A linear bilevel programming algorithm: A comment

Candler, Wilfred

doi:10.1016/0305-0548(88)90043-3

Cited by 33 publications

(14 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…x = 2 1 x x ∪ is the set of decision vector, N 1 + N 2 = N total number of decision variables and M is the total number of constraints in the system. 1 C , 2 C and B are constant vectors. 1 A , 2 A are constant matrices.…”

Section: Formulation Of Qblppmentioning

confidence: 99%

“…1 C , 2 C and B are constant vectors. 1 A , 2 A are constant matrices. 1 D , 2 D are constant symmetric matrices.…”

Section: Formulation Of Qblppmentioning

confidence: 99%

“…The bi-level programming problem (BLPP) has received increasing attention in the literature. Candler and Townsley [1] as well as Fortuny-Amat and McCarl [2] presented the formal formulation of BLPP. Anandalingam [3] proposed Stackelberg solution concept to multi-level programming problem (MLPP) as well as bi-level decentralized programming problem (BLDPP).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Pramanik¹,

Dey²,

Ghosh³

et al. 2011

IJSEA

View full text Add to dashboard Cite

show abstract

Section: Formulation Of Qblppmentioning

confidence: 99%

“…1 C , 2 C and B are constant vectors. 1 A , 2 A are constant matrices. 1 D , 2 D are constant symmetric matrices.…”

Section: Formulation Of Qblppmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Pramanik¹,

Dey²,

Ghosh³

et al. 2011

IJSEA

View full text Add to dashboard Cite

show abstract

“…Each level DM independently controls a set of decision variables. Candler and Townsley [16] as well as Fortuny -Amart and McCarl [17] developed the formal BLPP. After that many researchers [18,19] studied BLPP in various perspectives.…”

Section: Introductionmentioning

confidence: 99%

Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem

Pramanik¹,

Banerjee²,

Giri³

2012

IJCA

View full text Add to dashboard Cite

We present fuzzy goal programming approach to solve chance constrained linear plus linear fractional bi-level programming problem. The chance constraints with right hand parameters as random variables of prescribed probability distribution functions are transformed into equivalent deterministic system constraints. We construct nonlinear membership functions based on deterministic system constraints. The nonlinear membership functions are transformed into linear membership functions by using first order Taylor's series approximation. In the bi-level decision making context, decision deadlock may arise due to the dissatisfaction of the lower level decision maker with the decision of upper level decision maker. To overcome this problem, decision maker of each level gives his preference bounds on decision variables under his/her control to provide some relaxation on their decisions. Fuzzy goal programming model is used to achieve highest membership goals by minimizing negative deviational variables. Euclidean distance function is used in order to find out the most satisfactory solution. We solve a chance constrained linear plus linear fractional bi-level programming problem to illustrate the proposed approach. General TermsBi-level programming, linear plus linear fractional programming.

show abstract

“…During the last three decades, bi-level programming problem (BLPP) [1,2] as well as multi-level programming problem (MLPP) [3,4,5] in general for hierarchical decentralized planning problems have been deeply studied and many methodologies have been developed to solve them. Sinha [6] studied multi-level programming technique based on fuzzy mathematical programming.…”

Section: Introductionmentioning

confidence: 99%

Bilevel Multiobjective Programming Problem with Fuzzy Parameters

Pramanik¹,

Partha²

2011

IJCA

View full text Add to dashboard Cite

This paper deals with fuzzy goal programming approach to bilevel multi-objective programming problem with fuzzy parameters. In the proposed approach, the tolerance membership functions for the fuzzily described objective functions are defined by determining individual optimal solution of the objective functions of each of the decision makers. Since the objectives are potentially conflicting in general, possible relaxations of both level decisions are considered by providing preference bounds on the decision variables for avoiding decision deadlock. Then fuzzy goal programming technique is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. An algorithm is presented with termination criteria. An illustrative numerical example is provided to demonstrate the efficiency of the proposed approach. General TermsBi-level multi-objective programming.

show abstract

A linear bilevel programming algorithm: A comment

Cited by 33 publications

References 3 publications

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Chance Constrained Linear Plus Linear Fractional Bi-level Programming Problem

Bilevel Multiobjective Programming Problem with Fuzzy Parameters

Contact Info

Product

Resources

About