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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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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:*
.
1313 خــرداد، 25، جلــد 1شمــاره
22--1111صفحـــه صفحـــه
hhttttpp::////IIJJIIEEPPMM..iiuusstt..aacc..iirr//
ISSN: 2008-4870
، ، ، ،
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ي هفشجانيسپيده مغاني قهرمانلوئي و کيامرث فتح هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان 7
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
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
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
DTCTP_d
(DTCTP_d
استوار بهينه سازي . روش2
:
.
.
n
c, l, u n A
nm bm
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ي هفشجانيسپيده مغاني قهرمانلوئي و کيامرث فتح هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان 7
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
}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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6 سپيده مغاني قهرمانلوئي و کيامرث فتحي هفشجاني هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
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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1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
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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8 سپيده مغاني قهرمانلوئي و کيامرث فتحي هفشجاني هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
Slack/Activity
Time
Slack/Duration
%100
jTS jp
j
SDTSDT
25.0
1. 2. 7.
1Slack Duration Threshold
7مدل
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ي هفشجانيسپيده مغاني قهرمانلوئي و کيامرث فتح هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان 1
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
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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19 سپيده مغاني قهرمانلوئي و کيامرث فتحي هفشجاني هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
CRXD
f
فرآيند حل مدل جديد .1مودار ن
حل مدل نوين با استفاده از الگوريتم ژنتيک. 2-4
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1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
.
nn
.
کروموزوم قالب. 1شکل
AON
موردي . مطالعه5
Feng Kuang
Xiong Zheng
Daisy
-
. اطالعات پروژه عمراني1 جدول
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12 سپيده مغاني قهرمانلوئي و کيامرث فتحي هفشجاني هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
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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1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
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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14 سپيده مغاني قهرمانلوئي و کيامرث فتحي هفشجاني هزينه گسسته-مدل استوار نوين در مسئله ي موازنه ي زمان
1شماره -27جلد -1717 خــردادنشريه بين المللي مهندسي صنايع و مديريت توليد،
DTCTP-b
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