Application of 0-1 Fuzzy Programming in Optimum Project Selection

In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.

Authors:

• S. Sadi-Nezhad
• K. Khalili Damghani
• N. Pilevari

Keywords:

• Fuzzy Programming
• Fuzzy Knapsack
• FuzzyCapital Budgeting
• Fuzzy Project Selection

References:

[1] Akbar, M. M., M. S. Rahman, M. Kaykobad, E.G. Manning & G.C.
Shoja, "Solving the Multidimensional Multiple-choice Knapsack
Problem by constructing convex hulls", Computers & Operations
Research, Vol. 33, No. 5, pp1259-1273, 2006.
[2] Akinc, U., "Approximate and exact algorithms for the fixed-charge
knapsack problem", European Journal of Operational Research, Vol.
170, No. 2, pp363-375, 2006.
[3] Antonio, E. B., C. Hongbin & J. Luo, "Capital budgeting and
compensation with asymmetric information and moral hazard", Journal
of Financial Economics, Vol. 61, No. 3, pp311-344, 2001.
[4] Balev, S., N. Yanev, A. Fréville & R. Andonov, "A dynamic
programming based reduction procedure for the multidimensional 0-1
knapsack problem", European Journal of Operational Research,
Vol.186, No. 1, pp63-76, 2008.
[5] Bektas, T., O. O─ƒuz, "On separating cover inequalities for the
multidimensional knapsack problem", Computers & Operations
Research, Vol. 34, No. 6, pp1771-1776, 2007.
[6] Chan, Y., J. P. DiSalvo & M. Garrambone, "A goal-seeking approach to
capital budgeting". Socio-Economic Planning Sciences, Vol. 39, No. 2,
pp165-182, 2005.
[7] Cho, K. I., S. H. Kim, "An improved interactive hybrid method for the
linear multi-objective knapsack problem". Computers & Operations
Research, Vol. 24, No. 11, pp991-1003, 1997.
[8] Coldrick, S., P. Longhurst, P. Ivey & J. Hannis, "An R&D options
selection model for investment decisions", Technovation, Vol. 25, No.3,
pp185-193, 2005.
[9] Dumitru, V., F. Luban, "On some optimization problems under
uncertainty", Fuzzy Sets and Systems, Vo. 18, No. 3, pp257-272, 1986.
[10] Elhedhli, S., "Exact solution of a class of nonlinear knapsack
problems", Operations Research Letters, Vol. 33, No. 6, pp615-624,
2005.
[11] Fréville, A., "The multidimensional 0-1 knapsack problem", An
overview. European Journal of Operational Research, Vol. 155, No. 1,
pp1-21, 2004.
[12] Gabrel, V., M. Minoux , "A scheme for exact separation of extended
cover inequalities and application to multidimensional knapsack
problems", Operations Research Letters, Vol. 30, No. 4, pp252-264,
2002.
[13] Huang, X., "Chance-constrained programming models for capital
budgeting with NPV as fuzzy parameters", Journal of Computational
and Applied Mathematics, Vol. 198,No 1, pp149-159, 2007.
[14] Huang, X., "Credibility-based chance-constrained integer
programming models for capital budgeting with fuzzy parameters",
Information Sciences, Vol. 176, No. 18, pp2698-2712, 2007.
[15] Huang, X., "Mean-variance model for fuzzy capital budgeting",
Computers & Industrial Engineering, In Press, Corrected
Proof, Available online 8 December, 2007.
[16] Huang, X., "Optimal project selection with random fuzzy parameters",
International Journal of Production Economics, Vol. 106, No. 2, pp513-
522, 2007.
[17] Kaparis, K., A. N. Letchford, "Local and global lifted cover
inequalities for the 0-1 multidimensional knapsack problem", European
Journal of Operational Research, Vol. 186, No. 1, pp91-103, 2008.
[18] Kolliopoulos, S. G., G. Steiner, "Partially ordered knapsack and
applications to scheduling", Discrete Applied Mathematics, Vol. 155,
No. 8, pp889-897, 2007.
[19] Liang, R., J. Gao, "Chance Programming Models for Capital
Budgeting in Fuzzy Environments", Tsinghua Science & Technology,
Vol. 13, pp117-120, 2008.
[20] Liang, R., J. Gao., "Dependent-Chance Programming Models for
Capital Budgeting in Fuzzy Environments", Tsinghua Science &
Technology, Vol. 13, No. 1, pp117-120, 2008.
[21] Lee, B. N., J. S. Kim, "Capital budgeting model with flexible budget",
Computers & Industrial Engineering, Vol. 27, No. 1-4, pp317-320,
1994.
[22] Masood, A. Badri, D. Davis & D. Davis, "A comprehensive 0-1 goal
programming model for project selection", International Journal of
Project Management, Vol. 19, No. 4, pp243-252, 2001.
[23] Padberg, M., M. J. Wilczak, "Optimal project selection when
borrowing and lending rates differ", Mathematical and Computer
modelling, Vol. 29, No. 3, pp63-78, 1999.
[24] Slagmulder, R., W. Bruggeman & L. van Wassenhove, "An empirical
study of capital budgeting practices for strategic investments in CIM
technologies", International Journal of Production Economics, Vol. 40,
No. 2-3, pp121-152, 1995.
[25] Steuer, R. E., Na. Paul, "Multiple criteria decision making combined
with finance: A categorized bibliographic study". European Journal of
Operational Research, Vol. 150, No. 3, pp496-515, 2003.
[26] Timothy, Ch., U. Kalu, "Capital budgeting under uncertainty: An
extended goal programming approach", International Journal of
Production Economics, Vol. 58, No. 3, pp235-251, 1999.
[27] Taylor, R. G., "A general form for the capital projects sequencing
problem". Computers & Industrial Engineering, Vol. 33, No. 1-2, pp47-
50, 1997.
[28] Vasquez, M., Y. Vimont, "Improved results on the 0-1
multidimensional knapsack problem". European Journal of Operational
Research, Vol. 165, No. 1, pp70-81, 2005.