Considering the nature of fuzzy demand in lot-sizing problems, this study investigates the optimality of Wagner-Whitin dynamic economic lot size model. (WW algorithm) in single-level lot-sizing problems with fuzzy demand. Under the assumption that period demands can be represented as the triangular fuzzy numbers, the basic model for single-level lot-sizing problems with fuzzy demand will be called FSLP, and we prove that the FWW algorithm --- the fuzzy lot-sizing method revised from the WW algorithm --- is indeed an optimization method for FSLP. We also prove the optimality costs (FSLP-1,FSLP-2). In the practical environments, there are many lot-sizing problems that demands are fuzzy. Our results can be applied to the single-level lot-sizing problems with fuzzy demand, to find the optimal solution and to evaluate the performance among different heuristics.
