Application of 0-1 Fuzzy Programming in Optimum Project Selection

Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

Abstract:

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.

Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081063

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.