A Novel Robust Model for Discrete Time -Cost Trade off...

713 محمد جعفر تارخ، مير بهادر قلي آريا نژاد، مصطفي اختياري و مهدي يزداني مديريت ريسك اعتباري تحت عدم قطعيت با استفاده از...

A Novel Robust Model for Discrete Time-Cost Trade

off Problem

S. Moghani Ghahremanlouie & K. Fathi Hafashjani*

Sepide Moghani Ghahremanlouie-M.A Student, Department of Industrial management, South Tehran Branch, Islamic Azad University, Tehran Iran Kiamars Fathi Hafshejani-Assistance Professor, Department of Industrial management, South Tehran Branch, Islamic Azad University, Tehran

Keywords

1 ABSTRACT

In project scheduling, the activity durations can often be reduced by

dedicating additional resources. Time/Cost Trade-off Problem

considers the compromise between the total cost and project

duration. The discrete version of the problem assumes a number of

time/cost pairs, so called modes, and selects a mode for each

activity. In this paper, we consider the Discrete Time/Cost Trade-off

Problem. We study the problem of minimizing total cost subject to a

deadline on project duration so called Deadline problem. Projects

are often subject to various sources of uncertainties that have a

negative impact on activity durations and costs. Therefore, it is

crucial to develop effective approaches to generate robust project

schedules that are less vulnerable to disruptions caused by non-

controllable factors. We propose a novel robust model for the

DTCTP in which interval uncertainty is assumed for the unknown

cost parameters. We use genetic algorithms to solve the proposed

robust optimization model. Our computational results on large-sized

problem instances have revealed the satisfactory behavior of our

algorithms.

© 2014 IUST Publication, IJIEPM. Vol. 25, No. 1, All Rights Reserved

**

Corresponding author. Kiyamars Fathi Hafshajani Email: [email protected]

May 2014, Volume 25, Number 1

pppp.. 11--1144

hhttttpp::////IIJJIIEEPPMM..iiuusstt..aacc..iirr//

IInntteerrnnaattiioonnaall JJoouurrnnaall ooff IInndduussttrriiaall EEnnggiinneeeerriinngg && PPrroodduuccttiioonn MMaannaaggeemmeenntt ((22001144))

Discrete Time-Cost Trade off

Problem,

Robust Optimization,

Uncertainty,

Project Scheduling,

Genetic Algorithm

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http://ijiepm.iust.ac.ir/article-1-794-fa.html

ي هفشجانيسپيده مغاني قهرمانلوئي و کيامرث فتح هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان 713

1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،

نه گسستهيهز-زمان يموازنه ين در مسئله يمدل استوار نو

* يهفشجان يامرث فتحيکي و قهرمانلوئ يده مغانيسپ

چکيده: يکلمات کليد

1. مقدمه1

.

11/4/19تاريخ وصول:

13/4/11تاريخ تصويب: سپيده مغاني قهرمانلوئي،

[email protected] کيامرث فتحي هفشجانيدکترنويسنده مسئول مقاله:*

[email protected]

.

1313 خــرداد، 25، جلــد 1شمــاره

22--1111صفحـــه صفحـــه

hhttttpp::////IIJJIIEEPPMM..iiuusstt..aacc..iirr//

ISSN: 2008-4870

، ، ، ،

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Deadline Problem

Budget Problem

NP-hard

.

DTCTP-d

.

AARC

(STCTP

.

)

.

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4 سپيده مغاني قهرمانلوئي و کيامرث فتحي هفشجاني هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان


DTCTP_d

(DTCTP_d

استوار بهينه سازي . روش2

:

.

.

n

c, l, u n A

nm bm

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}A},...,2,1عدم قطعيت روي ماتريس nN

A

ija~Nj

]ˆ,ˆ[ ijijijij aaaa

ija

ijAija

ija

c :cjNjبردار هزينه عدم قطعيت روي

[cj, cj+ dj] dj

cj

A

CMIP

ii = 0,1,2,….m

i

0

i

i=1,2,….m

i [0, |Ji| ]

} 0 ija = {j |Jii

JiiA

0i

iA

Ji

i

i [0, |Ji| ]

j Ji ija

ii

A

itaita ii

0

C0 [0, |J0|

]} 0 jd {j |=J00

MIP

Zi ,Yj ,Pij ,Z0

.

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nm

2n+m+l2n+m+l

m

i iJl0

||

هزينه گسسته با زمان –. مسئله استوار موازنه زمان7 (DTCTP-d) اتمام مورد نظر

MIPDTCTP-d

n

N,A)G=N A

N n

0,n+1

NNA

j j ={1,2,...,| M j |}

|Mj

Mjj

mjMm

jmpjmc

jC

j

jmX jMm

j

i , j

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jmp

jmc

DTCTP-dB&S

n

0

n

DTCTP-d

B&S

1مدل n 0

jmCn-

jmc

j djm

djm j

MIP

SNNS

S

S

XD

DTCTP-dMax

S

nUjBn

n

1Uj djm

2مدل

n

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Slack/Activity

Time

Slack/Duration

%100

jTS jp

j

SDTSDT

25.0

1. 2. 7.

1Slack Duration Threshold

7مدل

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نتيجه گيري مدلهاي ارائه شده. 1-7

DTCTP-d

DTCTP-d

هزينه گسسته –. مدل نوين مسئله موازنه زمان 4 استوار و حل آن

1. 2. 7. 4.

مدل نوين پيشنهادي. 1-4

DTCTP-d

MIP

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CRXD

f

فرآيند حل مدل جديد .1مودار ن

حل مدل نوين با استفاده از الگوريتم ژنتيک. 2-4

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.

nn

.

کروموزوم قالب. 1شکل

AON

موردي . مطالعه5

Feng Kuang

Xiong Zheng

Daisy

-

. اطالعات پروژه عمراني1 جدول

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0

. مقادير بازه اي هزينه محاسبه شده2 جدول

يعمران پروژه نمودار. 2شکل

0

7

مدل 7. نتايج حل 7 جدول

7,5,3

3

6,3

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2 مدل در نهيهز -اتمام زمان نمودار. 7شکل

375

585

6,3

7 مدل در نهيهز -اتمام زمان نمودار .4شکل

نينو مدل در نهيهز -اتمام زمان نمودار. 7 شکل

. نتيجه گيري6

B&S

DTCTP-d

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DTCTP-b

مراجع

Hafizoğlu, A.B., "Discrete Time/Cost Trade-Off

Problem In Project Scheduling", A Thesis

Submitted To The Graduate School Of Natural And

Applied Sciences Of Middle East Technical

University, 2007.

[1]

De, .P.E., Dunne, J., Ghosh, J.B., Wells, C.E.,

"Complexity of the Discrete Time/Cost Trade off

Problem for Project Networks" , Operations

Research, 45, 1997, 302–306.

[2]

Demeulemeester, E., De Reyck, B., Foubert, B.,

Herroelen, W., Vanhoucke, M., "New

Computational Results for the Discrete Time/Cost

Trade-off Problem in Project Networks" , Journal of

the Operational Research Society 49, 1998, 1153–

1163.

[3]

Skutella, M., "Approximation Algorithms for the

Discrete Time–Cost Trade-off Problem",

Mathematics of Operations Research, 23, 1998,

195–203.

[4]

Akkan, C., Drexl, A., Kimms, A., "Network

Decomposition-Based Benchmark Results for the

Discrete Time–Cost Trade-off Problem ", European

Journal of Operational Research, 165, 2005, 339–

358.

[5]

Vanhoucke, M., Debels, D., "The Discrete

Time/Cost Trade-off Problem Under Various

Assumptions Exact and Heuristic Procedures ",

Journal of Scheduling, 10, 2007, 311–326.

[6]

Hafızog˘lu, A.B., Azizog˘lu, M., "Linear

Programming Based Approaches for the Discrete

Time/Cost Trade-off Problem in Project Networks",

Journal of the Operational Research, Society 61 (4),

2010, 676–685.

[7]

Cohen, I., Golany, B., Shtub, A., "The Stochastic

Time/Cost Trade-off Problem: a Robust

Optimization Approach" , Networks 49, 2007, 175–

188.

[8]

Klerides, E., Hadjiconstantinou, E., "A

Decomposition-Based Stochastic Programming

Approach for the Project Scheduling Problem

under Time/Cost Trade-off Settings and Uncertain

Durations" , Computers and Operations Research,

37 (12), 2010 , 2131–2140.

[9]

Ben-Tal, A., El Ghaoui, L., Nemirovski, A.,

"Robust Optimization ", Princeton University Press,

Princeton and Oxford, 2008.

[10]

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

Uncertainty—Survey and Research Potentials",

European Journal of Operational Research 165,

2005, 289–306.

[11]

Bertsimas, D., Sim, M., "Robust Discrete

Optimization and Network Flows", Mathematical

Programming, 98, 2003, 49–71.

[12]

Soyster, A.L., "Convex Programming with Set-

Inclusive Constraints and Applications to Inexact

Linear Programming", Operation Research, 21,

1973, 1154-1157.

[13]

Ben-Tal, A., Nemirovski, A., "Robust Solutions to

Uncertain Programs", Operations Research Letters,

25, 1999 , 1-13.

[14]

Hazır, O., Erdal, E., Yavuz, G., "Robust

Optimization Models for the Discrete Time - Cost

Trade-off Problem", International Journal of

Production Economics , 130 , 2011, 87–95.

[15]

Bertsimas, D., Brown, D., Caramanis, C., " Theory

and Applications of Robust Optimization ", 2007.

[16]

Xiong, Y., Kuang, Y., "Applying an Ant Colony

Optimization Algorithm-Based Multi Objective

Approach for Time-Cost Trade-Off ", Journal of

Construction Engineering and Management, 134(2),

2008, 153-156.

[17]

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A Novel Robust Model for Discrete Time -Cost Trade off...

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