Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables
Facility location decision is basically viewed as a long-term strategy, so the inherited uncertainty of main parameters ought to be taken into account in order to make models applicable. In this paper, we examine the impact of uncertain transportation costs and customers’ demands on the choice of op...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/472623 |
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| author | Xuejie Bai Ying Liu |
| author_facet | Xuejie Bai Ying Liu |
| author_sort | Xuejie Bai |
| collection | DOAJ |
| description | Facility location decision is basically viewed as a long-term strategy, so the inherited uncertainty of main parameters ought to be taken into account in order to make models applicable. In this paper, we examine the impact of uncertain transportation costs and customers’ demands on the choice of optimal location decisions and allocation plans. This leads to the formulation of the facility location-allocation (FLA) problem as a fuzzy minimum risk programming, in which the uncertain parameters are assumed to be characterized by type-2 fuzzy variables with known type-2 possibility distributions. Since the inherent complexity of type-2 fuzzy FLA may be troublesome, existing methods are no longer effective in handling the proposed problems directly. We first derive the critical value formula for possibility value-at-risk reduced fuzzy variable of type-2 triangular fuzzy variable. On the basis of formula obtained, we can convert original fuzzy FLA model into its equivalent parametric mixed integer programming form, which can be solved by conventional numerical algorithms or general-purpose software. Taking use of structural characteristics of the equivalent optimization, we design a parameter decomposition method. Finally, a numerical example is presented to highlight the significance of the fuzzy FLA model. The computational results show the credibility and superiority of the proposed parametric optimization method. |
| format | Article |
| id | doaj-art-d009dfeb51c84097a37702c12e4d7090 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-d009dfeb51c84097a37702c12e4d70902025-02-03T05:43:57ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/472623472623Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy VariablesXuejie Bai0Ying Liu1College of Science, Agricultural University of Hebei, Baoding, Hebei 071001, ChinaCollege of Management, Hebei University, Baoding, Hebei 071002, ChinaFacility location decision is basically viewed as a long-term strategy, so the inherited uncertainty of main parameters ought to be taken into account in order to make models applicable. In this paper, we examine the impact of uncertain transportation costs and customers’ demands on the choice of optimal location decisions and allocation plans. This leads to the formulation of the facility location-allocation (FLA) problem as a fuzzy minimum risk programming, in which the uncertain parameters are assumed to be characterized by type-2 fuzzy variables with known type-2 possibility distributions. Since the inherent complexity of type-2 fuzzy FLA may be troublesome, existing methods are no longer effective in handling the proposed problems directly. We first derive the critical value formula for possibility value-at-risk reduced fuzzy variable of type-2 triangular fuzzy variable. On the basis of formula obtained, we can convert original fuzzy FLA model into its equivalent parametric mixed integer programming form, which can be solved by conventional numerical algorithms or general-purpose software. Taking use of structural characteristics of the equivalent optimization, we design a parameter decomposition method. Finally, a numerical example is presented to highlight the significance of the fuzzy FLA model. The computational results show the credibility and superiority of the proposed parametric optimization method.http://dx.doi.org/10.1155/2014/472623 |
| spellingShingle | Xuejie Bai Ying Liu Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables The Scientific World Journal |
| title | Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables |
| title_full | Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables |
| title_fullStr | Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables |
| title_full_unstemmed | Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables |
| title_short | Minimum Risk Facility Location-Allocation Problem with Type-2 Fuzzy Variables |
| title_sort | minimum risk facility location allocation problem with type 2 fuzzy variables |
| url | http://dx.doi.org/10.1155/2014/472623 |
| work_keys_str_mv | AT xuejiebai minimumriskfacilitylocationallocationproblemwithtype2fuzzyvariables AT yingliu minimumriskfacilitylocationallocationproblemwithtype2fuzzyvariables |