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This paper analyzes a distribution network design problem for a four\u2010echelon supply chain. The problem is represented as an inventory\u2010location model with uncertain demand and a continuous review inventory policy. The decision variables include location at the intermediate levels and product flows between echelons. The related safety and cyclic inventory levels can be computed from these decision variables. The problem is formulated as a mixed integer nonlinear programming model to find the optimal design of the distribution network. A linearization of the nonlinear model based on a piecewise linear approximation is proposed. The objective function and nonlinear constraints are reformulated as linear formulations, transforming the original nonlinear problem into a mixed integer linear programming model. The proposed approach was tested in 50 instances to compare the nonlinear and linear formulations. The results prove that the proposed linearization outperforms the nonlinear formulation achieving convergence to a better local optimum with shorter computational time. This method provides flexibility to the decision\u2010maker allowing the analysis of scenarios in a shorter time.<\/jats:p>","DOI":"10.1155\/2018\/4139601","type":"journal-article","created":{"date-parts":[[2018,11,12]],"date-time":"2018-11-12T23:31:33Z","timestamp":1542065493000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Design of a Logistics Nonlinear System for a Complex, Multiechelon, Supply Chain Network with Uncertain Demands"],"prefix":"10.1155","volume":"2018","author":[{"given":"Aaron","family":"Guerrero Campanur","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7943-3869","authenticated-orcid":false,"given":"Elias","family":"Olivares-Benitez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4885-4200","authenticated-orcid":false,"given":"Pablo A.","family":"Miranda","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rodolfo Eleazar","family":"Perez-Loaiza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3030-8474","authenticated-orcid":false,"given":"Jose Humberto","family":"Ablanedo-Rosas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2018,11,12]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"45","article-title":"Distribution network design: an integrated planning support framework","volume":"9","author":"Mourits M.","year":"1995","journal-title":"Logistics Information Management"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2014.988889"},{"key":"e_1_2_9_3_2","unstructured":"OICA International Organization of Motor Vehicle Manufacturers Production statistics 2017 http:\/\/www.oica.net\/category\/production-statistics\/2017-statistics\/."},{"key":"e_1_2_9_4_2","volume-title":"Facility Location: Applications and Theory","author":"Hamacher H.","year":"2002"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032343"},{"key":"e_1_2_9_6_2","volume-title":"Location Theory: A Unified Approach","author":"Nickel S.","year":"2005"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2008.05.007"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-7572-0"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20282-2"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1108\/01443579810206299"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1366-5545(98)00010-6"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1080\/07408170008963888"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1366-5545(01)00007-2"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(00)00234-4"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020763400324"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.37.1.40.12823"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2003.08.006"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1040.0140"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2005.03.076"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-010-0732-z"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11067-006-7684-5"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2006.04.002"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/nav.20282"},{"key":"e_1_2_9_24_2","unstructured":"MirandaP. 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