A Profit Maximizing Solid Transportation Model Under a Rough Interval Approach

Das, Amrit; Bera, Uttam Kumar; Maiti, Manoranjan

doi:10.1109/tfuzz.2016.2556010

Cited by 42 publications

(14 citation statements)

References 24 publications

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“…Definition 11 [36] (p. 487): The qualitative value B R is called a rough interval (RI) when one can assign two closed intervals B L and B U on a real number set R to it, where B L ⊆ B U . Moreover, (i) If y ∈ B L , then B R surely takes y (denoted by y ∈ B R ).…”

Section: Triangular Fuzzy Number Tfnsmentioning

confidence: 99%

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

2019

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Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible.

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Section: Triangular Fuzzy Number Tfnsmentioning

confidence: 99%

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

2019

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“…Most of the researchers developed two-dimensional or three-dimensional problems that motivated us to form a four-dimensional real transportation problem. [2] 3-dimension one × × -crisp Haley [29] 3-dimension one × × -crisp Hirsch and Dantzig [11] 2-dimension one × × crisp Verma et al [14] 2-dimension one × × × fuzzy Shafaat and Goyal [15] 2-dimension one × × × crisp Saad and Abbas [16] 2-dimension one × × × fuzzy Jimenez et al [24] 3-dimension one × × × fuzzy Tao et al [28] 3-dimension one × × × rough Ojha et al [30] 2-dimension multi-item × × fuzzy Liu et al [31] 3-dimension one × × × type-2 fuzzy Kundu et al [27] 3-dimension multi-item × × × type-2 fuzzy Yang et al [3] 2-dimension one × × fuzzy Giri et al [32] 3-dimension multi-item × × fuzzy Kocken et al [4] 3-dimension one × × × fuzzy Das et al [6] 3-dimension one × × × rough Present Paper…”

Section: Motivationmentioning

confidence: 99%

“…Step 2: In this step, LPIC-1 again transformed into two linear programming problem where crisp coefficients are considered i.e., LP-1 and LP-2 given by respectively the problems (5) and (6) and similarly from LPIC-2 as LP-3 and LP-4 given by (7) and (8), respectively.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…Moreover, due to the constantly changing business environment, the parameters related to transportation are imprecise. This situation has been recently dealt with in two recent investigations Das et al [6] and Bera et al [7]. Again, the transportation of multi-items may be substitutable and/or complementary because more options/choices of items bring more customers.…”

Section: Introductionmentioning

confidence: 99%

“…Tao et al [28] applied rough multiple objective programming in STP. Das et al [6] developed a profit-maximizing STP with parameters represented by rough intervals. Recently, Bera et al [7] solved multi-item 4D TPs under budget constraints using rough interval values for TP parameters.…”

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confidence: 99%

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Constrained FC 4D MITPs for Damageable Substitutable and Complementary Items in Rough Environments

et al. 2019

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Very often items that are substitutable and complementary to each other are sent from suppliers to retailers for business. In this paper, for these types of items, fixed charge (FC) four-dimensional (4D) multi-item transportation problems (MITPs) are formulated with both space and budget constraints under crisp and rough environments. These items are damageable/breakable. The rates of damageability of the items depend on the quantity transported and the distance of travel i.e., path. A fixed charge is applied to each of the routes (independent of items). There are some depots/warehouses (origins) from which the items are transported to the sales counters (destinations) through different conveyances and routes. In proposed FC 4D-MITP models, per unit selling prices, per unit purchasing prices, per unit transportation expenditures, fixed charges, availabilities at the sources, demands at the destinations, conveyance capacities, total available space and budget are expressed by rough intervals, where the transported items are substitutable and complementary in nature. In this business, the demands for the items at the destinations are directly related to their substitutability and complementary natures and prices. The suggested rough model is converted into a deterministic one using lower and upper approximation intervals following Hamzehee et al. as well as Expected Value Techniques. The converted model is optimized through the Generalized Reduced Gradient (GRG) techniques using LINGO 14 software . Finally, numerical examples are presented to illustrate the preciseness of the proposed model. As particular cases, different models such as 2D, 3D FCMITPs for two substitute items, one item with its complement and two non substitute non complementary items are derived and results are presented.

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Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Seikh

Dutta

2021

Int J Intell Syst

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Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual-layer information. In real-life problems, there are many situations where players of a matrix game cannot assess their pay-offs by using fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. RIs are used as an excellent tool to handle such situations. This paper explores matrix games with RI pay-offs and investigates two different solution methodologies to solve such a game. In the first approach, a pair of auxiliary linear programming problems with RI coefficients for the players has been constructed. Then each of the two auxiliary programming problems is converted into two linear programming problems with interval coefficients (LPPICs) using lower and upper approximation intervals of the RI. Finally from each LPPIC, two classical linear programming problems (LPPs) are constructed. In the second approach, the expected value technique for RI is used for transforming auxiliary mathematical programming models under the RI environment to crisp LPP. A case study on the telecom market share problem is considered to show the applicability of the proposed approaches and results are compared and analyzed with an existing method.

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A Profit Maximizing Solid Transportation Model Under a Rough Interval Approach

Cited by 42 publications

References 24 publications

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers

Constrained FC 4D MITPs for Damageable Substitutable and Complementary Items in Rough Environments

Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

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