Supply chain coordination when demand is shelf-space dependent

Consider a manufacturer or wholesaler who supplies some item to retailers facing demand rates that depend on the shelf or display space that is devoted to that product by themselves and their competitors. The manufacturer, via the use of financial levers at her disposal, wishes to coordinate this decentralized chain while making a profit. We model the physical scenario as one of constant displayed inventory level (on which demand rate depends positively) and continuous replenishment. With a single retailer, we show that to coordinate the channel and make a profit the manufacturer needs to augment the wholesale price lever by another – an inventory holding costs subsidy offered to the retailer. When multiple retailers compete in that product's market, there are two ways to envision and model the demand and market split. One assumes that market demand depends on aggregate inventory displayed, and then splits according to individual display levels. The other ‘assigns’ customers to retailers according to their display levels, and then assumes that purchases are a function of the display level at the retailer selected. We characterize retailers' Nash equilibria in these models, and we explore whether the manufacturer can coordinate such channels.