A STABILITY AND EFFICIENCY ORIENTED RESCHEDULING

APPROACH FOR SOFTWARE PROJECT MANAGEMENT

Yujia Ge

Department of Computer Science and Technology, Zhejiang Gongshang University, Hangzhou, China

Lijun Bai

Department of Logistics and Management, Zhejiang Gongshang University, Hangzhou, China

Keywords: Rescheduling, Genetic Algorithm, Software Project Management.

Abstract: Rescheduling gains more attention in recent years by researchers who focus their study on scheduling

problem under uncertain situations. But in software engineering circumstances, it has not been

widely

explored. In this paper we propose a GA-based approach for rescheduling by applying a multi-objective

objective function considering both efficiency and stability to produce new schedules after managers take

control options to catch up their initial schedules. We also conducted case studies by simulation data. The

results show the effectiveness of the rescheduling method in supporting decision making in a dynamic

environment.

1 INTRODUCTION

During software project executions, changes seem to

be inevitable which cause schedule slip from the

initial plan. Ineffectual project control is the main

cause of project over budget and behind schedule

(

Lederer, 1995). Software project managers feel the

difficulties intrinsic to taking decisions especially

when a large team of engineers work together. So an

effective monitoring and rescheduling system is

needed to support control decision making.

Recently rescheduling techniques are proposed

n the areas, such as job shop problems (Pfeiffer,

2006; Cowling and Johansson, 2002). Nevertheless

there is still very limited support under software

projects circumstances. Sukhodolsky uses discrete

optimization techniques for finding optimal control

actions the manager should take to meet project’s

deadline (Sukhodolsky, 2001). But it is not practical

as the situations in real projects may not be as simple

as it is stated in the paper. Padberg applies

simulated-based techniques for schedule

optimization (Padberg, 2005). But the computational

effort for the exact optimization of a Markov

decision process in general grows exponentially with

the size of the problem and the model currently can

not fit in realistic problems.

An ideal situation for software managers is:

when

any factors change or status becomes bad to

projects, the task assignment can be automatically

updated by software management tools. So first, a

model is constructed which is suitable to software

project management and realistic problems. Then

computing with reasonable complexity should be

made to generate optimal control strategies.

Based on a relative simple model of software

project

management, a rescheduling approach is

proposed based on Genetic Algorithms, In general,

these scheduling or rescheduling problems are NP

complete. GAs provides better solution to the

complex project management problems than some

other methods (Chang, 2001). Our previous models

include task-based model (Chang, 2001) and

capability-based model (Ge, 2006). In this paper, we

further extend our work to facilitate control decision

making.

In summary, this paper reports the following

work.

(1) Modeling software project scheduling;

(2)Applying Genetic Algorithms on rescheduling

with

considering both efficiency and stability;

162

Ge Y. and Bai L. (2007).

A STABILITY AND EFFICIENCY ORIENTED RESCHEDULING APPROACH FOR SOFTWARE PROJECT MANAGEMENT.

In Proceedings of the Second International Conference on Software and Data Technologies - SE, pages 162-167

DOI: 10.5220/0001337301620167

 SciTePress

(3) Conducting case studies.

2 UNCERTAINTY OF SOFTWARE

PROCESS AND

RESCHEDULING STRATEGIES

Two common rescheduling strategies are known:

dynamics scheduling strategies and predictive-

reactive strategy (

Pfeiffer, 2006). In this paper, we

focus on predictive-reactive strategies. Predictive-

reactive strategy includes periodic, event-driven and

hybrid. When a specified event occurs during

schedule execution which has significant affect on

the further execution, the schedule must be revised.

Such an event in software project can be

turnover of essential personnel, technical approaches

that may not work, unavailability of development or

testing equipment and facilities (

Kitchenham, 1997).

Successful project control is based on the tracking of

actual execution versus the project plan. Traditional

EVA (Earned Value Analysis) techniques can be

adopted for comparing a project plan and its

execution. When a threshold reaches, rescheduling

happens.

3 OUR APPROACH

3.1 The Model

In our software project scheduling model, a project

is represented as a Task Precedence Graph (TPG).

z A TPG is an acyclic directed graph consisting

of a set of tasks V={T

, T

, …, T

} and a set of

task precedence relations P={ (P

); i<>j,

1<=i<=n, 1<=j<=n}, where P

= 1 if T

must be

first completed before T

can start, and zero if

not.

z Associated with each task T

is the estimated

effort which can be obtained from any known

estimation methods (such as COCOMO and

COCOMO II) and required skills.

Resource modeling focuses on team members for

a software project since they are major resources for

any software project. Employees have a list of skills

they possess, their salary rates, and their maximum

workloads (a limit to the amount of work load they

can be assigned). Proficiency levels of skills are not

described since our previous research experiences

suggest that too detailed modeling techniques lack of

practical usage in dynamic situations. The combined

skill set of the employees assigned to T

(SK_EMP(i)) should include all the skills required

by the task (SK_TASK(i)), i.e., SK _ EMP(i) ⊇ SK

_TASK(i).

Efficiency

There are many performance objectives for project

execution. The most common ones are minimum

project duration and minimum total cost. Our

efficiency measure is shown in Equation 1.

Efficiency = W1/OverLoad

norm

W2/Cost

norm

+ W3/Time

norm

(1)

OverLoad (minimum level of overtime) is the

amount of time worked beyond the individual over

time limits which is summed over all employees, and

it is treated as a global objective for a project.

OverLoad

norm

is computed by normalizing Overload.

When applying GA in Section 3.2, OverLoad

norm

achieved by dividing overload by the maximum

overload in the population. Similarly, cost and time

are also normalized as Cost

norm

and Time

norm

. Cost

(minimum cost) is the total labor cost of performing

the project, computed using the labor rates of each

resource and the hours applied to the tasks. Time

(minimum of time span) is the total time span

required to finish the project, from the start of the

first task until the end of the last. W1, W2 and W3

are the weights chosen by managers for these three

sub-objectives respectively.

Stability

When only considering efficiency measure of a

schedule, a newly generated schedule will be often

radically different from the initial one. Then the high

cost of the changing staffing profile can not be

neglected under this case. Practically speaking,

managers are in favor of rescheduling strategies

addressing continuity.

To minimize the impact of disruptions induced

by new schedule, the performance measurement,

stability, is applied. Two kinds of stability are

recognized, i.e. ex post stability, ex ante stability

(

Herroelen, 2005). Ex post stability is considered here.

There are several possible solutions for stability.

Here Equation 2 (

Pfeiffer, 2006) is adapted in our

model to calculate stability in our objective function.

The value is achieved by adding starting time

deviation and actuality penalty.

A STABILITY AND EFFICIENCY ORIENTED RESCHEDULING APPROACH FOR SOFTWARE PROJECT

MANAGEMENT

163

Penalty for Stability

(

)

nTtktt

jjj

//|'|

⎥

⎦

⎤

⎢

⎣

⎡

−+−

∑

∈

(2)

where B is the set of tasks that need to be

rescheduled. They are the tasks that remained

unprocessed in the initial schedule and still need to

be processed under new circumstances. n is the

number of tasks in B. is the predicted start time

of task j in the new schedule. is the predicted

start of job j in the initial schedule . T is the current

time.

The related objective function is shown in

Equation 3.

Stability = W4/penalty for stability

norm

(3)

Penalty for stability

norm

is achieved by dividing

penalty for stability by the maximum penalty for

stability in the population

The composite objective function for evaluating

a schedule considering efficiency and stability is

shown in Equation 4.

The objective function= Efficiency *

+Stability * W

(4)

3.2 Stability and Efficiency Oriented

Re-scheduling by Applying GA

Genetic algorithms which belong to stochastic

search method have been widely used in many

optimization fields and also provide good solutions

in our previous research (Chang, 2001; Ge 2006). It

remains our optimization method of choice.

The principle that using whatever encoding is the

most natural to your problem and then devising a

GA with that encoding has been widely accepted

unless there is more theoretical progress on GAs.

The genome here is an orthogonal 2D array with one

dimension for task, the other for employee. The

percent of an employee's labor that can be

committed to any give task was constrained to a

discrete set of values that are 0, 0.25, 0.5, 0.75 and

Table 1 shows an example genome in which the

number of row i and column j represents the

commitment of Employee i to Task j. 0.25 means

Employee 1 is assigned 25% of his working hours

on Task 1.

Table 1: An example genome.

T1 T2 T3 T4

Employee1 0.25 0 1 0.5

Employee2 0.5 0.5 0 0

When rescheduling is necessary, tasks and

employees with changed profiles need to be updated

first. Then the GA scheduler sets the initial schedule

produced by preceding GA as the initial population

of the new GA which takes advantage of previous

result for the stability purpose. With the rows and

columns of new employees or new tasks, genetic

operator assigns each individual a specific value, for

example, 0.25. The initializer results in a population

that initially occupies only a small region of the total

solution space but, if the GA propagation parameters

are selected at all well, it will rapidly produce

populations containing individuals with high figures

of merit. Crossover operator is one-point crossover

on 2D array and element flip is used as mutation

operator.

Since genetic algorithms are non-deterministic,

factors as population size, generation number,

mutation probability and crossover probability not

only influence the time required to perform the GA

algorithm but also affect the quality of the result.

The parameters for the proposed GA scheduler are

determined after a set of test runs. The performance

is better when the population size is bigger. But

population size between 50 and 100 can still produce

good results. Crossover probability is chosen

between 0.4-0.8. Mutation probability is set

between 0.01 and 0.1.

4 CASE STUDIES

Several simulation based tests were conducted. The

settings for the GA are as follows: population size is

100, crossover probability is 0.4, and mutation

probability rate is set to 0.01.

One case consists of 18 tasks for which 10

employees were available. Table 1 shows task

properties. Employee properties are listed in Table 2.

ICSOFT 2007 - International Conference on Software and Data Technologies

164

Table 2: Task information table.

Task PersonWeek Skill Ancestor

T0 15 0, 2 1, 2

T1 10 0, 2 7

T2 10 3, 4 3, 4

T3 10 1, 3 5

T4 15 1, 2 5, 8, 9

T5 10 2, 3, 4 6, 8

T6 20 0, 4 8

T7 10 1, 4 11, 14

T8 25 0, 2 14

T9 15 0, 3 10, 12

T10 20 2, 4 12

T11 10 2, 3 13

T12 10 3, 4 14

T13 10 0, 4 14

T14 20 1, 2 15

T15 20 1, 2 16

T16 20 1, 2 17

T17 20 1, 2 /

Table 3: Employee information table

Emp Id Skill list Salary/week

P1 0,1,3 1750.00

P2 0, 2 1000.00

P3 1 1000.00

P4 0, 3 1250.00

P5 1, 4 1250.00

P6 1, 3, 4 1500.00

P7 2, 4 1250.00

P8 1, 2, 3 1500.00

P9 0, 2, 4 1750.00

P10 2, 3 1250.00

The initial task assignment plan is shown in

Table 4 and its corresponding Gantt graph is

presented in Figure 1.

Table 4: Initial task assignment.

T0 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17

E1 1 0.5 0.8 0.5 1 0.5 0.8 0.5 0.3 0.8 0 0.3 0 0.3 1 0.5 1 1

E2 1 0.8 1 1 0 0.8 0.5 0.8 0.8 0.5 0.5 0 0.3 0.8 1 0.8 1 1

E3 0.80.30.50.5 1 00.50.3 10.80.80.80.8 0 1 10.30.5

E4 1 0. 3 0. 8 0. 8 0. 75 0. 8 0. 8 0. 3 0. 8 0 0. 5 0. 5 1 0. 5 1 0. 5 0. 5 1

E5 1 0. 8 0. 3 0. 8 0. 5 0. 8 0. 8 0. 5 1 0 0. 8 1 0. 5 0. 5 0. 5 0. 8 1 1

E6 1 1 1 0 0. 75 0. 5 0. 8 0. 5 0. 8 0. 3 0. 5 0. 5 1 0. 8 0. 8 1 1 1

E7 10.8 10.3 1 00.80.8 10.80.80.50.8 00.8 1 10.8

E8 0. 8 0 0. 8 0. 8 1 0. 3 0. 5 0 0. 8 0. 5 0. 8 1 0. 8 0. 8 0. 8 0. 5 0. 3 0. 8

E9 0.80.30.50.5 1 1 10.3 10.80.30.3 0 00.80.80.5 1

1111

Figure 1: Initial schedule.

Suppose at the beginning of the 7th week T

, T

have been completed and other tasks

have not yet been initiated. The project is greatly

behind the plan notified by tracking real execution

data.

To bring any remaining project tasks into

alignment with the planned schedule, managers have

various project control actions to take, such as,

adding people to the project, extending the time to

completion, cutting out non-essential or less

essential requirements. If option 1 is taken, genetic

algorithm can easily generate a new schedule with

the updated employees’ information. If option 2 is

used, it is just right-shift rescheduling and no genetic

algorithm calculation needs to be done. If option 3

is taken, our model still easily fits by updating

original task information tables.

The result going after option 2 is shown as

follows. Suppose manager would like to add

another engineer (as shown in Table 5) into this

team to catch up the schedule.

A STABILITY AND EFFICIENCY ORIENTED RESCHEDULING APPROACH FOR SOFTWARE PROJECT

MANAGEMENT

165

Table 5: Newly added employee’s information.

Skill list Salary/wee

Employee 11 0, 2, 3 1250

Our rescheduling approach is applied for the

remaining tasks that have not been started and Table

6 shows the comparison from the best newly

generated schedule versus the initial schedule. t

start

lists the start time of a specific task and d means the

duration of this task. Rescheduling approach

produced acceptable results both with stability

=0, W

=1) and without stability (W

=1, W

=1).

Table 6: Generated schedule versus initial schedule.

Initial schedule

Results from

Rescheduling

=0, W

=1)

Results from

Rescheduling

=1,W

=1)

start

d t

start

T5 5.03 2.11 7.00 1.38 7.00 1.54

T6 7.13 3.08 8.38 11.24 8.54 2.58

T8 10.21 3.33 11.24 2.63 11.12 2.5

T9 5.03 3.16 7.00 2.14 7.00 3.33

T10 8.19 3.48 9.14 3.33 10.33 2.16

T11 5.92 1.90 7.00 2.11 7.00

1.90

T12 11.67 1.82 12.48 1.25 12.50

1.29

T13 7.83 2.50 9.11 2.22

8.90 1.43

T14 13.54 2.35 13.87 2.00

13.79 2.11

T15 15.90 2.58 15.87 2.11

15.89 2.50

T16 18.48 2.67 17.95 2.00

18.39 2.76

T17 21.14 2.22 19.95 1.95

21.15 2.35

Time

(week)

23.36 21.90

23.50

Cost

($)

263664 264570

265234

But the efficiency performance is affected by the

stability measure. We can also see from the table

that the schedule (W

=0, W

=1) has better

efficiency performance over the schedule (W

=1, W

=1). Several other tests are conducted when control

option 2 is taken. In all 4 cases, schedules without

considering stability all have better performance as

we expected. In case 1, 2 and 4, all of the generated

new schedules without stability and with stability

can be finished in or close to original deadline and

budget. In case 3, generated schedule is far worse

than it initial schedule which means managers may

take other control options to reduce schedule slip for

this situation.

Table 7: Comparison of schedules with stability versus

schedules without stability

Intial

schedule

Rescheduling

=0, W

=1)

Rescheduling

=1,W

=1)

task

emp

Time

(Week

)

Cost

($)

Mean

Time

Mean

Cost

Mean

Time

Mean

Cost

1 5 5 7.52 98K 5.67 95K 7.23 99K

2 10 5 19.35 120

17.62 124K 18.12 131K

3 10 10 14.32 210

16.35 230K 16.42 232K

4 18 10 23.36 234

22.10 244K 23.67 266K

5 CONCLUSIONS AND FUTURE

WORK

In this paper, we propose a software project

rescheduling approach considering efficiency and

stability. This approach is based on formulating

software project scheduling and rescheduling

situation as a multi-objective optimization problem

via a genetic algorithm. The proposed method will

help a manager to do scheduling with the option he

made to put the project back on track. By case

studies, the model can easily and efficiently do

rescheduling under different kinds of control options.

Still, there are areas that can be improved. The

parameters of stability and efficiency are determined

in current research. Sensitivity study should be

directed to balance the effect of stability and

efficiency in different situations. In addition,

evaluations of possible impact of all the available

control options should be integrated in the model to

support control decision making in software process.

REFERENCES

Cowling, P., & Johansson, M., 2002. Using Real Time

Information for Effective Dynamics Scheduling,

European J. of Operational Research, 139(2), 230-244.

Chang, C. K., Christensen, M., & Zhang, T., 2001.

Genetic algorithms for project management, Annals of

Software Engineering 11(1), 107-139.

Ge, Y., Chang, C. K. 2006. Capability-based Project

Scheduling with Genetic Algorithms.

CIMCA/IAWTIC 2006,161.

ICSOFT 2007 - International Conference on Software and Data Technologies

166

Herroelen, W., Leus, R., 2005. Project Scheduling Under

Uncertainty: Survey and Research Potential, European

J. of Operational Research, 165(2), 289-306.

Kitchenham, B., & linkman, S., 1997. Estimates,

Uncertainty, and Risk, IEEE Software, 14( 3),69-74.

Lederer, A. L., & Prasad, J., 1995. Causes Of Inaccurate

Software Development Cost Estimates. Journal of

Systems & Software, 31( 2), 125-134.

Padberg, F., 2005. On the Potential of Process Simulation

in Software Project Schedule Optimization,

Proceeding of COMPSAC 2005, 127-130.

Pfeiffer, A. , Kadar, B., & Monostori, L., 2006. Stability-

oriented Evaluation of Hybrid Rescheduling Methods

in a Job-shop With Machine Breakdowns. In

proceedings of MITIP2006 - 8th International

Conference on The Modern Information Technology

in the Innovation Processes of the Industrial

Enterprises, 457- 462.

Sukhodolsky, J., 2001. Optimizing Software Process

Control, Software Engineering Notes, 26(2), 59-63.

A STABILITY AND EFFICIENCY ORIENTED RESCHEDULING APPROACH FOR SOFTWARE PROJECT

MANAGEMENT

167