Capacity Allocation Using Past Sales: When to Turn-and-Earn

Consider a supplier selling to multiple retailers. Demand varies across periods, but the supplier’s capacity and wholesale price are fixed. If demand is high, the retailers’ needs exceed capacity, and the supplier must implement an allocation mechanism to dole out production. We examine how the choice of mechanism impacts retailer actions and supply chain performance. In particular, we analyze turn-and-earn allocation, a method commonly used in the automobile industry. This scheme bases current allocations on past sales and thus enables retailers to influence their future allocations; they compete for scarce capacity even if they do not compete for customers. We show that turn-and-earn induces the retailers to increase their sales when demand is low and the supplier’s capacity is otherwise underutilized. Supplier profits thus increase. The impact on the supply chain depends on how restrictive capacity is. With mildly tight capacity, the retailers’ higher sales rate does not significantly lower their profits but does reduce the cost of idle capacity. Supply chain performance improves. With extremely tight capacity, the retailers’ intense competition dissipates more profits than the supplier gains, and supply chain performance suffers. Consequently, turn-and-earn does not generally coordinate the system. It is best characterized as a means for the supplier to increase her profits at the expense of the retailers and potentially even the supply chain. Furthermore, these results hold even if the retailers can hold inventory in anticipation of scarce capacity. (Capacity Allocation; Bullwhip Effect; Supply Chain Management; Game Theory)