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When only partial demand distribution information is available, it is important for decision makers to order a reliable quantity to immunize against the distribution uncertainty. The main contribution of this paper is to develop a new distributionally robust optimization method for single-period inventory problem, in which the uncertain market demand is characterized by generalized parametric interval-valued (PIV) possibility distribution and its associated uncertainty distribution set. The formulation of our distributionally robust optimization model is based on the proposed uncertainty distribution set, so it can generate a reliable solution to immunize against distribution uncertainty. Under two assumptions on the underlining decision-making environment, the robust counterpart of the original uncertain optimization problem is proposed for single-period inventory problem. To solve the robust single-period inventory model, this paper discusses the computational issue about the infinitely many Lebesgue-Stieltjes (L\u2013S) integral constraints and reformulates the robust counterpart problem as its equivalent deterministic inventory sub-models. According to the structural characteristics of the deterministic inventory sub-models, a domain decomposition method is designed to find the robust optimal solution to our single-period inventory problem. Finally, some computational results are reported about a practical single-period inventory problem to show the primary benefit of using the proposed distributionally robust fuzzy optimization method.<\/jats:p>","DOI":"10.3233\/jifs-172128","type":"journal-article","created":{"date-parts":[[2018,7,13]],"date-time":"2018-07-13T13:36:52Z","timestamp":1531489012000},"page":"1007-1019","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":13,"title":["Modelling single-period inventory problem by distributionally robust fuzzy optimization method"],"prefix":"10.1177","volume":"35","author":[{"given":"Zhaozhuang","family":"Guo","sequence":"first","affiliation":[{"name":"College of Management, Hebei University, Baoding, Hebei, China"},{"name":"Fundamental Science Department, North China Institute of Aerospace Engineering, Langfang, Hebei, 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