Capacity Allocation over a Long Horizon: The Return on Turn-and-Earn

We consider a supply chain in which a supplier sells products to multiple retailers. When orders from the retailers exceed the supplier's capacity, she must employ an allocation mechanism to balance supply and demand. In particular, we consider a commonly used allocation scheme in the automobile industry: turn-and-earn, which uses past sales to allocate capacity. In essence, retailers "earn" an allotment of a vehicle after they sell one. In contrast to turn-and-earn, fixed allocation ignores past sales and gives each retailer an equal share of the capacity. Earlier work has demonstrated that turn-and-earn induces more sales in a two-period setting compared to fixed allocation. The question remains unanswered whether turn-and-earn induces similar behaviors over a long horizon when retailers possess private demand information. We construct a dynamic stochastic game of order competition over an infinite horizon to track the order dynamics of the supply chain. We obtain a richer set of equilibrium behaviors than existing models predict. Instead of a symmetric allocation outcome, we observe that sales leadership may arise in equilibrium and that retailers with different past sales adopt distinct ordering strategies to respond to demand uncertainty. Transient sales dynamics suggest that sales leadership may not be persistent and can be eliminated by the occurrence of extremely low demand. This provides a theoretical explanation for several behavioral observations of some U.S. automobile dealers. In addition to the sales-inducing effect, interestingly, turn-and-earn also causes the retailers to absorb local demand variability.