Continuous review inventory models under service level constraint with probabilistic fuzzy number during uncertain received quantity

This paper investigates continuous review inventory models involving service level constraint in which lead time, reorder point, ordering cost and order quantity are treated as decision variables and quantity received is uncertain. The lead time can be shortened at an extra crashing cost which has two different forms. First, it can be decomposed into several components; each has a crashing cost for the reduced lead time. Second, the lead time dependent cost follows a power function. The assumption of normal distribution on lead time demand was given and the uncertainty of average demand was handled with triangular fuzzy number. The signed distance method was employed to defuzzify the average demand. To obtain the optimal policies of the proposed models in partial backorder case, we construct Lagrange function, and solution algorithms are then derived. Moreover, two different examples were used to illustrate the proposed models and solution procedures.