Dual Channel Selling in Online Stores: Simultaneous Auctions and Posted Prices

Abstract

The growth in the size and reach of the World Wide Web has given a boost to online selling. The physical location of buyers is immaterial for online selling. Such a situation is particularly favorable for conducting auctions. Auctions are efficient in price discovery and allocation of goods, but they require the simultaneous participation of all buyers. Online stores provide buyers with the flexibility to participate in auctions without being physically present, thereby popularizing online auctions. For sellers, online stores provide flexibility in price setting and choice of selling mechanism. The revenue maximization problem of an online seller selling simultaneously through posted prices and auctions is studied here. Buyers have the choice to purchase in either of the channels. Buyers’ choice depends upon their own valuation, likely competition, and the posted price. The seller has to incorporate buyer behavior in his decision making and also consider the uncertainty of demand; both in terms of buyer arrivals and buyer valuations. The seller’s problem is to choose the posted price, quantity for sale during the period, and auction allocation rules. Typically, auction rules comprise of auction duration, acceptable bid range, winner selection criteria, price determination rules and quantity for sale. The seller starts selling with an optimal starting inventory and no subsequent reordering. The selling environment and buyer behavior is modeled as described. The seller starts with an initial stock and sells it within a given time horizon with no reordering. Buyer arrival rate follows a Poisson process with a known arrival rate, and buyer valuations are drawn from a known uniform distribution. The seller announces a posted price at which buyers can purchase instantly. For the auction, the seller announces the number of units to be sold in the auction, the acceptable bid ranges, and the duration of the auction. Those who choose to buy at the posted price can get the item instantly, others can bid in the auction and thus have to wait until the end of the period when the auction closes and allocation is announced. Auctions are conducted according to sealed bid k+1 price format. Under such a setting, the best strategy for bidders is to bid their valuation. The presence of a posted price limits the bid on the upper side. Buyers with valuation above the posted price can either buy at the posted price, or bid in the auction. Buyers with valuation below the posted price cannot buy at the posted price, and hence may bid or choose to stay out. Since the auction participation cost is zero, it is assumed that they will participate in the auction. High valuation bidders’ decision to participate in the auction depends upon the discount that they can get by buying in the auction store, weighed against the uncertainty of getting the item and price uncertainty in the auction. The seller has to design the auction and choose the posted price so as to maximize revenues. The cases with endogenous and exogenous auction participation decisions were studied separately using stochastic as well as deterministic models. The choice of optimal starting inventory and optimal posted price is found to be the critical factor that determines revenues. The basic model is extended to consider two problem cases. In the first case(Qa-Exact), an exact pre-announced quantity is set aside for the auction to be conducted at the end of the period. In the other case(Qa-Plus), a pre-announced quantity and any unsold quantity from the posted price channel is auctioned. The revenues depend upon the quantity that is set aside for the auction in both the cases. In the Qa-Exact auction, the optimal quantity to be set aside for auction is non-decreasing in the total quantity put up for sale. In the Qa-Plus auction, the optimal quantity to be set aside is found to be zero. These two problem variants serve as building blocks for the two period model. It is found that the choice of total starting inventory, the initial quantity to be set aside for auction, and posted price are critical to the revenue maximization for the two period case. Further, it is observed that in the absence of any waiting cost on part of the low valuation customers, it is optimal to have a single period auction. The analytical and computational results from the models offer practical insights for designing the dual channel selling mechanism.