Quantity Flexibility for Multiple Products in a Decentralized Supply Chain

One of the major complicating factors in decentralized supply chains is the long procurement/manufacturing lead times, which forces the upstream members to commit resources to production based on forecasted demand. Downstream members (the retailer for the rest of the manuscript) would like to have a higher production quantity to be able to satisfy the demand whereas upstream members (the manufacturer for the rest of the manuscript) would like to have some sort of assurance about the demand so that they will not be building unnecessary capacity. Traditionally, such a conflict is resolved by an initial estimate provided by the retailer. However, the manufacturer is aware that the retailer is likely to manipulate this initial order; hence, the initial estimate provides little incentive for the manufacturer to build the capacity that the retailer would like to have. One resolution offered in the literature to overcome this issue is the Quantity Flexibility contract, where the retailer guarantees to order no less than a certain percentage of the initial estimate and the manufacturer guarantees to deliver a certain percentage above