This paper considered a case of supplier selection problem in a glove manufacturer located at Yogyakarta, Indonesia that uses genuine sheep leather as the raw material. The problem is solved using both Analytical Hierarchy Process (AHP) and Fuzzy AHP, in which three versions of Fuzzy AHP are applied i.e. Extent Analysis proposed by Chang (1996) [Chang, D. Y. (1996). Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, 95(3), 649-655.], Extent Analysis proposed by Wang (2008) [Wang, Y. M., Luo, Y., & Hua, Z. (2008). On the extent analysis method for fuzzy AHP and its applications. European Journal of Operational Research,186(2), 735-747.], and the modified Fuzzy LLSM proposed by Wang (2006) [Wang, Y. M., Elhag, T. M., & Hua, Z. (2006). A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process. Fuzzy Sets and Systems, 157(23), 3055-3071.]. Moreover, the research is conducted by incorporated four expert respondents, who have more than 12 years of experience in the problem. It is found that the top four priorities obtained from AHP are similar with those from Fuzzy AHP with Extent Analysis proposed by Chang (1996) and Fuzzy AHP with the modified Fuzzy LLSM proposed by Wang (2006). This priority list of supplier can be used by the manufacturer to select the raw material supplier.

A real inventory system for single item with specific demand characteristics motivates this works. The demand can be seen as two types of independent demand, where compound Poisson process describes the characteristics of each demand. The first type of demand is rarely occurred with relatively large size, while the second type of demand is often happened with relatively small size. In order to maintain inventory level, every time the first type of demand occurs a replenishment of stock is conducted which follows order-up-to-level inventory policy. In order to find the optimal inventory decision for that system, a mathematical model of the system is developed with the objective to minimize expected total inventory cost. Some of model assumptions are infinite replenishment, deterministic lead time, and completely backlogged shortages. To solve the model, it is then divided into two sub-problems and classical optimization technique is employed to help find the solution of each sub problem.