Wyniki wyszukiwania - BazTech

1

Fuzzy programming for multi-choice bilevel transportation problem

Arora Ritu, Gupta Kavita

Operations Research and Decisions

|

2021

|

Vol. 31, No. 3

5--21

EN

Multi-choice programming problems arise due to the diverse needs of people. In this paper, multichoice optimization has been applied to the bilevel transportation problem. This problem deals with transportation at both the levels, upper as well as lower. There are multiple choices for demand and supply parameters. The multi-choice parameters at the respective levels are converted into polynomials which transmute the defined problem into a mixed integer programming problem. The objective of the paper is to determine a solution methodology for the transformed problem. The significance of the formulated model is exhibited through an example by applying it to the hotel industry. The fuzzy programming approach is employed to obtain a satisfactory solution for the decision-makers at the two levels. A comparative analysis is presented in the paper by solving the bilevel multi-choice transportation problem with goal programming mode as well as by the linear transformation technique. The example is solved using computing software.

2

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

Arora R., Gupta K.

Archives of Control Sciences

|

2020

|

Vol. 30, No. 4

683--699

EN

Bilevel programming problem is a non-convex two stage decision making process in which the constraint region of upper level is determined by the lower level problem. In this paper, a multi-objective indefinite quadratic bilevel programming problem (MOIQBP) is presented. The defined problem (MOIQBP) has multi-objective functions at both the levels. The followers are independent at the lower level. A fuzzy goal programming methodology is employed which minimizes the sum of the negative deviational variables of both the levels to obtain highest membership value of each of the fuzzy goal. The membership function for the objective functions at each level is defined. As these membership functions are quadratic they are linearized by Taylor series approximation. The membership function for the decision variables at both levels is also determined. The individual optimal solution of objective functions at each level is used for formulating an integrated pay-off matrix. The aspiration levels for the decision makers are ascertained from this matrix. An algorithm is developed to obtain a compromise optimal solution for (MOIQBP). A numerical example is exhibited to evince the algorithm. The computing software LINGO 17.0 has been used for solving this problem.

3

Branch and bound algorithm for discrete multi- level linear fractional programming problem

Arora R., Gupta K.

Operations Research and Decisions

|

2018

|

Vol. 28, No. 2

5--21

EN

An algorithm is proposed to find an integer solution for bilevel linear fractional programming problem with discrete variables. The method develops a cut that removes the integer solutions which are not bilevel feasible. The proposed method is extended from bilevel to multilevel linear fractional programming problems with discrete variables. The solution procedure for both the algorithms is elucidated in the paper.

4

Robust bi-level optimization for an opportunistic supply chain network design problem in an uncertain and risky environment

Golpîra H.

Operations Research and Decisions

|

2017

|

Vol. 27, No. 1

21--41

EN

This paper introduces the problem of designing a single-product supply chain network in an agile manufacturing setting under a vendor managed inventory (VMI) strategy to seize a new market oppor-tunity. The problem addresses the level of risk aversion of the retailer when dealing with the uncertainty of market related information through a conditional value at risk (CVaR) approach. This approach leads to a bilevel programming problem. The Karush–Kuhn–Tucker (KKT) conditions are employed to trans-form the model into a single-level, mixed-integer linear programming problem by considering some relaxations. Since realizations of imprecisely known parameters are the only information available, a data-driven approach is employed as a suitable, more practical, methodology of avoiding distribu-tional assumptions. Finally, the effectiveness of the proposed model is demonstrated through a numer-ical example

5

Bilevel limit analysis of self-hardening rod systemsunder moving load

Alawdin P., Urbańska K.

Computer Assisted Methods in Engineering and Science

|

2017

|

Vol. 24, no. 4

225--238

EN

This paper considers results of an analysis of self-hardening systems (SHS), i.e. load-carrying systemswith improved strength and rigidity. The indicated structural features can be only found if geometricalnonlinearity is taken into consideration. Material deforming diagrams can be non-monotonic and non-smooth, and constraints can be unilateral, with gaps. Furthermore, optimisation of a mathematical modelof a rod structure as a discrete mechanical system withstanding dead (constant) and/or moving loadsis proposed. This model is formulated using bilevel mathematical programming. The limit parametersof standard loads and actions are found in the low-level optimisation. An extreme energy principle isproposed to obtain the limit parameters of these actions. Onthe upper level, the parameters of movingload are maximized. A positive influence of equilibrium or quasi-equilibrium constant load with the possiblepreloading of SHS is shown. A set of criteria for the stability of plastic yielding of structures, including non-smooth and non-convex problems of optimisation is given. The paper presents an exemplary application of the proposed method which takes into account the self-hardening effect.

6

Combined Reformulation of Bilevel Programming Problems

Pilecka M.

Schedae Informaticae

|

2012

|

Vol. 21

65--79

EN

In [19] J.J. Ye and D.L. Zhu proposed a new reformulation of a bilevel programming problem which compounds the value function and KKT approaches. In [19] partial calmness condition was also adapted to this new reformulation and optimality conditions using partial calmness were introduced. In this paper we investigate above all local equivalence of the combined reformulation and the initial problem and how constraint qualifications and optimality conditions could be defined for this reformulation without using partial calmness. Since the optimal value function is in general nondifferentiable and KKT constraints have MPEC-structure, the combined reformulation is a nonsmooth MPEC. This special structure allows us to adapt some constraint qualifications and necessary optimality conditions from MPEC theory using disjunctive form of the combined reformulation. An example shows, that some of the proposed constraint qualifications can be fulfilled.

7

A new genetic approach for transport network design and optimization

Dinu S., Bordea G.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2011

|

Vol. 59, nr 3

263-272

EN

This paper presents an improved Genetic Algorithm to solve the Transportation Network Design Problem (CTNDP) with interactions among different links. The CTNDP is formulated in an optimal design as a bi-level programming model. A key factor in the present approach is the combination of diploid based complex-encoding with meiosis specific features. The novel mutation operator proposed is another improvement that leads to a better robustness and convergence stability. The computational results obtained by comparing the performance of the proposed algorithm and other Genetic Algorithms for a test network demonstrates its better local searching ability, as well as its high efficiency. Finally, suggestions for further research and extensions are given.