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INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303
A Greedy Heuristic Approach for Sprint Planning in
Agile Software Development
S.Jansi1
1
Sona College of Technology,Department of CSE
sumithaselvaraj00@gmail.com
Mrs.K.C.Rajeswari2
2
Sona College of Technology, Department of CSE
rajeswari.chinnasamy@gmail.com
Abstract—The sprint planning phase in agile software development has a major impact on the project success. The optimality
of a sprint plan depends on several factors of the user stories. The factors are estimated complexity, risk values and business
value of the user stories. So these factors must be included in each sprint. To achieve this, planning problem is first converted
into a generalized problem. Then the problem is solved using the linear program in IBM ILOG CPLEX optimizer. The feasible
value for the large sized problem takes time to compute and cannot be used for operational use. So, Greedy Heuristic approach
is given as a proposal to integrate with the CPLEX optimizer to obtain the optimal solution. The computational result of
Greedy heuristic is an effective and takes less time than the time taken by CPLEX optimizer.
Keywords—Agile methods, greedy heuristic, optimization model, scrum framework,sprint planning.
1 INTRODUCTION
Agile software development is mainly focused on the completion of
customer‘s requirement within in the time. For that it uses several
methods such as Extreme programming (XP), scrum and lean
software development. Here the consideration is about sprint
planning which comes under scrum. Scrum is a framework for the
large scale new product development. During the incremental and
iterative design implementation in scrum, the software is described
in terms of user functionalities (user stories) and at each iteration
(sprint) the team should deliver the set of user stories that maximizes
the utility of the users. Sprint planning is that within the estimated
duration of the sprint, assigned tasks have to be completed.
Durations can be limited by assigning the related tasks within the
sprints. One user story should be delivered before another one is
realized.
In sprint planning, user stories are estimated by the sprint team‘s
experience that they have faced before. Estimation plays a vital role
in the sprint plan, as it decides the successful project‘s sprint plan.
Based on the estimation, user stories are prioritized for the sprint
plan. It includes complexity, risk, and correlation among the user
stories. Sprint planning effectiveness is mainly depends on taking all
the variables and constraints into the consideration. So that optimal
solution will be obtained within less time.
Some tools are available to support agile project management.
Scrum works [5] and Mingle [4], provides a set of parameters to deal
with user story risk, complexity and utility. But these tools lack in
providing the correctoptimization solution for the operational use.
2 LITERATURE SURVEY
Agile software development practices accomplish improved software
quality and increased development team productivity. Flexibility was
acquired by systematically responding to customer requirements and
changes. Most important features of agile are (1) achievement of
IJTET©2015
customer satisfaction through continuous delivery of software (2)
co-operative working of product owners and scrum team, and (3) by
the face-to-face communication in the team [2].
Agile methodology is specifically developed to facilitate
communication and coordination within a dynamic team
environment [11]. This includes practices such as shared team
rooms to encourage recurrent informal communication. Then the
informative workplace environment provides ubiquitous information
dissemination and spontaneous feedbacks throughout the
development of the product. So that customer representative can
have close partnership with the product development by providing
the feedback. Rather than adhering to traditional methods of
requirements gathering and design before software production, agile
teams deal with the complexity of software development by
practicing rapid iterative development from project inception.
Agile software development method includes: Dynamic Systems
Development Methods (DSDM) [2], Feature Driven Design [3],
Crystal [4], Scrum [5], Extreme Programming (XP) [6] and more
recently Lean Software Development [7].
InterMod methodology [1] was proposed, its aim is to help
the development of high quality software with accuracy. This
methodology allows gathering and validation of the requirement as
an incremental process. Approach concentrates on demonstrator
diagram through which flexibility on planning and facing unexpected
changes was analyzed in earlier stage. Then the prior validation of
the model allows to progress and guide subsequent activities of the
user functionalities. It improves the lack of consistency by means of
continuous integration of models in the agile process.
Time-boxing is a common practice used to assist simple design and
scheduling. User functionalities Development are split into separate
time periods, with a set number of hours allowed for each task. For
each time period, deadlines and resources are fixed, while
deliverables are more flexible. Thus the scope of the development
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INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303
effort is adjusted to meet scheduling constraints. The functionalities
which are not fit into the current time period are dropped or
reconsidered based on the customer satisfaction. At the end of the
time-box each task should be completed [12].
HDP (Hybrid Dynamic Programming) heuristics is to attain
processing time similar to the one of dynamic programming
algorithm applied to a classical Knapsack Problem (KP) to have a
good performance in terms of gap. Cooperation of BB (Branch and
Bound) algorithm with HDP is to obtain an exact solution. This
combination gives processing time similar to the one of a classical
branch and bound method. Though the cooperative method improves
the optimal value, solution is an alternative to limit the processing
time [13].
In a previous work [8], the sprint planning problem for
agile projects proposed an optimization model that is also based on
the team estimates and a set of development constraints. This model
produces the optimal sprint plan by maximizing the business value
perceived by the user. ILOG CPLEX optimizer (IBM, 2011) was
used with optimization model to acquire the feasible solution for
medium-sized problem. But it is a time consuming process for large-
sized operational use problem.
The sprint planning problem for agile Data Warehouse
design was formalized and proposed a multi-knapsack model to
solve it. Model was tested on both the synthetic and real projects,
and then found that the exact solution is determined for the medium
sized problem in a time that is fully compatible with the
development process. But for the large sized problems, a heuristic
solution that is just a few percentage points far from the exact one
can be returned in a couple of seconds. To present the plan in a more
effective way, optimization module was coupled with the existing
software‘s for agile project management.
Here, Greedy heuristic approach is proposed that will
provide less computing time for large-sized sprint planning problem.
Optimal solution is also acquired through this approach. Therefore,
approach is integrated to the optimization model that could be used
interactively and coupled with existing software for the agile project
management.
2.2Outline
The paper is organized as follows section 2 summarizes the agile
practices with the goal of sprint planning problem. Section 3
summarizes the mathematical formulation with notation and section
4 ends up with conclusion.
3 PROPOSED SYSTEM
Sprint planning phase is within an iterative and incremental
approach which ensures the criticality of project success. New
requirements may arise during the project and the plan should be
flexible enough to accommodate them. In sprint planning, tasks are
estimated and completed according to their schedule. Track of the
project is recognized through these assessments in sprint planning.
Scrum lifecycle embraces the sprint planning phase to acquire the
success of the project.
IJTET©2015
In fig1, initially user stories are the user functionalities which are
chunked into tasks. Individual tasks are estimated by the expert‘s
past experience and knowledge. Utility and complexity factors are
estimated by the story points of the user story. Planning poker
method is used to estimate the complexity of user stories by
assigning the story points. Then the user stories are prioritized based
on their estimated values. Critical risk and uncertainty risk are the
two typical risks on the user stories.
Fig.1Scrum Lifecycle
Mainly, critical risk has a main impact on the user stories.
For example, if the user story 1 has a risk and most probably it affect
the story 2. The uncertainty risk is about the unexpected problem
occurring during the project progress. Both types of risks are
estimated within the following values, risk 1(no risk found), 1.3(low
risk found), 1.7(medium risk found) and 2(high risk found). The user
stories are correlated by the means of OR and AND dependency.
Based on the prioritization, the product backlog is
composed and then partitioned into sprints. User stories are allocated
to the sprints through the estimation of complexity, development
velocity and affinity of the user story. Sprint backlog carries out the
details of the user stories from the product backlog. Sprint backlog
have the information about the user stories which are in progress and
not yet started. It will also have status of unsatisfied user stories
which are not delivered. If the user stories are satisfied, then it will
19
INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303
be delivered. Here the planning problem is converted into a
generalized problem and solved using linear programming model by
accepting the constraints in it. Objective function is to maximize the
cumulative utility of the project.
Sprint planning problem has a major impact on the project success.
To achieve the project success, following goals have to be satisfied
in sprint planning:
1. Customer satisfaction – It is achieved by,(i) Delivering
the user stories with high utility based on the customer
expectations.(ii) To maximize the user value, include the
affine stories in the same sprint.
2. Risk Management –It is achieved by advancing a critical
and unpredictable user stories to avoid a late side effects.
Then by distributing the risky stories uniformly.
Fig.2 System Architecture
In fig.2, Sprint planning problem is assigned to be a large scale
problem which means allocation of user stories in sprint plan
should be higher. Then the sprint planning problem is framed into a
general assignment problem. The framed problem should be
understandable to CPLEX optimizer. In user data, number of user
stories and sprint availability details have to be given as input. The
MILP model constraints and greedy heuristic constraints are given
as the enhancement to the CPLEX optimizer. The solution obtained
is with less time when compared to the execution before
enhancement.
4 MATHEMATICAL FORMULATION
In this section, greedy heuristic approach is proposed to minimize
IJTET©2015
the time taken for computing the large-sized sprint planning
problem in the IBM ILOG CPLEX optimizer. Let U = {1…n} be the
set of n user stories to be allotted to the sprints. Here the procedure
starts by optimizing sprint i=1 and then optimizes the remaining
sprints in them, one at a time. Therefore at each iteration, greedy
heuristic procedure consider a sprint i∈S and assigns to the stories
that maximize the utility by solving the sub-problems.
Given a set of m sprint S and a set of n user stories U. let:
- 𝑤𝑖𝑗 =1, iff story j is included in sprint i, otherwise 0.
- 𝑈𝑗 , be the utility of the story j.
- 𝑞𝑗 , be the number of story points of story j.
- 𝑄𝑖, be the capacity of sprint i, measured in story
points.
- 𝑅 𝐶𝑅𝑗 , be the criticality risk of story j.
- 𝑅 𝑈𝑁𝑗 , be the uncertainty risk of story j.
- 𝐶𝑗 , be the affinity between the story in j.
- 𝑋𝑗 , be the set of similar stories to the story j.
- 𝑥𝑖𝑗 , be an accessory variable related to the number of
stories in 𝑋𝑗 included in sprint i.
To maximize the utility by solving the sub-problems by
the following mixed integer linear programming model:
(𝑆𝑖)𝑍𝑆 𝑖
= 𝑚𝑎𝑥 𝑚 − 𝑖 + 1𝑛
𝑗 =1 𝑈𝑗
(𝑅 𝐶𝑅𝑗 𝑤𝑖𝑗 + 𝐶𝑗 𝑥𝑖𝑗 ) (1)
s.t 𝑞𝑗
𝑛
𝑗=1 𝑅 𝑈𝑁𝑗 𝑤𝑖𝑗 ≤ 𝑄𝑖, i∈ 𝑆 (2)
𝑥𝑖𝑗 ≤ 𝑤𝑖𝑘
𝑛
𝐾∈𝑋 𝑗
, j∈U (3)
𝑤𝑖𝑗 ∈ {0, 1}, j∈U𝐵𝑖 (4)
𝑤𝑖𝑗 = 0, j∈ 𝐵𝑖 (5)
𝑥𝑖𝑗 ≥ 0, i∈S, j∈U (6)
Where 𝐵𝑖 represent the stories already assigned to the sprints
considered in the previous iteration.
The mainly objective function is to (1) maximize the cumulative
utility of the sub-problems. The utility 𝑈𝑗 for each story is increased
by increment of criticality risk 𝑅 𝐶𝑅𝑗 . So that critical stories are
considered in the earlier stage of the project and then by increment of
affinity 𝐶𝑗 of the story, similar stories are included in the same sprint.
Constraint (2) ensures the overall complexity of all the stories
assigned to each sprint does not exceed the estimated sprint capacity
value. To strengthen constraint (2), sprint capacity or weight of the
user stories are modified to reduce the computing time. Constraint
(3) ensures correct evaluation of 𝑥𝑖𝑗 which does not require any
20
INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303
integrality constraint. This mathematical formulation can be solved
by a MIP solver.
Sub-problem should follow the forthcoming strategies:
(i) If there is no user story j in sprint I, then fix 𝑤𝑖𝑗 =0 and re-
optimize the knapsack problem(𝑆𝑖 ).
(ii) To increase the profit in every knapsack problem 𝑆𝑖 by
multiplying the profit with 𝐾𝑗 (ie, coefficient 𝐾𝑗 is defined for user
story j. By having 𝑤𝑖𝑗 =0 in the current solution, increase the
coefficient(𝐾𝑗 ). Then restart the greedy heuristic from the first sprint
i=1. This strategy requires too much iteration to reach a feasible
solution.
Then the unchanged user stories should be distributed among the
sprints:
𝑤𝑖𝑗
𝑛
(𝑖,𝑗)∈𝑤= ≥ L’ (7)
Where w represent the subset of variables{𝑤𝑖𝑗 }set to one in
the previous sprint planning and L is the minimum number of
variables of subset w that do not have to change. Then L‘ is the
difference between L and the story that already got changed in the
previous sprints.
4 CONCLUSION
In this paper, an approach for the sprint planning in agile methods
based on an integer linear programming model is provided. The
mathematical formulations are solved by a general purpose MIP
solver, IBM ILOG CPLEX optimizer. However, the computing time
to solve to optimality of the medium sized problem is very large. In
an attempt to reduce the computing time, reduction and sub-problem
are solved. Sprint planning problem is framed by gathering the risk,
complexity, utility and affinity values of the user stories. Constraints
and these factors values are given as input to the sprint plan. Optimal
solution for medium-sized instances is solved easily within less time.
But for the large instance, the problem prevails in solving the sprint
plan. Since solving the model to optimality in MIP solver, is not
suitable for an operational use and takes some time to solve this
problem. So that Greedy heuristic approach is given as a proposal. In
this approach, planning problem are chunked into sub-problem and
solved separately in iterations. From the iteration of sub-problem,
best feasible solution is retrieved at each step. The computational
result using greedy heuristic approach will be able to attain a feasible
and optimal solution with very quick time constraints. This approach
can be improved by identifying the risk and designing a plan in a real
IJTET©2015
time approach. Then by identifying the skill of each expert, sprint
plan can be designed to obtain a further better feasible value as a
result.
REFERENCES
[1] BegonaLosada, MaiteUrretavizcaya, Isabel Fernandez- Castro, A guide to
agile development of interactive software with a ‗‗User Objectives‘‘, 78 (2013)
2268–2281.
[2]J. M. Bass, ‗Agile Method Tailoring in Distributed Enterprises: Product
Owner Teams‘, in Proc. IEEE 8th Int. Conf. on Global Software Engineering,
Bari, Italy, 2013, pp. 154–63.
[3] P.Coad, E. LeFebvre, and J.D. Luca, Java Modeling in Color. Englewood
Cliffs, NJ: Prentice Hall, 1999.
[4] A.Cockburn, Agile Software Development. Reading, MA: Addison
Wesley, 2001.
[5] K.Schwaber and M. Beedle, Agile Software Development with Scrum,
2001.
[6] K. Beck and C. Andres, Extreme Programming Explained, 2nd ed. Addison
Wesley, 2004.
[7] M.Poppendieck and T.Poppendieck, Lean Software Development: An
Agile Toolkit. Addison-Wesley Longman Publishing Co., Inc., 2003.
[8] Matteo Golfarelli, Stefano Rizzi, and Elisa Turricchia, ‖Sprint Planning
Optimization in Agile Data Warehouse Design―, 40136 Bologna, Italy.
[9] Kolisch. R. Padman. R, An integrated survey of deterministic project
scheduling. Omega 29, 249–272, 2001.
[10] Herroelen, W., Leus, R., Demeul -emeester, E., ―Critical chain project
scheduling: do not over-simplify‖, Project Management Journal 33, 48–60.,
2002.
[11] Stavros Stavru, ―A critical examination of recent industrial surveys on
agile method usage‖ P.B. 48, 1164 Sofia,
[12] Golfarelli M, Rizzi S, Turricchia E. Multi-sprint planning and smooth re-
planning: an optimization model. Journal of Systems and Software 2013;
86(9):2357–70.
[13]. V. Boyer, Didier EL BAZ, MoussaElkihel LAAS-CNRS, ―Solution of
Multi-dimensional Knapsack Problem via Cooperation Of Dynamic
Programming And Branch And Bound‖, 31077.
[14]. Boschetti M, Hadjinconstantinou E, Mingozzi A,‖ New upper bounds for
the finite two-dimensional orthogonal non-guillotine cutting stock
problem‖,2002;13:95–119.
[15]. Boschetti M, Maniezzo V, Roffilli M, BolufeRohlerA, ―Matheuristics
:optimization, simulation and control, vol. 5818. Springer; 2009.p.171–7.
[16].Boschetti M, Mingozzi A. The two-dimensional finite bin packing
problem, 2003; 1:27–42.
[17]. Boschetti M A, Montaletti L. An exact algorithm for the two- dimensional
strip- packing problem.OperationsResearch2010; 58 (November (6)):1774–91.
21

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A Greedy Heuristic Approach for Sprint Planning in Agile Software Development

  • 1. INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 A Greedy Heuristic Approach for Sprint Planning in Agile Software Development S.Jansi1 1 Sona College of Technology,Department of CSE sumithaselvaraj00@gmail.com Mrs.K.C.Rajeswari2 2 Sona College of Technology, Department of CSE rajeswari.chinnasamy@gmail.com Abstract—The sprint planning phase in agile software development has a major impact on the project success. The optimality of a sprint plan depends on several factors of the user stories. The factors are estimated complexity, risk values and business value of the user stories. So these factors must be included in each sprint. To achieve this, planning problem is first converted into a generalized problem. Then the problem is solved using the linear program in IBM ILOG CPLEX optimizer. The feasible value for the large sized problem takes time to compute and cannot be used for operational use. So, Greedy Heuristic approach is given as a proposal to integrate with the CPLEX optimizer to obtain the optimal solution. The computational result of Greedy heuristic is an effective and takes less time than the time taken by CPLEX optimizer. Keywords—Agile methods, greedy heuristic, optimization model, scrum framework,sprint planning. 1 INTRODUCTION Agile software development is mainly focused on the completion of customer‘s requirement within in the time. For that it uses several methods such as Extreme programming (XP), scrum and lean software development. Here the consideration is about sprint planning which comes under scrum. Scrum is a framework for the large scale new product development. During the incremental and iterative design implementation in scrum, the software is described in terms of user functionalities (user stories) and at each iteration (sprint) the team should deliver the set of user stories that maximizes the utility of the users. Sprint planning is that within the estimated duration of the sprint, assigned tasks have to be completed. Durations can be limited by assigning the related tasks within the sprints. One user story should be delivered before another one is realized. In sprint planning, user stories are estimated by the sprint team‘s experience that they have faced before. Estimation plays a vital role in the sprint plan, as it decides the successful project‘s sprint plan. Based on the estimation, user stories are prioritized for the sprint plan. It includes complexity, risk, and correlation among the user stories. Sprint planning effectiveness is mainly depends on taking all the variables and constraints into the consideration. So that optimal solution will be obtained within less time. Some tools are available to support agile project management. Scrum works [5] and Mingle [4], provides a set of parameters to deal with user story risk, complexity and utility. But these tools lack in providing the correctoptimization solution for the operational use. 2 LITERATURE SURVEY Agile software development practices accomplish improved software quality and increased development team productivity. Flexibility was acquired by systematically responding to customer requirements and changes. Most important features of agile are (1) achievement of IJTET©2015 customer satisfaction through continuous delivery of software (2) co-operative working of product owners and scrum team, and (3) by the face-to-face communication in the team [2]. Agile methodology is specifically developed to facilitate communication and coordination within a dynamic team environment [11]. This includes practices such as shared team rooms to encourage recurrent informal communication. Then the informative workplace environment provides ubiquitous information dissemination and spontaneous feedbacks throughout the development of the product. So that customer representative can have close partnership with the product development by providing the feedback. Rather than adhering to traditional methods of requirements gathering and design before software production, agile teams deal with the complexity of software development by practicing rapid iterative development from project inception. Agile software development method includes: Dynamic Systems Development Methods (DSDM) [2], Feature Driven Design [3], Crystal [4], Scrum [5], Extreme Programming (XP) [6] and more recently Lean Software Development [7]. InterMod methodology [1] was proposed, its aim is to help the development of high quality software with accuracy. This methodology allows gathering and validation of the requirement as an incremental process. Approach concentrates on demonstrator diagram through which flexibility on planning and facing unexpected changes was analyzed in earlier stage. Then the prior validation of the model allows to progress and guide subsequent activities of the user functionalities. It improves the lack of consistency by means of continuous integration of models in the agile process. Time-boxing is a common practice used to assist simple design and scheduling. User functionalities Development are split into separate time periods, with a set number of hours allowed for each task. For each time period, deadlines and resources are fixed, while deliverables are more flexible. Thus the scope of the development 18
  • 2. INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 effort is adjusted to meet scheduling constraints. The functionalities which are not fit into the current time period are dropped or reconsidered based on the customer satisfaction. At the end of the time-box each task should be completed [12]. HDP (Hybrid Dynamic Programming) heuristics is to attain processing time similar to the one of dynamic programming algorithm applied to a classical Knapsack Problem (KP) to have a good performance in terms of gap. Cooperation of BB (Branch and Bound) algorithm with HDP is to obtain an exact solution. This combination gives processing time similar to the one of a classical branch and bound method. Though the cooperative method improves the optimal value, solution is an alternative to limit the processing time [13]. In a previous work [8], the sprint planning problem for agile projects proposed an optimization model that is also based on the team estimates and a set of development constraints. This model produces the optimal sprint plan by maximizing the business value perceived by the user. ILOG CPLEX optimizer (IBM, 2011) was used with optimization model to acquire the feasible solution for medium-sized problem. But it is a time consuming process for large- sized operational use problem. The sprint planning problem for agile Data Warehouse design was formalized and proposed a multi-knapsack model to solve it. Model was tested on both the synthetic and real projects, and then found that the exact solution is determined for the medium sized problem in a time that is fully compatible with the development process. But for the large sized problems, a heuristic solution that is just a few percentage points far from the exact one can be returned in a couple of seconds. To present the plan in a more effective way, optimization module was coupled with the existing software‘s for agile project management. Here, Greedy heuristic approach is proposed that will provide less computing time for large-sized sprint planning problem. Optimal solution is also acquired through this approach. Therefore, approach is integrated to the optimization model that could be used interactively and coupled with existing software for the agile project management. 2.2Outline The paper is organized as follows section 2 summarizes the agile practices with the goal of sprint planning problem. Section 3 summarizes the mathematical formulation with notation and section 4 ends up with conclusion. 3 PROPOSED SYSTEM Sprint planning phase is within an iterative and incremental approach which ensures the criticality of project success. New requirements may arise during the project and the plan should be flexible enough to accommodate them. In sprint planning, tasks are estimated and completed according to their schedule. Track of the project is recognized through these assessments in sprint planning. Scrum lifecycle embraces the sprint planning phase to acquire the success of the project. IJTET©2015 In fig1, initially user stories are the user functionalities which are chunked into tasks. Individual tasks are estimated by the expert‘s past experience and knowledge. Utility and complexity factors are estimated by the story points of the user story. Planning poker method is used to estimate the complexity of user stories by assigning the story points. Then the user stories are prioritized based on their estimated values. Critical risk and uncertainty risk are the two typical risks on the user stories. Fig.1Scrum Lifecycle Mainly, critical risk has a main impact on the user stories. For example, if the user story 1 has a risk and most probably it affect the story 2. The uncertainty risk is about the unexpected problem occurring during the project progress. Both types of risks are estimated within the following values, risk 1(no risk found), 1.3(low risk found), 1.7(medium risk found) and 2(high risk found). The user stories are correlated by the means of OR and AND dependency. Based on the prioritization, the product backlog is composed and then partitioned into sprints. User stories are allocated to the sprints through the estimation of complexity, development velocity and affinity of the user story. Sprint backlog carries out the details of the user stories from the product backlog. Sprint backlog have the information about the user stories which are in progress and not yet started. It will also have status of unsatisfied user stories which are not delivered. If the user stories are satisfied, then it will 19
  • 3. INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 be delivered. Here the planning problem is converted into a generalized problem and solved using linear programming model by accepting the constraints in it. Objective function is to maximize the cumulative utility of the project. Sprint planning problem has a major impact on the project success. To achieve the project success, following goals have to be satisfied in sprint planning: 1. Customer satisfaction – It is achieved by,(i) Delivering the user stories with high utility based on the customer expectations.(ii) To maximize the user value, include the affine stories in the same sprint. 2. Risk Management –It is achieved by advancing a critical and unpredictable user stories to avoid a late side effects. Then by distributing the risky stories uniformly. Fig.2 System Architecture In fig.2, Sprint planning problem is assigned to be a large scale problem which means allocation of user stories in sprint plan should be higher. Then the sprint planning problem is framed into a general assignment problem. The framed problem should be understandable to CPLEX optimizer. In user data, number of user stories and sprint availability details have to be given as input. The MILP model constraints and greedy heuristic constraints are given as the enhancement to the CPLEX optimizer. The solution obtained is with less time when compared to the execution before enhancement. 4 MATHEMATICAL FORMULATION In this section, greedy heuristic approach is proposed to minimize IJTET©2015 the time taken for computing the large-sized sprint planning problem in the IBM ILOG CPLEX optimizer. Let U = {1…n} be the set of n user stories to be allotted to the sprints. Here the procedure starts by optimizing sprint i=1 and then optimizes the remaining sprints in them, one at a time. Therefore at each iteration, greedy heuristic procedure consider a sprint i∈S and assigns to the stories that maximize the utility by solving the sub-problems. Given a set of m sprint S and a set of n user stories U. let: - 𝑤𝑖𝑗 =1, iff story j is included in sprint i, otherwise 0. - 𝑈𝑗 , be the utility of the story j. - 𝑞𝑗 , be the number of story points of story j. - 𝑄𝑖, be the capacity of sprint i, measured in story points. - 𝑅 𝐶𝑅𝑗 , be the criticality risk of story j. - 𝑅 𝑈𝑁𝑗 , be the uncertainty risk of story j. - 𝐶𝑗 , be the affinity between the story in j. - 𝑋𝑗 , be the set of similar stories to the story j. - 𝑥𝑖𝑗 , be an accessory variable related to the number of stories in 𝑋𝑗 included in sprint i. To maximize the utility by solving the sub-problems by the following mixed integer linear programming model: (𝑆𝑖)𝑍𝑆 𝑖 = 𝑚𝑎𝑥 𝑚 − 𝑖 + 1𝑛 𝑗 =1 𝑈𝑗 (𝑅 𝐶𝑅𝑗 𝑤𝑖𝑗 + 𝐶𝑗 𝑥𝑖𝑗 ) (1) s.t 𝑞𝑗 𝑛 𝑗=1 𝑅 𝑈𝑁𝑗 𝑤𝑖𝑗 ≤ 𝑄𝑖, i∈ 𝑆 (2) 𝑥𝑖𝑗 ≤ 𝑤𝑖𝑘 𝑛 𝐾∈𝑋 𝑗 , j∈U (3) 𝑤𝑖𝑗 ∈ {0, 1}, j∈U𝐵𝑖 (4) 𝑤𝑖𝑗 = 0, j∈ 𝐵𝑖 (5) 𝑥𝑖𝑗 ≥ 0, i∈S, j∈U (6) Where 𝐵𝑖 represent the stories already assigned to the sprints considered in the previous iteration. The mainly objective function is to (1) maximize the cumulative utility of the sub-problems. The utility 𝑈𝑗 for each story is increased by increment of criticality risk 𝑅 𝐶𝑅𝑗 . So that critical stories are considered in the earlier stage of the project and then by increment of affinity 𝐶𝑗 of the story, similar stories are included in the same sprint. Constraint (2) ensures the overall complexity of all the stories assigned to each sprint does not exceed the estimated sprint capacity value. To strengthen constraint (2), sprint capacity or weight of the user stories are modified to reduce the computing time. Constraint (3) ensures correct evaluation of 𝑥𝑖𝑗 which does not require any 20
  • 4. INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 integrality constraint. This mathematical formulation can be solved by a MIP solver. Sub-problem should follow the forthcoming strategies: (i) If there is no user story j in sprint I, then fix 𝑤𝑖𝑗 =0 and re- optimize the knapsack problem(𝑆𝑖 ). (ii) To increase the profit in every knapsack problem 𝑆𝑖 by multiplying the profit with 𝐾𝑗 (ie, coefficient 𝐾𝑗 is defined for user story j. By having 𝑤𝑖𝑗 =0 in the current solution, increase the coefficient(𝐾𝑗 ). Then restart the greedy heuristic from the first sprint i=1. This strategy requires too much iteration to reach a feasible solution. Then the unchanged user stories should be distributed among the sprints: 𝑤𝑖𝑗 𝑛 (𝑖,𝑗)∈𝑤= ≥ L’ (7) Where w represent the subset of variables{𝑤𝑖𝑗 }set to one in the previous sprint planning and L is the minimum number of variables of subset w that do not have to change. Then L‘ is the difference between L and the story that already got changed in the previous sprints. 4 CONCLUSION In this paper, an approach for the sprint planning in agile methods based on an integer linear programming model is provided. The mathematical formulations are solved by a general purpose MIP solver, IBM ILOG CPLEX optimizer. However, the computing time to solve to optimality of the medium sized problem is very large. In an attempt to reduce the computing time, reduction and sub-problem are solved. Sprint planning problem is framed by gathering the risk, complexity, utility and affinity values of the user stories. Constraints and these factors values are given as input to the sprint plan. Optimal solution for medium-sized instances is solved easily within less time. But for the large instance, the problem prevails in solving the sprint plan. Since solving the model to optimality in MIP solver, is not suitable for an operational use and takes some time to solve this problem. So that Greedy heuristic approach is given as a proposal. In this approach, planning problem are chunked into sub-problem and solved separately in iterations. From the iteration of sub-problem, best feasible solution is retrieved at each step. The computational result using greedy heuristic approach will be able to attain a feasible and optimal solution with very quick time constraints. This approach can be improved by identifying the risk and designing a plan in a real IJTET©2015 time approach. Then by identifying the skill of each expert, sprint plan can be designed to obtain a further better feasible value as a result. REFERENCES [1] BegonaLosada, MaiteUrretavizcaya, Isabel Fernandez- Castro, A guide to agile development of interactive software with a ‗‗User Objectives‘‘, 78 (2013) 2268–2281. [2]J. M. Bass, ‗Agile Method Tailoring in Distributed Enterprises: Product Owner Teams‘, in Proc. IEEE 8th Int. Conf. on Global Software Engineering, Bari, Italy, 2013, pp. 154–63. [3] P.Coad, E. LeFebvre, and J.D. Luca, Java Modeling in Color. Englewood Cliffs, NJ: Prentice Hall, 1999. [4] A.Cockburn, Agile Software Development. Reading, MA: Addison Wesley, 2001. [5] K.Schwaber and M. Beedle, Agile Software Development with Scrum, 2001. [6] K. Beck and C. Andres, Extreme Programming Explained, 2nd ed. Addison Wesley, 2004. [7] M.Poppendieck and T.Poppendieck, Lean Software Development: An Agile Toolkit. Addison-Wesley Longman Publishing Co., Inc., 2003. [8] Matteo Golfarelli, Stefano Rizzi, and Elisa Turricchia, ‖Sprint Planning Optimization in Agile Data Warehouse Design―, 40136 Bologna, Italy. [9] Kolisch. R. Padman. R, An integrated survey of deterministic project scheduling. Omega 29, 249–272, 2001. [10] Herroelen, W., Leus, R., Demeul -emeester, E., ―Critical chain project scheduling: do not over-simplify‖, Project Management Journal 33, 48–60., 2002. [11] Stavros Stavru, ―A critical examination of recent industrial surveys on agile method usage‖ P.B. 48, 1164 Sofia, [12] Golfarelli M, Rizzi S, Turricchia E. Multi-sprint planning and smooth re- planning: an optimization model. Journal of Systems and Software 2013; 86(9):2357–70. [13]. V. Boyer, Didier EL BAZ, MoussaElkihel LAAS-CNRS, ―Solution of Multi-dimensional Knapsack Problem via Cooperation Of Dynamic Programming And Branch And Bound‖, 31077. [14]. Boschetti M, Hadjinconstantinou E, Mingozzi A,‖ New upper bounds for the finite two-dimensional orthogonal non-guillotine cutting stock problem‖,2002;13:95–119. [15]. Boschetti M, Maniezzo V, Roffilli M, BolufeRohlerA, ―Matheuristics :optimization, simulation and control, vol. 5818. Springer; 2009.p.171–7. [16].Boschetti M, Mingozzi A. The two-dimensional finite bin packing problem, 2003; 1:27–42. [17]. Boschetti M A, Montaletti L. An exact algorithm for the two- dimensional strip- packing problem.OperationsResearch2010; 58 (November (6)):1774–91. 21