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Devnath S, Giri PK, Mondal SS, Maiti M. Multi-item two-stage fixed-charge 4DTP with hybrid random type-2 fuzzy variable. Soft comput 2021. [DOI: 10.1007/s00500-021-06371-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Jana SH, Jana B. Application of random triangular and Gaussian type-2 fuzzy variable to solve fixed charge multi-item four dimensional transportation problem. Appl Soft Comput 2020. [DOI: 10.1016/j.asoc.2020.106589] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Sengupta D, Das A, Dutta A, Bera UK. A carbon emission optimization model with reduction method of type-2 zigzag uncertain variable. Neural Comput Appl 2020. [DOI: 10.1007/s00521-018-3811-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Fixed charge 4D-TP for a breakable item under hybrid random type-2 uncertain environments. Inf Sci (N Y) 2020. [DOI: 10.1016/j.ins.2020.03.050] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Constrained FC 4D MITPs for Damageable Substitutable and Complementary Items in Rough Environments. MATHEMATICS 2019. [DOI: 10.3390/math7030281] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
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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Samanta S, Jana DK. A multi-item transportation problem with mode of transportation preference by MCDM method in interval type-2 fuzzy environment. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-3093-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Ebrahimnejad A. New method for solving Fuzzy transportation problems with LR flat fuzzy numbers. Inf Sci (N Y) 2016. [DOI: 10.1016/j.ins.2016.04.008] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Jana DK, Pramanik S, Maiti M. A Parametric Programming Method on Gaussian Type-2 Fuzzy Set and Its Application to a Multilevel Supply Chain. INT J UNCERTAIN FUZZ 2016. [DOI: 10.1142/s0218488516500239] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, distribution centers, and customers. Plants manufacture several products that are delivered to distribution centers. If a distribution center is used then fixed cost is charged. Customers are replenished by an only one distribution center. To characterize the uncertainty that typically occurs in many practical decision environments, this paper considers the supply capacities, demands as Gaussian type-2 fuzzy variables. To provide a modelling framework for optimization problems with multi-fold uncertainty, different reduction methods are proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method. Then the transportation problem is reformulated as a chance-constrained expected value model enlightened by the credibility optimization method. The deterministic models are then solved using two different soft computing techniques (i) Generalized Reduced Gradient (Lingo-14.0), and (ii) modified Particle Swarm Optimization(PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrate the application and effectiveness of the proposed solution approaches.
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Affiliation(s)
- Dipak Kumar Jana
- Department of Engineering Science, Haldia Institute of Technology, Haldia, Purba Midna Pur-721657, West Bengal, India
| | - Sutapa Pramanik
- Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India
| | - Manoranjan Maiti
- Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India
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Mean and CV reduction methods on Gaussian type-2 fuzzy set and its application to a multilevel profit transportation problem in a two-stage supply chain network. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2202-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Wang L, Gao Z, Yang L. Criteria for the a Priori Shortest Path Generation in Uncertain Time-Varying Transportation Networks. INT J UNCERTAIN FUZZ 2015. [DOI: 10.1142/s021848851550035x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper proposes a new definition of uncertain time-varying network to capture the uncertain and dynamic characteristics of the network with discrete uncertain link travel times. To find the a priori non-dominated paths in this type of network, three comparison criteria based on the uncertain measure, namely, deterministic dominance rule, first-order uncertain dominance rule and uncertain expected value dominance rule, are proposed to generate non-dominated paths in a single time interval and a time period, as more than one path may exist between an origin and destination for a given departure time. The proposed comparison methods are then applied to solving a simple uncertain time-varying network. The computational results verify the efficiency of three dominance rules for finding non-dominated paths.
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Affiliation(s)
- Li Wang
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 10004, China
| | - Ziyou Gao
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 10004, China
| | - Lixing Yang
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 10004, China
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Pramanik S, Jana DK, Mondal S, Maiti M. A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments. Inf Sci (N Y) 2015. [DOI: 10.1016/j.ins.2015.07.012] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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