-
.
外文原文
Study
on
Human
Resource
Allocation
in
Multi-Project
Based
on the Priority and
the Cost of Projects
Lin Jingjing ,
Zhou Guohua
SchoolofEconomics
and
management,
Southwest
Jiao
tong
University ,610031
,China
Abstract----This paper put
forward the a
ffecting factors of
project’s
priority. which is introduced
into a multi-objective optimization model
for
human
resource
allocation
in
multi-project
environment
.
The
objectives of the model were the
minimum cost loss due to the delay of
the time limit of the projects and the
minimum delay of the project with
the
highest priority .Then a Genetic Algorithm to
solve the model was
introduced.
Finally,
a
numerical
example
was
used
to
testify
the
feasibility of the model and the
algorithm.
Index
Terms
—
Genetic
Algorithm,
Human
Resource
Allocation,
Multi-
project’s project’s
priority .
1.
INTRODUCTION
More and more
enterprises are facing the challenge of multi-
project
management, which has been the
focus among researches on
project
management. In multi-project
environment ,the share are competition
of
resources
such
as
capital
,
time
and
human
resources
often
occur .Therefore , it’s critical to
schedule projects in order to
satisfy
the different resource demands and to shorten the
projects’
duration
time
with
resources
constrained
,as
in
[1].For
many
enterprises ,the human resources are
the most precious asset .So
enterprises
should
reasonably
and
effectively
allocate
each
resource
,
especially the human resource ,in order
to shorten the time and cost
of
projects
and
to
increase
the
benefits .Some
literatures
have
.
.
.
discussed
the
resource
allocation
problem
in
multi-
project
environment with resources
constrained. Reference [1] designed an
iterative
algorithm
and
proposed
a
mathematical
model
of
the
resource-
constrained
multi-project
scheduling
.Based
on
work
breakdown
structure (WBS) and Dantzig-Wolfe decomposition
method ,a
feasible multi-project
planning method was illustrated , as in [2] .
References
[3,4]
discussed
the
resource-constrained
project
scheduling based on Branch Delimitation
method .Reference [5] put
forward the
framework of human resource allocation in multi-
project
in Long-term ,medium-term and
short-term as well as research and
development(R&D)
environment
.Based
on
GPSS
language,
simulation
model
of
resou
rces
allocation
was
built
to
get
the
project’s
duration
time and resources
distribution, as in [6]. Reference [7] solved the
engineering project’s resources
optimization problem using Genetic
Algorithms.
These
literatures
reasonably
optimized
resources
allocation in multi-project, but all
had the same prerequisite that
the
project’s importance is the same to each other
.This paper will
analyze
the
effects
of
project’s
priority
on
human
resource
allocation
,which
is
to
be
introduced
into
a
mathematical
model finally
,a Genetic Algorithm is used to solve the model.
2.
EFFECTS OF
PROJECTS PRIORITY ON HUMAN
RESOUCE
ALLOCATION
AND THE
AFFECTING
FACTORS OF PROJECT’S PRIORITY
Resource
sharing
is
one
of
the
main
characteristics
of
multi-project
management
.The
allocation
of
shared
resources
relates
to
the
efficiency
and rationality of the use of resources .When
resource
conflict occurs ,the resource
demand of the project with highest
priority
should
be
satisfied
first.
Only
after
that,
can
the
projects
with lower priority
be considered.
Based
on
the
idea
of
project
classification
management
,this
paper
.
.
.
classifies the affecting factors of
project’s priority into three
categories ,as the project’s benefits
,the complexity of project
management
and
technology
,
and
the
strategic
influence
on
the
enterprise’s
future
development
.
The
priority
weight
of
the
project
is the function of the above three
categories, as shown in (1).
W=f(I,c,s…) (1)
Where w refers to project’s priority
weight; I refers to the
benefits of the
project; c refers to the complexity of the
project,
including the technology and
management; s refers to the influence
of the project on enterprise .The
bigger the values of the three
categories, the higher the priority is.
3.
HUMAN RESOURCE
ALLOCATION MODEL IN MULTI-PROJECT ENVIRONMENT
3.1
Problem
Description
According
to
the
constraint
theory,
the
enterprise
should
strictly
differentiate the
bottleneck resources and the non-bottleneck
resources
to
solve
the
constraint
problem
of
bottleneck
resources .This paper will stress on
the limited critical human
resources
being
allocated
to
multi-project
with
definite
duration
times and priority.
To
simplify
the
problem,
we
suppose
that
that
three
exist
several
parallel
projects
and
a
shared
resources
storehouse,
and
the
enterprise’s operation
only involves one kind of critical human
resources. The supply of the critical
human resource is limited,
which cannot
be obtained by hiring or any other ways during a
certain period .when resource conflict
among parallel projects
occurs,
we
may
allocate
the
human
resource
to
multi-project
according
to
project’s
priorities
.The
allocation
of
non-critical
independent
human
resources
is
not
considered
in
this
paper,
which supposes that the independent resources that
each
.
.
.
project needs
can be satisfied.
Engineering
projects
usually need
massive critical skilled human
resources in some critical chain ,which
cannot be substituted by
the other kind
of human resources .When the critical chains of
projects
at
the
same
time
during
some
period,
there
occur
resource
conflict
and
competition
.The
paper
also
supposes
that
the
corresponding network planning of
various projects have already
been
established
,and
the
peaks
of
each
project’s
resources
demand have been
optimized .The delay of the critical chain will
affect the whole project’s duration
time .
3.2 Model
Hypotheses
The following hypotheses
help us to establish a mathematical
model:
(1)The
number
of
mutually
independent
projects
involved
in
resource
allocation
problem
in
multi-project
is
N.
Each
project is indicated with
Q
i
,while i=1,2,
… N.
(2)The
priority
weights
of
multi-project
have
been
determined ,which are respectively w
1
,w
2
…w
n
.
(3)The total
number of the critical human resources is R ,with
r
k
standing for
each person ,while k=1,2, …,R
?
1
humanresou
rce
r
k
toprojectQ
i
(4)
Δ
k
i
=
?
0
others
?
(5)Resources
capturing
by
several
projects
begins
on
time.
t
E
i
is
the
expected
duration
time
of
project
I
that
needs
the
critical
resources
to
finish
some
task
after
time
t
,on
the
premise
that
the
human resources demand can be satisfied .tAi is
the real
duration time of project I
that needs the critical resource
to
finish some task after time t .
(6)According
to
the
contract
,if
the
delay
of
the
project
happens
.
.
.
the
daily
cost
loss
due
to
the
delay
is
△
c
i
for
project
I
.According to the project’s importance ,the delay
of a
project
will
not
only
cause
the
cost
loss
,but
will
also
damage
the prestige and
status of the enterprise .(while the latent
cost is difficult to quantify ,it isn’t
considered in this
article
temporarily.)
(7)From the hypothesis
(5) ,we can know that after time t ,the
time-gap
between
the
real
and
expected
duration
time
of
project
I
that
needs
the
critical
resources
to
finish
some
task
is
△
t
i
,(
△
t
i
=t
A
i
-t
E
i
).
For
there
exists
resources
competition,
the
time
–
gap
is
necessarily
a
positive
number.
(8)According to hypotheses (6) and (7),
the total cost loss of
project I is
C
i
(C
i
=
△
t
i
*
△
C
i
).
(9)The
duration
time
of
activities
can
be
expressed
by
the
workload
of
activities
divided
by
the
quantity
of
resources ,which can be
indicated with following expression
of
t
A
i
=η
i
/
R
i
*
,.In
the
expression
,
η
i
refers
to
the
workload
of
projects
I
during
some
period
,which
is
supposed
to
be
fixed
and
pre-
determined
by
the
project
managers
on
project
planning
phase
;
R
i
*
refers
to
the
number
of
the
critical
human
resources
being allocated to
projects I actually, with the equation
R
i
*
=
?
?
k
?
1
R
ki
existing.
Due
to
the
resource
competition
the
resource demands of projects with
higher
Priorities may be guarantee,
while those projects with lower
priorities
may
not
be
fully
guaranteed.
In
this
situation,
the
decrease of the resource
supply will lead to the increase of
the
duration time of activities and the project, while
the
workload is fixed.
.
.
.
3.3
Optimization
Model
Based on the above
hypotheses, the resource allocation model
in multi-project environment can be
established .Here, the
optimization
model is :
F
i
=min
Z
i
= min
?
i
?
1
N
?
?
Ci
i
i
?
1
N
=min
?
i
?
1
N
?
?
?
t
?
c
(2)
i
i
i
i
?
1
N
=min
?
i
?
1
N
< br>?
?
N
?
?
i
?
R
i
?
t
i
E
?
c
i
?
?
i
?
1
?
?
?
ki
?
i
?
1
?
?
?
?
F
2
=min Z
2
=min
?
?
< br>t
i
?
=min
?
R
i
?
< br>t
i
E
(3)
?
?
?
?
ki
?
i
?
1
?
Where
wj=max(wi) ,(
?
i
,<
/p>
j
?
1
,
2
,
3
?
N
) (4)
Subject
to : 0
?
?
i
< br>?
1
N
?
?
k
?
1
R
ki
=R
(5)
The
model
is
a
multi-objective
one
.The
two
objective
functions
are respectively to minimize the total
cost loss ,which is to
conform to the
economic target ,and to shorten the time delay
of
the
project
with
highest
priority .The
first
objective
function
can
only
optimize
the
apparent
economic
cost
;therefore
the
second
objective
function
will
help
to
make
up
this
limitation
.For
the
project
with
highest
priority
,time
delay
will
damage
not
only
the
economic
benefits
,but
also
the
strategy
and
the
prestige
of
the
enterprise
.Therefore
we
should
guarantee that the most important project be
finished
on time or ahead of schedule .
.
.
.
4.
SOLUTION TO THE MULTI-OBJECTIVE MODEL
USING GENETIC ALGORITHM
4.1
The
multi-objective
optimization
problem
is
quite
common
.Generally
,each
objective
should
be
optimized
in
order
to
get the
comprehensive objective optimized .Therefore the
weight
of
each
sub-objective
should
be
considered
.Reference
[8]
proposed
an improved ant
colony algorithm to solve this problem .Supposed
that the weights of the two optimizing
objectives are α
and
β
,where
α+β=1 .Then
the
comprehensive
goal
is
F
*
,where
F
*
< br>=αF
1
+βF
2
.
4.2
The
Principle of Genetic Algorithm
Genetic
Algorithm
roots
from
the
concepts
of
natural
selection
and
genetics
.It’s
a
random
search
technique
for
global
optimization
in
a
complex
search
space
.Because
of
the
parallel
nature
and
less
restrictions ,it has the key features
of great currency ,fast
convergence and
easy calculation .Meanwhile ,its search scope is
not limited ,so it’s an effective
method to solve the resource
balancing
problem ,as in [9].
The main steps of
GA in this paper are as follow:
(1)
Encoding
An integer string is short, direct and
efficient .According
to the
characteristics of the model, the human resource
can
be assigned to be a code object
.The string length equals to
the total
number of human resources allocated.
(2)
Choosing the
fitness function
This
paper
choose the objective
function as the foundation of
fitness
function
.To
rate
the
values
of
the
objective
function ,the
fitness of the n-th individual is
1/
n
。
(3)
Genetic
operation
It’s
the
core
of
GA .This
process
include
s
three
basic
.
.
.
operators:
selection
operator,
crossover
operator,
and
mutation operation.
1)
Selection
operation
is
to
select
the
good
individuals
among
the group .The probability of a string
to be selected as
a parent is
proportional to its fitness .The higher the
string’s fitness is, the greater the
probability of the
string to be
selected as a parent will be.
2)
Crossover
operator
The
so-called
crossover
is
that
the
paten
chromosomes
exchange
some
genes to
yield
two
offspring
strings
in
some
rule
.We
can
use
uniform
crossover
,that
the
two
chromosomes
exchange the
genes on the same positions with the same
crossover probability to yield two new
individuals.
3)
Mutation operator
Mutation
adds
to the diversity of
a population and
thereby
increases the likelihood that the
algorithm will generate
individuals
with
better
fitness
values
.The
mutation
operator
determines
the
search
ability
of
GA
,maintain
the
diversity
of
a
population
,and
avoid
the
prematurity
.There
are several mutation is quite easy .
4)
Standard for
the terminal of GA
Without
human
control
,the
evolution
process
of
the
algorithm will never end .The
population size affects the
final
result
and
the
operation
speed .If
the
size
is
greater
,the
diversity of the population
can be added
,and
the
best
result
can
be
obtained
easier .However
,the
efficiency
is
reduced .Recently ,in most
GA progress ,
the
biggest evolvement algebra is
determined by human-beings
to control
the course the algorithm.
.
.