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Frontiers of Engineering Management

ISSN 2095-7513

ISSN 2096-0255(Online)

CN 10-1205/N

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Front. Eng    2020, Vol. 7 Issue (2) : 223-237    https://doi.org/10.1007/s42524-020-0097-1
RESEARCH ARTICLE
Multi-objective optimization for the multi-mode finance-based project scheduling problem
Sameh Al-SHIHABI1(), Mohammad AlDURGAM2
1. Industrial Engineering Department, University of Jordan, Amman 11942, Jordan
2. Systems Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Kingdom of Saudi Arabia
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Abstract

The finance-based scheduling problem (FBSP) is about scheduling project activities without exceeding a credit line financing limit. The FBSP is extended to consider different execution modes that result in the multi-mode FBSP (MMFBSP). Unfortunately, researchers have abandoned the development of exact models to solve the FBSP and its extensions. Instead, researchers have heavily relied on the use of heuristics and meta-heuristics, which do not guarantee solution optimality. No exact models are available for contractors who look for optimal solutions to the multi-objective MMFBSP. CPLEX, which is an exact solver, has witnessed a significant decrease in its computation time. Moreover, its current version, CPLEX 12.9, solves multi-objective optimization problems. This study presents a mixed-integer linear programming model for the multi-objective MMFBSP. Using CPLEX 12.9, we discuss several techniques that researchers can use to optimize a multi-objective MMFBSP. We test our model by solving several problems from the literature. We also show how to solve multi-objective optimization problems by using CPLEX 12.9 and how computation time increases as problem size increases. The small increase in computation time compared with possible cost savings make exact models a must for practitioners. Moreover, the linear programming-relaxation of the model, which takes seconds, can provide an excellent lower bound.
Keywords multi-objective optimization      finance-based scheduling      multi-mode project scheduling      mixed-integer linear programming      CPLEX     
Corresponding Author(s): Sameh Al-SHIHABI   
Just Accepted Date: 21 February 2020   Online First Date: 30 March 2020    Issue Date: 27 May 2020
 Cite this article:   
Sameh Al-SHIHABI,Mohammad AlDURGAM. Multi-objective optimization for the multi-mode finance-based project scheduling problem[J]. Front. Eng, 2020, 7(2): 223-237.
 URL:  
https://academic.hep.com.cn/fem/EN/10.1007/s42524-020-0097-1
https://academic.hep.com.cn/fem/EN/Y2020/V7/I2/223
Paper Single/Portfolio Objective Solution methodology
Elazouni and Gab-Allah (2004) Single Min. duration IP
Elazouni and Metwally (2005) Single Min. duration GA
Liu and Wang (2008) Single Max. profit CP
Abido and Elazouni (2009) Single Min. duration GA
Elazouni (2009) Portfolio Multiple Heuristic
Afshar and Fathi (2009) Single Multiple GA & Fuzzy Sets
Fathi and Afshar (2010) Single Multiple GA
Liu and Wang (2010) Portfolio Max. profit CP
Abido and Elazouni (2011) Portfolio Multiple Heuristic
Elazouni and Abido (2011) Single Multiple Heuristic
Alghazi et al. (2012) Single Min. duration Frog-leaping Algorithm, GA, Simulated Annealing
Alghazi et al. (2013) Single Min. duration GA
Elazouni et al. (2015) Single Min. duration Frog-leaping Algorithm, GA, Simulated Annealing
Gajpal and Elazouni (2015) Single Min. duration Heuristic
Al-Shihabi and AlDurgam (2017) Single Min. duration Max-Min Ant System
Alavipour and Arditi (2018a) Single Min. cost LP
Alavipour and Arditi (2018b) Single Min. cost LP
Tab.1  Summary of FBSP-related publications
Paper Single/Portfolio Objective Solution methodology
Elazouni and Metwally (2007) Single Min. duration Max. profit GA
Ali and Elazouni (2009) Portfolio Min. duration Max. profit GA
Elazouni and Abido (2014) Single Multi-objective Heuristic
El-Abbasy et al. (2016) Portfolio Multi-objective GA
El-Abbasy et al. (2017) Portfolio Multi-objective GA
Alavipour and Arditi (2019b) Single Max. profit GA & LP
Alavipour and Arditi (2019a) Single Max. profit GA & LP
Tab.2  Summary of MMFBSP-related publications
Fig.1  Cumulative expenses versus income profile.
Fig.2  Iterative algorithm to minimize project duration.
Fig.3  Hypothetical cash balance for R = LP = V = 4.
Fig.4  Hypothetical cash balance for R≠ LP.
Fig.5  Fig. 5 Finding alternative solutions using the populate( ) method.
Activity Option Duration (week) Cost ($) Time-cost function Number of modes
Upper Lower Lower Limit
A 1 28 22 100 130 Piecewise linear 15
2 22 18 140 210
3 28 22 100 130
B 1 20 14 50 80 Linear with gaps 10
2 10 8 120 300
C 1 15 15 75 75 Discrete points 3
2 8 8 240 240
2 4 4 500 500
D 1 18 12 70 220 Linear and discrete points 8
2 5 5 360 360
E 1 26 18 40 80 Piecewise linear 22
2 18 14 200 240
3 14 6 240 260
F 1 25 15 120 300 Linear 11
G 1 7 7 0 0 Discrete points 11
Tab.3  Contractor cost parameters of the MMTCTP example
Fig.6  Network representing the precedence relationships of the MMTCTP example.
Duration (week) Budget ($) Number of alternatives
76 911.0 22
75 910.0 22
74 909.0 23
73 908.0 25
72 907.0 25
71 906.0 906
70 905.0 21
69 904.0 21
68 903.0 21
67 902.0 21
66 901.0 21
65 900.0 20
64 917.0 21
63 933.0 21
62 944.5 22
61 956.0 23
60 973.0 24
Tab.4  Solutions of the MMTCTP example
Fig.7  Network representing the FBSP example.
Contract parameters ?Loan parameters
Data type Value ?Data type Value
BC $1958 ?APR 58.4%
MOB $7618 ?CL $4000
AP $19779 ?Comp daily
LP 1 week ?V weekly
LR 0 week ?rW 0.8%
MU 1.492
R 1 week
RP 5%
Tab.5  Contract and loan parameters of the FBSP example
Bidding parameters Contracting parameters Financing parameters
Data type Value Data type Value Data type Value
OF $100/day AP 1:1 × (MOB+ BC) CL $20000
MOB $10000 LP 4 weeks Comp daily
OB 2% LR 0 week rD 1%
OP 50% MU calculated V weekly
OV 10% R 4 weeks
RP 20%
Tab.6  Default bidding, contracting, and financing parameters of the experimental study
Fig.8  Solutions having different CL and profits for the 30-activity problem.
Duration (week) Min. CL ($) Max. Profit ($) Min. Interest ($)
34 29377 92610 636
35 28907 92930 618
36 26930 93543 577
37 27125 92250 556
38 26173 92375 548
39 24104 93659 516
40 24624 93425 489
Tab.7  Computation time experiment results of the 30-activity project example
Instance size CPM solution (week) LP-relaxation solution (week) LP-relaxation time (s) MILP solution (week) MILP solution time (s)
30 29 33 0 34 2
60 49 55 0 56 102
120 89 92 10 93 110
240 169 171 157 172 2433
Tab.8  Computation time experiment results for different project size
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