This paper focuses on a quantity flexibility contract through which two or more heterogeneous suppliers periodically deliver a single type of product to a buyer as promised in the contract. The buyer starts each period by informing each of the suppliers of the purchase amount for the period and the reservation quantity for all future periods within a planning horizon. The purchase amount for the current period is finalized according to the amount previously reserved, although this amount can be flexibly increased or decreased by a predetermined percentage of the reservation amount. In this paper, a linear programming model including several key features of a quantity flexibility contract is developed from the buyer`s perspective. A rolling horizon implementation strategy is suggested for the efficient implementation of the contract. Computational experiments demonstrate that the proposed method is capable of determining a cost effective solution for the buyer in a reasonable amount of time.