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In this study, a robust optimization model is introduced to deal with the inherent uncertainty of input data in the location and vehicle routing scheduling problems in cross-docking distribution networks. For this purpose, a new two-phase deterministic mixed-integer linear programming (MILP) model is proposed for locating cross-docks and scheduling vehicle routing with multiple cross-docks. Then, the robust counterpart of the proposed two-phase MILP model is proposed by employing the recent developments in robust optimization theory. Finally, to evaluate the robustness of obtained solutions by the new robust optimization model, a comparison is made with the obtained solutions by the deterministic MILP model in a number of realizations based on different test problems. Moreover, a meta-heuristic algorithm, namely self-adaptive imperialist competitive algorithm (SAICA), is presented for the multiple vehicle location-routing problems. Finally, this study provides various computational test problems to demonstrate the applicability and capability of the proposed robust two-phase MILP model and meta-heuristic solution approach.<\/jats:p>","DOI":"10.3233\/jifs-151050","type":"journal-article","created":{"date-parts":[[2017,1,17]],"date-time":"2017-01-17T12:57:38Z","timestamp":1484657858000},"page":"49-62","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":21,"title":["A robust approach to multiple vehicle\u00a0location-routing problems with\u00a0time\u00a0windows for optimization of\u00a0cross-docking under uncertainty"],"prefix":"10.1177","volume":"32","author":[{"given":"S. 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