  This paper presents an inventory model for imperfect quality items with
receiving a reparative batch and order overlapping in a fuzzy environment by
employing triangular fuzzy numbers. It is assumed that the imperfect items
identified by screening are divided into either scrap or reworkable items. The
reworkable items are kept in store until the next items are received.
Afterward, the items are returned to the supplier to be reworked. Also, a
discount on the purchasing cost is employed as an offer of cooperation from a
supplier to a buyer to compensate for all additional holding costs incurred to
the buyer. The rework process is error-free. An order overlapping scheme is
employed so that the vendor is allowed to use the previous shipment to meet the
demand by the inspection period. In the fuzzy model, the graded mean
integration method is taken to defuzzify the model and determine its
approximation of a profit function and optimal policy. In doing so, numerical
examples are rendered to represent the model behavior and, eventually, the
sensitivity analysis is presented.
