A multi-objective programming approach to 1.5-dimensional assortment problem

Gasimov, Rafail N.; Sipahioglu, Aydin; Saraç, Tuğba

doi:10.1016/j.ejor.2006.03.016

Cited by 26 publications

(13 citation statements)

References 8 publications

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“…These functions were used to define conical supporting surfaces in nonconvex analysis. One of the main application areas is the nonconvex vector optimization, where these functions were used to characterize efficient solutions (see e.g., [7,14,17,22,30,33]). Another application area of these functions is the single objective mathematical programming (see e.g., [11][12][13][25][26][27]) where the conical supporting surfaces were used to develop optimality conditions and algorithms for calculating optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence and characterization theorems in nonconvex vector optimization

Kasimbeyli

2014

J Glob Optim

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This paper presents existence conditions and characterization theorems for minimal points of nonconvex vector optimization problems in reflexive Banach spaces. Characterization theorems use special class of monotonically increasing sublinear scalarizing functions which are defined by means of elements of augmented dual cones. It is shown that the Hartley cone-compactness is necessary and sufficient to guarantee the existence of a properly minimal point of the problem. The necessity is proven in the case of finite dimensional space.

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Section: Introductionmentioning

confidence: 99%

Existence and characterization theorems in nonconvex vector optimization

Kasimbeyli

2014

J Glob Optim

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“…Efficient points corresponding to the obtained weights by using AHP and ANP have been calculated and the results compared. The conic scalarization method has also been applied to the 1.5-dimensional assortment problem with two objective functions by Gasimov et al [ 20 ]. In the study, the authors focused on the possible nonsupported or “hidden” efficient points.…”

Section: Introductionmentioning

confidence: 99%

“…In these situations a DM may not be sure whether all the efficient points corresponding to own preferences (weights) are found by using the weighted-sum scalarization. To overcome this drawback, Gasimov et al [ 20 ] proposed a way to obtain nonsupported efficient points based on the conic scalarization function.…”

Section: Introductionmentioning

confidence: 99%

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Interactive Reference Point Procedure Based on the Conic Scalarizing Function

Üstün

2014

The Scientific World Journal

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In multiobjective optimization methods, multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions. The conic scalarizing function is a general characterization of Benson proper efficient solutions of non-convex multiobjective problems in terms of saddle points of scalar Lagrangian functions. This approach preserves convexity. The conic scalarizing function, as a part of a posteriori or a priori methods, has successfully been applied to several real-life problems. In this paper, we propose a conic scalarizing function based interactive reference point procedure where the decision maker actively takes part in the solution process and directs the search according to her or his preferences. An algorithmic framework for the interactive solution of multiple objective optimization problems is presented and is utilized for solving some illustrative examples.

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“…To the best of our knowledge, the second objective function is not considered in the VRP literature previously. Earlier, the type minimization was considered in the literature, for cutting and assortment problems [12] and [19].…”

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confidence: 99%

Multiobjective mathematical models and solution approaches for heterogeneous fixed fleet vehicle routing problems

Takan¹,

Kasımbeyli²

2021

JIMO

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In this paper, we study three types of heterogeneous fixed fleet vehicle routing problems, which are capacitated vehicle routing problem, open vehicle routing problem and split delivery vehicle routing problem. We propose new multiobjective linear binary and mixed integer programming models for these problems, where the first objective is the minimization of a total routing and usage costs for vehicles, and the second one is the vehicle type minimization, respectively. The proposed mathematical models are all illustrated on test problems, which are investigated in two groups: small-sized problems and the large-sized ones. The small-sized test problems are first scalarized by using the weighted sum scalarization method, and then GAMS software is used to compute efficient solutions. The large-sized test problems are solved by utilizing the tabu search algorithm.2010 Mathematics Subject Classification. Primary: 90C08, 90C11; Secondary: 90C29.

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A multi-objective programming approach to 1.5-dimensional assortment problem

Cited by 26 publications

References 8 publications

Existence and characterization theorems in nonconvex vector optimization

Existence and characterization theorems in nonconvex vector optimization

Interactive Reference Point Procedure Based on the Conic Scalarizing Function

Multiobjective mathematical models and solution approaches for heterogeneous fixed fleet vehicle routing problems

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