An Integrated Resource Planning
for Multiple Software Projects
指導教授：葉榮懋
學生：朱獻翔
學號：M97U0222
Contents
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Abstract
Introduction
Research Background
Workflow of Projects
Taguchi ' s Parameter Design
Experimental Results
Conclusion
Abstract
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
In a multi-project and multi-resource environment, a
resource planning is to decide what needs to be done, by
whom, when, and in which project. In this article, an
integrated method, which includes critical resource diagram,
heuristic methods and Taguchi's parameter design, is
proposed to solve resource planning problems for multiple
projects with different starting time.
Key Words：Parameter Design, Heuristic Method,
Resource Planning
Introduction

In a multi-project and multi-resource environment,
competitions arise for human resource among software
projects since skillful resources are difficult to find. In
this matter, some resources are assigned to multiple
software projects simultaneously to achieve a costeffectively resource planning. Those human resources
are called as common resources, otherwise are called as
non-common resources who are full time involved in a
single software project.
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Resources planning for multiple software projects
considers what tasks should be done, when, by whom, and
in which project. In this concern, there are two major
problems for resource planning.
Task Priority
Resource policy
For the first problem of task priority, researchers
discussed heuristic methods for multiple software projects
and multiple resources over decades. Scheduling heuristic
methods are used to prioritize competing activities for
allocating constrained resources.
Fendley ( 1968 ) recommended the “shortest operation first” rule
inferior to a “minimum slack” in the situation of a single project .
Patterson ( 1973 ) found that a “ shortest operation first ”rule
performed well in multi-project and multi-resource problems.
However, the “minimum slack ” as compared with several
heuristic methods by Davis and Patterson ( 1975 ) achieves
shortest duration.
 Later , Kurtulus and Davis ( 1982 ) examined heuristic methods
including “minimum slack” rule,“ shortest activity from Shortest
project”(SASP), and “maximum total work content”. They
recommended that the SASP rule and “maximum total work
content ” are better than “ minimum slack ”rule . Dumond and
Mabert (1988) found that the SASP method is more effective in
terms of reducing mean completion time in a dynamic
environment. 。
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For the second problem of resource policy, methods for achieving
optimal resource planning are widely discussed. Davis (1973)
classified the most popular solving procedures into two major
categories : optimal procedures and heuristic methods .
Simulation is also proposed by researchers to solve the resource
planning problems ( Van Slyke；1963 Schonberger 1981).
Design of experiment method is another effective procedure for
resource planning problems. antell, Jung , and Warner ( 1992 )
had applied Taguchi’s parameter design with PERT / CPM to
solve a single project management problem .
 Multiple software projects can be classified into two categories:
projects with same starting time and projects with different
starting time.
Research Background

Institute of Information Industry is a leading
organization in software industry in Taiwan. One of
their recent software products is reusable data
retrieval kernel software. By using this kernel
software, they started to implement many data
retrievable application systems for business, which
have highly similarity in system structure. The
kernel software had been proved as a successful
quick tool for developing application systems.

They held many application projects to meet
requirements of different customers. However, the
existing resources are limited. They have to decide
who will involve, in which project with how many
working hours. Therefore, the planning problem
occurs in a multi-project and multi -resource
environment. We then use this case as a
background example to develop an proposed
integrated method.
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The framework of an application system includes the following
software components:
DBa
DBd
DBb
DBk
DBf
Ma
Md
Mb
Qk
Qf
Those software components are developed by C language and each has
its own architecture and functions.
Workflow of Projects

Graphical scheduling tools are often used to describe the
relationships among project tasks and human resources,
such as PERT / CPM. Badiru (1992 and 1993) proposed a
critical resource diagram (CRD) takes a reverse view to
activity scheduling, and focuses on resource scheduling so
that the workflow among resources can be observed. Since
CRD can appropriately demonstrates the position of a
resource, in a project, it is adopted as the major scheduling
tool to show the workflow of the application project. In
Figure 1, each node refers to a task and its corresponding
resource unit, a human resource who is in charge of the task.

In this study, two application projects, denoted as
Project 1 and 2, are taken as examples for developing
proper project planning of multiple-software project
with multiple resources. To present the workflow of
these two projects, an augmenting CRD for both
projects is shown in Figure 2.
Taguchi ' s Parameter Design

In this section, Taguchi ' s parameter design is applied to
solve resource planning problems The general steps of
Taguchi ' s parameter design include : ( 1 ) define desired
improvement or objective ; ( 2 ) select factors and factor
levels ; ( 3 ) lay out design arrays ; ( 4 ) conduct
experiments ; and ( 5 ) evaluate performance .
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Cost Mode
The objective of multiple projects with n project with n
projects and m resources is to minimize the total project
cost including tardiness cost and resource cost . The
cost model is given below：
n
n
m
PC   (CTi  DTi )  DCi  (TLij  RC j )
i i
i 1 j 1
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Factors and Factor Levels
For the two projects, factors and factor levels are
illustrated with two major categories:
1. Resource Factors
2. Noise Factors
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Layout of Parameter Design
 The layout of this parameter design is set up as
follows : an inner array using a two -level factorial
design to include six controllable factors with 26 =
64 level combinations , and an outer array using
two L81 orthogonal arrays for Project 1 and 2 , each
contains ten noise factors of task complexity .
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EXPERIMENTS FOR MULTI – PROJECTS
First In, First serve (FIFS)
Based on the FIFS method, the first component for common
resource is completed in Project l, the next is in Project 2,
then back to Project 1, and will be continue alternatively
until all components are finished. Therefore, the back to
Project l, and will be until all components are task priorities
for common resources A and B will be [DBa – DBa’DBd – DBd’- DBb – DBb’] and [DBk – DBk’- DBf – DBf’],
respectively. These task priorities are presented by resource
links as shown in Figure4.

Each trial produces a critical duration time and its
corresponding project cost by following the computational
rule of CRD and the cost model Namely, for each
combination of controllable factors, there are 81response
data for each project , then its average , standard deviation ,
and SN ratio are obtained accordingly . An optimal
condition will be chosen by minimizing the summation of
average costs of projects. An optimal condition is
A1B2C1D2E1F2, which means that resources A , C , and E
need normal work rate only while resources B , D , and F
need overtime . In Table 3, some selected results for other
conditions are listed for comparison.
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Shortest Activity form Shortest Project (SASP)
The method of SASP determines task priority by judging
task duration and the remaining critical path time. Since the
scale of Project 2 is much smaller that Project l, the critical
path time of Project 2 is much shorter than Project 1. In this
case, task priorities for common resources will do all the
responded tasks first in Project 2, then back to Project 1 to
finish the rest of tasks. Therefore , the task priorities for
common resources A and B will be [DBa – DBa’-DBd’DBb’- DBd - DBb] and [ DBk – DBk’- DBf’ - DBf]
respectively These task priorities are presented by resource
links as shown in Figure 5.

An optimal condition is A1B2C1D2E1F1, which
means that only B and D need overtime . Some
selected results of two projects by using SASP are
listed in Table 4 for comparison.
Experimental Results
In this section, experimental results of FIFS and SASP heuristic
methods for multiple software projects are compared and
summarized as follows:
1. The optimal condition is A1B2C1D2E1F2 by using FIFS, while
A1B2C1D2E1F1by using SASP. It is clear that overtime is not
necessary for resource F.
2. For FIFS method, the resulting total cost is $ 458,560 =343029 +
1115531 for Project 1 and 2; for SASP method, the total cost is $
441,949=343882 + 98067. Hence SASP can achieve lower cost
than FIFS.
3 For Project 1, both, heuristic methods achieve same project
duration time of 86 day. For Project 2, SASP obtains shorter
duration time (29 Days) than FIFS (43 Days). On the other hand,
since the objective in this experiment is total project cost instead
of duration, it is clear that duration for the optimal condition it
minimized.
Conclusions

In this study , an integrated method , which
includes critical resource diagram ( CRD ) ,
heuristic methods such as SASP or FIFS，and
Taguchi ' s parameter design , was proposed to
solve resource planning for multiple projects with
different starting time .
 The main purpose of the integrated method is to
determine the work rate level of each resource
(normal or overtime) to achieve robust performance
of multiple projects against noise factors of task
complexity.

In this article, we have discussed resource
planning problems for multiple projects
having different project starting time,
resource planning for multiple projects With
same starting time can be further discussed.
Moreover, other heuristic methods for task
priority can be studied and compared.
讀後心得

在期刊論文中，使用啟發式田口解法，覺得在很複
雜，應用實驗設計的L81，再使用64的組合，出作
FIFS與SASP的最佳成本預估，但文中說到延遲的成
本，說的很不清楚，也沒有作出來，讀後感覺作者
留一伏筆，最後建議也寫到可用其他解法與派工方
法作為比較，在討論資源規劃問題中多個專案都有
不同的專案開始的時間，資源規劃對於多個專案同
時啟動時間可以進一步討論，此外，其他啟發式方
法的優先作業順序，可以再研究和比較。