IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING IEEJ Trans 2014; 9: 484–493 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI:10.1002/tee.21997 Paper A Parametric Assessment Approach to Solving Facility-Location Problems with Fuzzy Demands Pei-Chun Lin ∗a , Non-member Junzo Watada ∗ , Member Berlin Wu ∗∗ , Non-member In real-world applications, sometimes randomness and fuzziness may coexist. In facility-location problems, the data expressed in natural language may contain vague information. We discuss the uncertainty included in demands in facility-location problems. The uncertain demand is called fuzzy demand in this paper. In the facility-location model, the parameters of fuzzy demand are determined by calculating the estimated expected value of the fuzzy demand, which is obtained by using the estimated parameters of the underlying probability distribution function of the fuzzy data. Moreover, we propose a defuzzification formula of the fuzzy demand called the realization of fuzzy demand. The defuzzification formula of fuzzy demand comprises the upper bound and the lower bound of the fuzzy demand. Moreover, the error of the fuzzy demand is assessed as the mean absolute percentage error of the fuzzy demand. Empirical studies show that we can solve real-life location problems by using the defuzzification formula of fuzzy demand and get higher profit in our facility-location model than by using conventional methods.  2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. Keywords: fuzzy data, uncertain demand, probability distribution function, fuzzy statistic, location decision Received 29 October 2012; Revised 14 January 2014 1. Introduction and Literature Review Facility-location selection is one of the most critical and strategic issues in supply-chain design and management. Choosing proper locations for facilities or even selecting the set of location alternatives is often one of difficult elements in the planning process. Especially, optimizing the locations is often complicated because of many constraints such as the developments of the city, the environment where we site the facility, and transportation in that city. Many researchers have dealt with the facility-location problems to find the most effective and efficient method. Larson and Sadig [15] discussed facility-location problem with L 1 metric in the presence of barriers to travel. Katz and Cooper [9] discussed the L 2 distance facility-location problem with only one forbidden circle. In both the above studies, uncertain situations are not considered in the facility-location problem. But, sometimes randomness and fuzziness may coexist in real facility-location problems [21]. We face vague information when describing data in natural language [23]. Hence, this paper deals with the uncertainty of both randomness and fuzziness. The use of fuzzy random variables, initiated by Kwakernaak [13, 14], is one of the appropriate ways to describe such hybrid uncertainty. Wang et al. [30] have developed a two-stage fuzzy- random facility-location model with recourse under a hybrid uncertain environment. Other approaches to the treatment of randomness and fuzziness are by Wang and Watada [29], Puri and a Correspondence to: Pei-Chun Lin. E-mail: peichunpclin@gmail.com * The Graduate School of Information, Production and Systems, Waseda University, 2-7 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808- 0135, Japan ** Department of Mathematical Sciences, National Chengchi University, NO.64, Sec.2, ZhiNan Road, Wenshan District, Taipei City 11605, Taiwan (R.O.C) Ralescu [26, 27], Klement et al. [10], Kruse [11], Kruse and Meyer [12], and Negoita and Ralescu [22]. In this paper, we consider the uncertainty of demands in facility- location problems, where the uncertain demand is called the fuzzy demand. Using fuzzy demand, we build up a facility-location model. To determine the parameters of fuzzy demand, in surveying the demand of customers, we use the fuzzy data expression. Hence, our objective is to solve the facility-location model. In the literature, we can find various discussions on the parameters of fuzzy demand. Some research works have discussed fuzzy demand. Fung et al. [5] used uncertain market demands and capacities in a production environment. They developed a fuzzy multiproduc- tion model and solved it by using parametric programming. Also, Ohtake and Nishida [25] proposed a parametric facility-location problem (PFLP) based on various demands of customers and gave a new concept of parametric analysis to improve the computa- tional efficiency of the algorithm. Moreover, Nishida et al. [24] employed the uncertain demand in the facility-location problem and proposed a branch-and-bound algorithm to find an exact solu- tion. Additionally, Tohyama et al. [28] treated an uncapacitated facility-location problem (UFLP) and proposed a genetic algorithm for solving it. UFLP was a fundamental optimization problem to select of locations where some facilities supply the same service. To express fuzzy random events in facility-location problems, the first step is to understand the probability distribution function of fuzzy data [8]. Conventional research works in the past did not recognize the underlying probability distribution function of fuzzy data in their problems. Lin et al. [18] proposed a way to find out the probability distribution function of fuzzy demand and solved the facility-location model by using a two-stage fuzzy-random facility-location model with recourse. The method is more accurate in considering the fuzzy data of actual demand, but consumes much computation time in solving the mathematical programming problem. In fact, when we work with fuzzy data, the underlying probability distribution function of fuzzy data is not known. On the other hand, it is not easy to describe vague data in statistical  2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.