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, dealers earn allotment of a vehicle after they sell one. In contrast to turn-and-earn, fixed allocation ignores past sales and gives retailers equal share of the capacity. Earlier work has demonstrated that turn-and-earn induces more sales (compared to fixed allocation) when demand is low and the supplier's capacity is otherwise underutilized in a two-period setting. The question remains unanswered whether turn-and-earn induces similar strategic retailer behavior over a long horizon. We construct a dynamic stochastic game of order competition over an infinite horizon to track the order dynamics of the supply chain. We numerically solve for the Markov perfect equilibria using an iterative algorithm. Our results show that turn-and-earn induces more sales. The return on a larger allocation depends on capacity tightness and demand characteristics. Sales leadership may not be persistent and can be eliminated by the occurrence of extremely low demand. In addition to increasing sales, turn-and-earn also induces the retailers to absorb local demand variability.