价格相依随机需求下的逆向拍卖采购与定价联合决策

Joint Reverse Auction Procurement and Pricing Decision-Making under Stochastic Price-Dependent Demand

研究价格相依随机需求下零售商的逆向拍卖采购与定价联合决策问题。假定零售商首先确定一个采购合同,然后供应商投标,通过逆向拍卖选取一个获胜的供应商,由该供应商确定采购量并传递给零售商,同时零售商做定价决策影响其需求,目标是寻求一个最优的采购与定价策略以最大化零售商的期望利润。对于一般的随机需求函数,引进期望销售弹性这一新的概念并利用其性质证明零售商的期望收益(不包括采购费用)是采购量的凹函数,从而得到其最优的采购与定价策略。特别地,对正态需求分布情形给出了零售商的采购量和利润函数的解析表达式并进行数值分析。

When facing demand uncertainty,many firms,such as Wal-Mart,Su-Ning,are using dynamic pricing strategies to manage their inventory.Online reverse auction,as one of dynamic pricing strategies,becomes an important procurement form due to the saving of considerable costs for the firms.A few management science scholars have been suggesting that firms should include the reverse auction into the supply chain management.In this paper,we study the joint decision on reverse auction procurement and pricing for a retailer under the stochastic pricedependent demand.It is assumed that there is one retailer and multiple potential suppliers who hold private information about their own production cost.The reverse auction needs to consider both purchase quantity and price.The retailer first designs a procurement contract that specifies a payment for each possible purchase quantity and invites suppliers to bid for this contract in the reverse auction.The auction can be conducted by quantity auction or supply contract auction.The winning supplier needs to make the right decision for the quantity produced and delivered.The pricing decision is made simultaneously by the retailer when the objective is to maximize the retailer＇s expected profit by seeking an optimal procurement and pricing marketing strategy.For general stochastic price-dependent demand function,we introduce a new concept——elasticity of expected sales.Under some relatively mild conditions,we show that price elasticity of expected sales increases in price and inventory elasticity of expected sales decreases in the inventory.On the basis of these properties,we further show that the retailer＇s expected revenue （excluding the procurement cost） is a concave function of the purchased quantity that can be used toobtain the optimal procurement and pricing decision for the retailer.Specially,we can analyze the purchased quantity and expected profit function under normal demand distribution for the retailer.Numerical examples show that the retailer is profitable when more suppliers participate in the auction or the cost value of suppliers is more dispersive.In summary,this paper studies the joint decision on inventory and pricing for a retailer facing the stochastic price-dependent demand under reverse auction procurement.By using the monotonicity conditions on elasticity of expected sales,we obtain the optimal procurement and pricing decision for the retailer.Numerical analyses are made under normal demand distribution.These results not only show the effect of reverse auction procurement mechanism on optimal procurement and pricing decision for the retailer,but also provide an important reference for managers to design the pricing marketing strategy based on auction procurement.