Project management decisions using fuzzy linear programming

This work presents an interactive fuzzy linear programming (FLP) approach for solving project management (PM) decision problems in a fuzzy environment. The proposed approach attempts to minimize total costs with reference to direct, indirect and penalty costs, durations of activities, specified project completion time and total allocated budget. A numerical example demonstrates the feasibility of applying the proposed FLP approach to actual PM decision problems. Accordingly, the proposed approach yields an efficient solution and determines the overall degree of decision maker (DM) satisfaction. Moreover, the proposed approach offers a systematic framework that facilitates the decision-making process, enabling a DM to interactively modify the range of the results when the environment data are vague until a satisfactory solution is obtained. In particular, several significant characteristics of the proposed FLP approach are elucidated in contrast to those of the main PM decision methods.

[1]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[2]  B. Werners An interactive fuzzy programming system , 1987 .

[3]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[4]  C. Carlsson,et al.  A parametric approach to fuzzy linear programming , 1986 .

[5]  H. F. Wang,et al.  Fuzzy resource allocations in project management when insufficient resources are considered , 1996, Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium.

[6]  Richard Y. K. Fung,et al.  Fuzzy modelling and simulation for aggregate production planning , 2003, Int. J. Syst. Sci..

[7]  C. Hwang,et al.  Interactive fuzzy linear programming , 1992 .

[8]  Zülal Güngör,et al.  An application of fuzzy goal programming to a multiobjective project network problem , 2001, Fuzzy Sets Syst..

[9]  J. Ramík,et al.  Inequality relation between fuzzy numbers and its use in fuzzy optimization , 1985 .

[10]  Elsayed A. Elsayed,et al.  Algorithms for project scheduling with resource constraints , 1982 .

[11]  K. M. Mjelde Fuzzy resource allocation , 1986 .

[12]  Edward W. Davis,et al.  A Comparison of Heuristic and Optimum Solutions in Resource-Constrained Project Scheduling , 1975 .

[13]  Pandian Vasant,et al.  Application of Fuzzy Linear Programming in Production Planning , 2003, Fuzzy Optim. Decis. Mak..

[14]  H. Rommelfanger Interactive decision making in fuzzy linear optimization problems , 1989 .

[15]  Didier Dubois,et al.  Refinements of the maximin approach to decision-making in a fuzzy environment , 1996, Fuzzy Sets Syst..

[16]  Elden L. Deporter,et al.  Optimization of project networks with goal programming and fuzzy linear programming , 1990 .

[17]  Tien-Fu Liang,et al.  Project management decisions with multiple fuzzy goals , 2004 .

[18]  S. Chanas,et al.  THE USE OF FUZZY VARIABLES IN PERT , 1981 .

[19]  J. Dombi Membership function as an evaluation , 1990 .

[20]  D. Dubois,et al.  Systems of linear fuzzy constraints , 1980 .

[21]  Stanislaw Heilpern,et al.  Representation and application of fuzzy numbers , 1997, Fuzzy Sets Syst..

[22]  Chung-lun Li Scheduling to minimize the total resource consumption with a constraint on the sum of completion times , 1995 .

[23]  Reay-Chen Wang,et al.  Aggregate production planning with multiple objectives in a fuzzy environment , 2001, Eur. J. Oper. Res..

[24]  Saeed Karshenas,et al.  Economic optimization of construction project scheduling , 1990 .

[25]  M. Sakawa,et al.  An interactive fuzzy satisficing method for multiobjective linear fractional programming problems , 1988 .

[26]  H. Zimmermann DESCRIPTION AND OPTIMIZATION OF FUZZY SYSTEMS , 1975 .

[27]  E. Hannan Linear programming with multiple fuzzy goals , 1981 .

[28]  R. Słowiński A multicriteria fuzzy linear programming method for water supply system development planning , 1986 .

[29]  H. Zimmermann Fuzzy programming and linear programming with several objective functions , 1978 .

[30]  Didier Dubois,et al.  Computing improved optimal solutions to max-min flexible constraint satisfaction problems , 1999, Eur. J. Oper. Res..

[31]  Robert A. Russell,et al.  A comparison of heuristics for scheduling projects with cash flows and resource restrictions , 1986 .

[32]  H. Rommelfanger Fuzzy linear programming and applications , 1996 .

[33]  Pawel Zielinski,et al.  Critical path analysis in the network with fuzzy activity times , 2001, Fuzzy Sets Syst..