Two-wholesale-price contracts: Push, pull, and advance-purchase discount contracts

The allocation of inventory ownership affects the inventory availability in a supply chain, which in turn determines the supply chain performance. In this paper, we consider a supplier‐retailer supply chain in which the supplier starts production well in advance of the selling season, and the retailer is offered two ordering opportunities at different points in time. An early order is allowed before the supplier's production decision, and a late order is allowed after the completion of production and after observing the demand. When the two wholesale prices change, we illustrate how the inventory decision rights and ownership are shifted and/or shared between the two firms, resulting in push, pull, or advance–purchase discount contracts. We then characterize the complete set of Pareto–dominant contracts for any given two–wholesale–price contract. We find that Pareto improvement can be achieved when inventory ownership is shifted from individual to shared and sometimes vice versa. In the latter case, push contracts not only are more likely to offer Pareto improvement, but also can achieve higher supply chain efficiency than pull contracts. We also identify conditions that enable Pareto improvement by introducing a new ordering opportunity to firms that had been bound by a single ordering opportunity without renegotiating the existing wholesale price, and we demonstrate through a numerical study that the adoption of the new ordering opportunity can significantly improve supply chain efficiency. We show that such Pareto improvement is more likely to happen when demand is more volatile.