. System Analysis
6.1.
Basic system requirement
•
Implement the designed algorithm for rostering
•
Generate roster for any number of days
•
staff information editing
•
Shift setting editing
•
Shift constrains editing
•
Demand setting editing
•
Store setting and roster data in database
•
With users login level to restrict changing of staff and shift
information, as well as the user login information
6.2.
Functional specification
1. The system software contains an integrated user interface.
2. It is divided into 6 parts, namely “User Management”, “Staff
settings”, “Shift settings”, “Demand settings”, “Fitness Function”
and “Rostering”.
2.1 User management
•
Manage user levels and module accessibility
•
Add a new user with suitable access right depend on their
job nature and grade seniority.
•
Edit user information (username, password and user right)
•
Remove existing user who left the company.
•
This module can only be accessed by Super User
•
2.2 Staff settings
•
Maintain (insert/update/delete) staff and update
corresponding information.
Lam Chi Wo MSC 50447402
2.3 Shift setting
•
Maintain (insert/update/delete) shift and update
corresponding information
•
Maintain (insert/update/delete) shift constrains. Allow user
to define shift pattern block.
2.4 Demand setting
•
Allow user to select any number of days
•
Load demands within selected day range from database
•
Update demand value
•
Save updated demand into the database
2.5 Fitness setting
•
View and update the weight factor of the fitness function
2.6 Rostering
1. Allow user to select any number of days for rostering
2. Generate roster of the date selected by user
3. Allow user to change the maximum step size
4. Save the generated roster into the database
Lam Chi Wo MSC 50447402
3. User’s Authority Right
Authority Right
1
Super user
General user
User management
Insert user
Update user
Delete user
2
Staff settings
Insert staff
Delete staff
3
Shift settings
Insert shift
Delete shift
Add shift pattern block
Delete shift pattern block
4
Demand setting
Load demand
Update demand
Safe demand
5
Fitness function
View weight factor
Update weight factor
6
Rostering
Generate roster
Save roster
4. Assumptions
•
The system software is using within a local area network where
database server can be accessed through the network
•
The program is used by single user simultaneously
•
User has to login with ID and password before using any functions
•
Lam Chi Wo MSC 50447402
6.3.
Use Cases analysis
RosterBuilder
Edit system user
Edit staff
information
Super user
Edit Shift setting
«inherits»
Edit fitness
fucntion
Edit demand setting
Generate roster
General user
Login System
Lam Chi Wo MSC 50447402
Lam Chi Wo MSC 50447402
6.4.
Use-case scenario
Name: Login System
Input: Login Name, Login Password
Output: No
Participant: General user, Super user
Goal: Start application and set the accessibility of function modules
according to user type if the login name and password is valid.
Pre-condition: User account valid
Name: Edit Demand Setting
Input: Start date, End date, Day demand
Output: No
Participant: General user, Super user
Goal: Update the demand stored in database for the day specified by start
date and end date
Pre-condition: Start date and end date valid (i.e. end date behind start date),
day demand is integer.
Name: Edit Staff information
Input: Staff ID, staff name and staff Type
Output: No
Participant: Super user
Goal: Update staff records stored in database
Pre-condition: Staff ID is unique
Name: Edit Shift setting
Input: Shift code, Shift name, shift type, shift constrains
Output: No
Participant: Super user
Goal: Update shifts records stored in database. Update shift constrains
stored in database
Pre-condition: Shift code is unique, shift code in shift constrain is valid.
Name: Edit Fitness function
Input: Weight factors for the terms in the fitness function
Output: No
Participant: Super user
Goal: Update the weight factor records stored in database
Pre-condition: weight factor records exist in database
Name: Generate roster
Input: Start date, end date, sampling strategy, settings for corresponding
strategy
Output: No
Participant: General user, Super user
Goal: Generate roster of the date specified by start and end date. Save the
generated roster into database.
Lam Chi Wo MSC 50447402
Pre-condition: Shift, Staff, Demand setting already entered and stored in
database.
Name: Edit system user
Input: login name, login password, user type.
Output: No
Participant: Super user
Goal: Update user records stored in database.
Pre-condition: login name is unique, password is not blank.
6.5.
ShiftManager
-acnwork
-acoff
-acwork
Conceptual Class diagram
uses
RosterManager
1
Rules
*
1
create
*
DemandManager
-startDate
-endDate
-dayDemand
TreeNode
creates
Roster
1
has
Tree
*
-rootNode
-treeSize
1 has
1
*
-childNodeList
-nodeLabel
-nodeLevel
-parentNode
*
UserManager
RosterRow
-totalNumOfRow
Manages
StaffManager
1
Staff
*
-staffID
Lam Chi Wo MSC 50447402
7. System Design
7.1.
Design Class Diagram
7.1.1. Presentation Layer
RosterBuilder::StartUpForm
-buttonDemand_Click()
-buttonRoster_Click()
-buttonRules_Click()
-buttonShift_Click()
-buttonStaff_Click()
-buttonUser_Click()
-setButtons()
+StartupForm()
RosterBuilder::LoginForm
RosterBuilder::StaffForm
RosterBuilder::UserForm
-exitButton_Click_1()
+getUserType()
-loginButton_Click_1()
+LoginForm()
+StaffForm()
+buttonBack_Click()
+laodStaffGrid()
+staffForm_Load()
+buttonAdd_Click()
+buttonBack_Click()
+buttonRemove_Click()
+loadUserGrid()
+UserForm()
+UserForm_Load()
RosterBuilder::ShiftForm
RosterBuilder::DemandForm
-buttonBack_Click()
-buttonGet_Click()
-buttonSave_Click()
+DemandForm()
-AddConstrainButton_click()
-backButton_Click_1()
-buttonConstrainSave_Click()
-loadShiftGrid()
#MoveDnButton_Click()
+ShiftForm()
+ShiftFromLoad()
RosterBuilder::RosterForm
+generateRoster()
+RosterForm()
+setStatusBar()
+showRoster()
+buttonBack_Click()
+buttonGenerate_Click()
+fromDatePicker_ValueChanged()
+RosterForm_Load()
+toDatePicker_ValueChanged()
RosterBuilder::MethodSetupForm
-buttonGo_Click()
-checkBox1_CheckedChanged()
-checkBox2_CheckedChanged()
-checkBox3_CheckedChanged()
-checkBoxConditions()
-comboBox1_SelectedIndexChanged()
+MethodSetupForm()
RosterBuilder::FitnessForm
+buttonBack_Click()
+buttonSave_Click()
+FitnessForm()
-FitnessForm_Load_1()
7.1.2. Domain Layer
RosterBuilder::ShiftManager
RosterBuilder::StaffManager
+code2Shift()
+getACNWrok()
+getACOff()
+getACWork()
+getNightShfits()
+getNumOfWorkShift()
+getOffShift()
+getShiftconstrains()
+getShiftList()
+getShiftTable()
+loadDbData()
+ShiftManager()
+getNumOfStaff()
+getStaff()
+getStaffList()
+getStaffTable()
+loadStaffData()
+StaffManager()
«utility»
RosterBuilder::DBConnector
+cloaseDB()
+connectDBAdaptor()
+connectDBNonQuery()
+connectDBNonQuerySP()
+connectDBQuerySP()
+connectDBReader()
-openConnection()
RosterBuilder::Staff
+getConsecutiveNight()
+getConsecutiveOff()
+getConsecutiveWork()
+getLastShiftCode()
+getMaxNumOfSol()
+getRosterRow()
+getStaffID()
+setRosterRow()
+Staff()
RosterBuilder::Rules
+buildCheck()
+checkConsecutiveNight()
+checkConsecutiveOff()
+checkConsecutiveWork()
+checkDemand()
+checkNightShfits()
+checkOffShifts()
+checkShiftsOrder()
+code2Shifts()
+evaluate()
+getDivider()
+getNumOfDay()
+getShifts()
+getTotalNumOfSolution()
+id2Sol()
+Rules()
+scoreOkSolution()
+sol2Id()
RosterBuilder::Statistic
+std()
RosterBuilder::UserManager
+checkLogin()
+getUserTable()
-loadDBData()
+refreshUserTable()
+updateUserData()
+UserManager()
RosterBuilder::RosterManager
-buildTree()
+getStaff()
+RosterManager()
-scoreOkSolution()
-searchMethod1()
-searchMethod2()
-searchMethod3()
+startGeneration()
RosterBuilder::GAIndividual
RosterBuilder::GAEngine
+crossOver()
+GAEngine()
-makeChromosome()
+makePopulation()
+checkEqual()
+getChromID()
+getChromosome()
+getScore()
+GAIndividual()
+setChromID()
+setChromosome()
+score()
RosterBuilder::TreeNode
RosterBuilder::Roster
+getNumOfDay()
+getOverallScore()
+getRosterList()
+getSolID()
+Roster()
+setDayDemand()
+setNightSTD()
+setOffSTD()
+vector2Roster()
RosterBuilder::DemandManager
RosterBuilder::RosterRow
+DemandManager()
+getDayDamand()
+saveDayDemand()
+getTotalRowNumber()
+getTreeListItem()
+RosterRow()
RosterBuilder::Tree
+buildTree()
+getTreeList()
+getTreeSize()
+node2List()
+Tree()
+addChild()
+getChildList()
+getChildNode()
+getConsecutiveNight()
+getConsecutiveOff()
+getConsecutiveWork()
+getLabel()
+getNodeLevel()
+getParent()
+getShiftCode()
+setConsecutiveNight()
+setConsecutiveOff()
+setConsecutiveWork()
+TreeNode()
Lam Chi Wo MSC 50447402
7.2.
Sequence Diagram
Generate Roster
System
Boundry
RosterForm
User
MethodSetupForm
RosterManager
StaffManager
ShiftManager
fromDatePicker_ValueChanged()
toDatePicker_ValueChanged()
buttonGenerate_Click()
MethodSetupForm()
buttonGo_Click()
generateRoster()
startGeneration()
getStaffList()
staffList
getShiftList()
shiftList
buildTree
searchMethod1
scoreOkSolution
showRoster()
Lam Chi Wo MSC 50447402
Get Demand
System
boundry
DemandForm
DemandManager
General User
buttonGet_Click()
getDayDamand()
dayDemand
Get Shift
System
boundry
ShiftForm
ShiftManager
Super User
ShiftFromLoad()
getShiftTable()
shiftTable
Since the sequence diagram of other operations are quite similar, they are
omitted in this report.
Lam Chi Wo MSC 50447402
Database Design
7.2.1. ER diagram
Lam Chi Wo MSC 50447402
7.2.2. Table listing
Table Name
Description
Roster
To store the ID and description of a saved
roster
rosterItem
To store individual item of a roster, each
item is pointing to one rosterID
Shift
To store the shift code and shift type.
Staff
To store the name and ID of staff that
should be included in the roster
Demand
To store the demand per shift per day
Constrains
To store the constrains of roster generation.
Constrains are stored as a constrain type
and constrain value pair.
Users
To store the login ID, password and type of
users will use the system
Casebase
To store records of solution found in the
past.
7.2.3. Table Details
Table: roster
rosterID
nvarchar
rosterDescription nvarchar
ID of roster
Description of roster
Table: rosterItem
itemID
int
ID of item
rosterID
nvarchar
Pointing to the corresponding roster
staffID
nvarchar
id of corresponding staff
itemDate
smalldatetime
Date of the item
itemShift
nvarchar
Id of the corresponding shift
Table: shift
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shiftCode
nvarchar
ID of shift
shiftName
nvarchar
Name of the shift for display
shiftType
nvarchar
Type of the shift. It can be:
“W” – normal working shift
“N” – night shift
“O” – day off
Table: Staff
staffID
nvarchar
ID of staff
staffName
nvarchar
Name of staff
lastShiftCode
nvarchar
To store the last shift of the staff in
previous roster. It is stored for faster
reference
lastConsecWork int
To store the number of accumulated
work shift at the end of last roster. It is
stored for faster reference
lastConsecNight int
To store the number of accumulated
night shift at the end of last roster. It is
stored for faster reference
lastConsecOff
int
To store the number of accumulated
day of at the end of last roster. It is
stored for faster reference
Table: demand
demandID
int
ID of demand item
demandItemDate smalldatetime Demanding date
demandItemShift nvarchar
Demanding shift
demandQty
Number of staff required
int
Table: constrains
constrainID
int
ID of constrain item
constrainType
nvarchar
Type of constrain
“Shift” – shift block pattern
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“DFF” – weight factor for “Day
fulfilment
“NDF” – weight factor for “Night shift
distribution”
“ODF” – weight factor for “Off shift
distribution
“MCN” – max number of consecutive
night shift allowed
“MCW” – max number of consecutive
work shift allowed
“MCO” – max number of consecutive day
off allowed
“SCV” – stop criteria value.
“MSS” – max step size in sampling
constrainValue nvarchar
The value of corresponding constrain
Table: caseBase
problemID
nvarchar
ID to the problem
solutionID
nvarchar
corresponding solution ID
username
nvarchar
Login name of user
userPassword
nvarchar
Login password of user
userType
nvarchar
Type of user:
Table: users
“Super” – user which can access all
functions
“General” – user which can access only
the “Rostering” and “Demand setting”
modules
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7.3.
Interface design
Since Visual Studio for .NET provides a powerful UI capability,
and a rich set of UI component, the GUI for the system is designed
directly inside Visual Studio.
Login Menu
Main Menu
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Rostering
Generate Roster – Linear Forward Search
Generate Roster – Multi-directions
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Generate Roster – Genetic Algorithm
Roster Result
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Demand Setting
Staff Setting
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Shift setting
Fitness Function setting
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User Management
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8. System Implementation
8.1.
Programming language
Before starting programming, an important step is to choose the
right programming language or programming tools. We have to
consider the performance, functions, database connectivity and
flexibility of the tools. In additions, we have to consider the form and
type of the program output, and of course the availability of the tools.
Since roster generation is an in-house process and there are
only a few users needed to operate the system, to reduce complexity
and improve performance, the system will be built as a stand-a-lone
application. As Microsoft Windows is the most commonly used OS,
the program will be built as a Windows application. With such criteria,
only Windows based tools are considered.
Looking around the programming tools available to the writer,
there are 3 candidate tools selected for consideration. They are:
•
Java of J2SE from Sun Microsystems
•
C# of Visual Studio for .NET from Microsoft
•
C++ of the C++ Builder from Borland
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A comparison between the tools is summarized in the table below:
Language type
Performance under
Java
C#
C++
Object Oriented
Object Oriented
Procedural
Poor
Good
Good
Good
Good
Medium
JDBC-ODBC
ADO.NET
BDE - ODBC
Windows
Functions (library
provided)
Database connectivity
• Multi-platform • Windows or Internet
Flexibility
(depends on
availability of
•
based
Windows
application
• .NET compatible
only
Visual Studio .NET
C++ Builder,
JVM)
• Can be
converted to
Web
application
Development
netBeans IDE,
Environment
JBuilder
Visual Studio .NET
Considered the comparison between tools, C# is chosen as the
development language used with the following reasons:
•
The target system require good performance
•
Object oriented language is preferred for easier development
and future expansion.
•
C # provides a one-level database access which having better
performance and reducing complexity in database connection.
•
Visual Studio for .NET provides a powerful development and
debugging environment.
•
Syntax similar to JAVA which shortened the learning time
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8.2.
Database System
Besides programming language, the choice of database system
is also vital. The criteria of choosing database system for our system
would be the storage and query capability. With the two commonly
used Windows based database system, Microsoft SQL server 2000 and
Microsoft Access, a comparison is summarized as the table below:
SQL Server 2000
Access 2003
Good
Basic
As an server
Yes
No
Backup and recovery
Yes
No
Form and Report building
No
Yes
Graphical User Interface
Basic
Good
Security
Good
Good
Storage capability
Good
Basic
Max. 2147483647
Max. 255
characters
characters
Max 262
Max 231
Database Engine
Data types – String/Text
Data types – Integer
With the comparison result shown above, Microsoft SQL
server 2000 is preferred with the following reasons:
•
Large number of records is needed for storing even single roster.
•
In our application, huge number will be processed and may be
stored in database, so the size limit of Access will lead to limitation
or even error in operation.
•
Roster is important information that a system with backup and
recovery is preferred.
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8.2.1. System Architecture
8.3.
System Testing
Besides class unit tests being done during development, to
check whether the system functions as what we designed after
integration, a use-case based testing are used.
Test Case
Test plan
Expected result
Login
System
Login system using correct
user name and password
with General user type
Application starts
with only “Generate
roster” and
“Demand setting”
enabled
Application starts
with all buttons
enabled
Warning message
prompt. Application
does not start.
Warning message
prompt. Application
does not start.
Demand of the days
between start date
and end date shows.
Warning message
prompt. After user
click to close the
message, the start
date change to 1
day before end date.
Successful message
prompt. Records in
database updated.
Login system using correct
user name and password
with Super user type
Login system with
incorrect user name
Login system with
incorrect password
Edit
Demand
setting
Get demand with correct
start date and end date
Change start date behind
end date
Modify the demand of the
any date and shift. Click
save button.
Testing
result
As expected
Classes involved
LoginForm,
DBConnector,
StartUpForm
As expected
As expected
As expected
As expected
DemandForm,
DemandManager,
DBConnector
As expected
As expected
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Successful message
prompt. Records in
database updated.
Add a staff with staff ID
Warning message
already stored in database
prompt. No
modification in the
database
Remove a staff
Successful message
shown. Records in
database removed
Edit shift
Add a shift with correct
Successful message
setting
shift ID
prompt. Records in
database updated.
Remove a shift
Successful message
shown. Records in
database removed
Add a shift constraint
Successful message
prompt. Records in
database updated.
Edit Fitness Modify a weight factor and Successful message
function
save.
prompt. Records in
database updated.
Roster generate and
Generate
Generate roster with
shown in Grid
roster
correct start date and end
table, the score of
date with one of the
the roster and time
methods.
used show in the
status bar
Warning message
Change the start date
behind end date
prompt. After user
click to close the
message, the start
date change to 1
day before end date.
As expected
Edit system Add a new user with
user
correct login name
As expected
Edit staff
Add a staff with correct
information staff ID
Add a new user with login
name already exist in the
database
Remove a user
Successful message
prompt. Records in
database updated.
Warning message
prompt. No
modification in the
database
Successful message
shown. Records in
database removed
StaffForm,
StaffManager
DBConnector
As expected
As expected
As expected
ShiftForm,
ShiftManager,
DBConnector
As expected
As expected
As expected
FitnessForm,
DBConnector
As expected
RosterForm,
RosterManager,
Rules,
Tree,
TreeNode,
Statistic,
Roster,
RosterRow,
GAEngine,
GAIndividual
DBConnector
DemandManager
ShiftManager.
StaffManager
As expected
UserForm,
UserManager,
DBConnector
As expected
As expected
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8.4.
System Evaluation
8.4.1. Performance Evaluation
To evaluate the performance of the system, a simple Genetic
Algorithm model was built for comparison. The GA model was run in
Microsoft Excel using a commercial GA engine – The GeneHunter. A
testing scenario was setup and was solved by the two systems. Several
performance indexes were used for analysis.
Besides comparing with other approach, the performances of
the three sampling strategies are also evaluated.
8.4.2. The Gene Hunter
GeneHunter is a Microsoft Excel add-in program which allows
the user to solve optimization problem from an Excel spreadsheet. It
provides ready-to-go GA functions and configurations that can be used
without any programming effort.
8.4.3. Simple GA model
The gene definitions are as follow:
Gene Definition
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Gene for staff 1
D
A
S
N
Off
S
N
Gene for staff 2
A
S
N
Off
D
S
N
……
The genes for each staff are joined to form the chromosome for
operation. So, for a gene for 10 staff and 7 days, the gene will have 70
elements.
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Fitness Function
For fair comparison, the same fitness function should be used
in both systems, however, as GA algorithm require more index to
guide the searching direction, so in addition to the terms used in the
original fitness function, a few more terms are added. And this updated
fitness function will be used for comparison of result.
The fitness function for GA is defined as follow
GAF
fitness
= 3 × ND + 2 × DF + OD + 10000 × SR + 10000 × DU + 100 × OCN
+ 100 × OCW + 100 × OCO
where,
ND=Night shift distribution
DF= Demand Fulfilment
OD= Off day distribution
SR= Shift order reversed, shift assigned are not follow shift order
DU=Demand under, number of staff assigned cannot meet the demand
OCN = Over consecutive night
OCW=Over consecutive work
OCO=Over consecutive off
Since the situations of “Demand under” and “Shift order reversed” are
highly unwanted, the weight factor for DU and SR is much larger than
the others
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GA Operation configurations
Objective
Minimize fitness function
Population size
50
Cross over rate
0.9
Mutation rate
0.01
Generation Gap
0.98
Diversity operator
Applied
Elitist Strategy
Applied
Stop criteria
Best fitness unchanged after 75 generations
8.4.4. Evaluation Scenario
The scenario is to prepare a 7 days roster for 10 staffs with the
shift and demand and constrains as follow:
Staff
Staff Name
Last shift
Accumulated
Accumulated
Accumulated
number of
number of
number of off
working day
night shift
day
Staff A
D
1
0
0
Staff B
A
2
0
0
Staff C
N
3
1
0
Staff D
Off
0
0
1
Staff E
D
1
0
0
Staff F
A
2
0
0
Staff G
N
3
2
0
Staff H
Off
0
0
2
Staff I
D
1
0
0
Staff J
A
2
0
0
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Shifts
Shift Code
Shift Description
Start time
End Time
D
Day Shift
07:30
16:30
A
Afternoon Shift
14:30
23:30
N
Night Shift
23:00
08:00
(next day)
Off
Day off
Demand
Shifts
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
D
3
3
3
3
3
3
3
A
2
2
2
2
2
2
2
N
2
2
2
2
2
2
2
Constrains
•
The shifts are in the order of D -> A -> N, which every shift must
be followed by the same shift or any shift behind itself in the order
list. That means, for shift “A”, it can be followed by Shift A, N or
Off. And shift “Off” can be followed by any shifts.
•
The maximum number of consecutive night shifts (N) allowed = 3
•
The maximum number of consecutive working day allowed = 6
•
The maximum number of consecutive off day allowed = 3
•
The night shift (N) and day off (Off) should be evenly distributed.
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8.4.5. Result
8.4.5.1. RosterBuilder Vs GeneHunter
The scenario is solved using RosterBuilder and the GeneHunter in
Excel.
Result obtained by RosterBuilder
Result obtained by GeneHunter
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8.4.5.2. Result Analysis
The results from both systems are compared as follow:
Time used
Fitness
RosterBuilder
GeneHunter
(Stop if 5 feasible solutions
(Stop if fitness not improved
found)
over 75 generations
22 mins.53 sec.
8 sec.
10.7097
20005.9169
It can be seen that the result of RosterBuilder is much better than
GeneHunter, however, the time used in GeneHunter is much less than
RosterBuilder.
So, in order to have a better comparison, the GeneHunter is rerun with the stopping criteria being set to allow the running time
similar to RosterBuilder. The result is shown as below
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RosterBuilder
GeneHunter
(Stop if 5 feasible solutions
(Stop if run for 23 mins)
found)
Time used
22 mins.53 sec.
23 mins
10.7097
10002.9169
Fitness
It can be seen that there is further improvement in the result
from GeneHunter, however it is still far away from the result obtained
by RosterBuilder.
Analyzing the results further as the table below, we found that
the high score of the GeneHunter fitness is due to one “Shift Reversed
Order” exist in its result. “Shift Reversed Order” is highly unwanted
because it means the rest time between two days of the staff cannot
meet the requirement set by the regulations.
RosterBuilder Result
GeneHunter Result
Demand Under
No
No
Demand Over
No
No
Shift Reversed Order
No
Yes
Over Consecutive Night
No
No
Over Consecutive Work
No
No
Over Consecutive Off
No
No
8.4.5.3. Observations from the results
According to the comparison between RosterBuilder and
GeneHunter, we can say that RosterBuilder is better than GeneHunter
in the sense that the results from RosterBuilder are promised to comply
with the hard constrains, while results from GeneHunter are not, even
the penalty for hard constrains are very high.
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8.4.6. Sampling Strategies in RosterBuilder
To evaluate the performance of the three sampling strategies,
the three sampling strategies are used to solve a smaller rostering
problem with different configurations. The following index is used:
1. Time used to discover the first one and first 5 solution.
2. Time use to discover the first with different problem size
3. The quality of the solution found.
8.4.7. Results
The results are shown as below:
1. Time to discover the first one and first 5 solution.
Time used to discover solution in a 4 days roster
600
Time used (sec)
500
400
300
200
100
0
Linear Forward
Multi-directions
Genetic Algorithm
Sampling Strategy
1st solution found
first 5 solutoins found
2. Time use to discover the first solution with different problem size
Running time vs Problem Size
Time used to found 1st solutoin
(sec)
10000
1000
100
10
1
0
1
2
3
4
5
6
0.1
0.01
Number of day in roster
Linear Forward
Multi-directions
Genetic Algorithm
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3. The quality of the solution found
Quality of the solution found
Solution Score (smaller is better)
2.5
2
1.5
1
0.5
0
2
3
4
Number of days in roster
Linear Forward
Multi-directions
Genetic Algorithms
8.4.8. Observations from the results
Referring to the results obtained, the following points are observed.
1. With the same problem size, “Linear Forward” is the fastest
method to find solution. And “Genetic Algorithm” is the
slowest.
2. Increasing the problem size (number of days in roster),
“Genetic Algorithm” has the fastest increase in running
time.
3. “Genetic Algorithm” has the higher chance to get “good”
solution comparing to the other 2 methods.
4. The speed and solution quality of Multi-directions method
lies between “Linear Forward” and “Genetic Algorithm”.
5. The running time of all methods increase rapidly with the
problem size (number of days in roster).
6. Each sampling strategy has its own strength and weakness
and are tabled below:
Linear Forward Multi-directions
Genetic Algorithm
Speed for 1st solution
Fast
Medium
Slow
Quality of solution
Low
Medium
High
Running time increase with
small
medium
large
problem size (comparatively)
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7. Recommendations: Using the case base to store past result
in the database, user can use the “Linear forward” or
“Multi-directions” to find the solution first, then use
“Genetic Algorithm” to look for better solution around the
solution found.
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9. Conclusion
9.1.
Achievements
The characteristic of the problem being solved is analysed, a
search on the literature is down to find possible solutions published are
explored. After studied approaches have been tried in the field, a
customized algorithm is designed using ideas obtained during literature
review. The algorithm is adjusted and modified several times to
improve its performance.
Having the algorithm defined, a rostering system, called
RosterBuilder, is built to implement the concepts. Before building the
system, an Object Oriented system analysis and design is done by
using UML and a database design is done by using ER diagram. The
system is then coded using C# and the database is built using SQL
server.
The functions of the system are tested with unit testing during
development. And a integration use-case based testing has been done
to verify the behaviour of the system as designed.
The performance of the system is evaluated using an evaluation
scenario. The scenario is also run using another algorithm, the Genetic
Algorithm, which is commonly used in recent research. The results
from two algorithms are compared and observations on the
performance are noted.
To test the effect of sampling strategy, three sampling strategies
are implemented and evaluated. The performances of the three
implemented strategy is evaluated with different problem configuration.
Recommendation has been made on the use of different sampling
stragegy.
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9.2.
Further development
With the result and observation in the evaluation, several
further development areas can be suggested.
1. Further reduction of the solution space size
In the algorithm presented in this paper, the size of the solution
space is reduced by using the horizontal constrains to limit the choice
of the rows. Although a large portion of rows are filtered using this
method, the size of the overall solution space is still very huge. So,
more constrains or methodology is needed to further reduce the size of
the solution space. One of the possible directions is to filter the rows
using the demand constrains. The idea is that if there is no demand for,
say, D shift for the first day, any row having “D” in the first day can be
ignored. Of course, further study on the details methodology and
performance is needed before implementing the idea.
2. Multi-skills consideration
In the system presented in this paper, skill is assumed
homogeneous for staff. That means every staff has only one skill. The
assumption is set solely because of simplicity. Since fitness function
scoring is used in the system, multi-skills problem should be solved by
redefining the fitness function. Of course more work is needed to
verify this approach in multi-skills situation.
Lam Chi Wo MSC 50447402
3. Demand estimation
In current system, the demand - which is one of the critical
factors to the problem - is entered by user. And users are assumed to be
experienced to enter the correct demand input and they estimate the
demand by their experience or memory. Actually, the staff demand in
aircraft maintenance can be calculated by the pre-noticed work list. So,
one of the valuable further development is to add demand estimation
capability to the system.
4. Reduce resources consumptions
In current system, large portion of system resources including
CPU time and memory are consummated even for generating a roster
for only a few days. Due to the limited resource in the computer used
for testing, roster with longer duration will result in lack of memory
error. This is mainly caused by the tree representation of the possible
row. Although tree already is an effective representation, it still
consume a lot of memory if the tree is extremely large, which occurs in
the case of long period roster. So, ways to further reduce the resources
consumptions are needed.
Lam Chi Wo MSC 50447402
References
[1]
Michael Pinedo
Scheduling Theory, Algorithms, and Systems
Prentice Hall
[2]
Glover, Fred.
Tabu Search
Boston : Kluwer Academic Publishers, c1997.
[3]
Michel Gendreau
An Introduction to Tabu Search
University of Montreal
[4]
John M. Usher
Preliminary Review of the Airline Scheduling Domain
Mississippi State University
[5]
NIKLAS KOHL, STEFAN E. KARISCH
Airline Crew Rostering: Problem Types, Modeling, and Optimisation
Annals of Operations Research 127, 223-257, 2004
[6]
A.T. ERNST, H. JIANG, M. KRISHNAMOORTHY, B. OWENS and D.
SIER
An Annotated Bibliography of Personnel Scheduling and Rostering
Annals of Operations Research 127, 21–144, 2004
[7]
Azmat, C.S., T. Hürlimann, and M. Widmer. (2004).
“Mixed Integer Programming to Schedule a Single-Shift Workforce under
Annualized Hours.”
Annals of Operations Research 128, Special Issue on Staff Scheduling and
Rostering, 199–215.
[8]
Eitzen, G., G. Mills, and D. Panton. (2004). “
Multi-Skilled Workforce Optimisation.”
Annals of Operations Research 127, Special Issue on Staff Scheduling and
Rostering, 359–372.
[9]
Alfares, H. (1988).
“Aircraft Maintenance Workforce Scheduling: A Case Study.”
Journal of Quality in Maintenance Engineering 5(2), 78–88.
[10]
Dijkstra, M., L. Kroon, J. van Nunen, and M. Salomon. (1991).
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“A DSS for Capacity Planning of Aircraft Maintenance Personnel.”
International Journal of Production Economics 23(1–3), 69–78.
[11]
Kroon, L., M. Salomon, and L. VanWassenhove. (1997).
“Exact and Approximation Algorithms for the Tactical Fixed Interval
Scheduling Problem.”
Operations Research 45(4), 624–638.
[12]
M.H. Alsuwaiyel
“Algorithms Design Techniques and Analysis”
World Scientific
[13]
Jawahar Puvvala and Alok Pota
“.NET for Java Developers”
Addison-Wesley
[14]
John Sharp and Jon Jagger
“Microsoft Visual C# .NET”
Microsoft Press
[15]
“GeneHunter” manual
AI Trilogy
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10. Appendix
10.1.
Project Schedule
Period
September 2004
October 2004
November 2004
December 2004
January 2005
February 2005
March 2005
April 2005
10.2.
Task
Background study
Background study
Literature review
Literature review
Literature review
Define & testing solution model
Define & testing solution model
System Analysis and design
System Design & Coding
System Coding & Testing
Documentation
Report writing
Presentation preparation
Attachment CD content
•
Report Document (Acrobat PDF format)
•
RosterBuilder Source Code (Visual Studio Project Format)
•
RosterBuilder Database (Microsoft SQL server 2000 backup file)
•
GeneHunter testing spreadsheet (Microsoft Excel Format)
10.3.
System requirements
•
•
•
OS: Windows XP with .NET framework installed
Database: Microsoft SQL server 2000
PC running the application and the database server are connected in
the same network.
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10.4.
Installation Guide
1. Restore the database backup in the CD (“\DB backup\”) to
Microsoft SQL server 2000 to a database named
“RosterBuilderDB”.
2. Copy all files in the
“\samproject\RosterBuilder\RosterBuilder\bin\Debug\” folder to a
new folder.
3. In the new folder created, edit the “config.xml” file using text
editor.
4. Modify the string value between the <Database> and </Database>
tags, change the sub-string “(local)” to the IP of the database server.
5. Double click the RosterBuilder icon to start the program. Default
login name and password are “Admin” and “123456”.
Lam Chi Wo MSC 50447402