The impact of capacity information on lexicographical capacity allocation

We consider a manufacturer that has a capacity constraint and allocates capacity according to the lexicographic mechanism, which involves assigning different priority levels to different retailers. The manufacturer sells products to two competing retailers: a high-priority one and a low-priority one. The manufacturer's capacity information is either public or private, which makes our paper the first to examine the impact of capacity information on the capacity allocation problem of a manufacturer. We investigate two contract types: wholesale-price and wholesale-price-and-quantity. Our results show that when capacity information is public, the manufacturer will always prefer a wholesale-price contract. Moreover, it can benefit from a lower capacity limit (capacity scarcity) due to the retailer's capacity-withholding behavior. Interestingly, the high-priority retailer may prefer that the manufacturer use a wholesale-price-and-quantity contract to limit how many items the retailer can order. When capacity information is private, the retailer can order more than the capacity of a low-type manufacturer to reveal the manufacturer's capacity level under the wholesale-price contract. At the same time, under a wholesale-price contract, the manufacturer may not want to supply all the order quantities to the retailers to avoid disclosing its capacity level. We find that pooling equilibrium can survive the Intuitive Criterion, and the manufacturer cannot benefit from capacity scarcity and withholding no longer occurs. Lastly, contrary to the case where capacity information is public, the manufacturer may prefer the wholesale-price-and-quantity contract when capacity information is private. Therefore, it is possible to achieve a win-win situation between supply chain partners with the right contract type, which is not possible when capacity information is public.