Improved bid prices for choice-based network revenue management

One of the latest developments in network revenue management (RM) is the incorporation of customer purchase behavior via discrete choice models. Many authors presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. However, in many implemented RM systems—most notably in the hotel industry—bid price control is being used, and this entails the problem that the recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects.We propose (1) a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector; this first guess could be, for example, dynamic estimates of the marginal value of capacity. Moreover, (2) we demonstrate that using these dynamic marginal capacity values directly as bid prices can lead to significant revenue loss as compared to using our heuristic to improve them. Finally, (3) we investigate numerically how much revenue performance is lost due to the confinement to product combinations that can be represented by a bid price.The heuristic is not restricted to a particular choice model and can be combined with any method that provides us with estimates of the marginal values of capacity. In our numerical experiments, we test the heuristic on some popular networks examples taken from peer literature. We use a multinomial logit choice model which allows customers from different segments to have products in common that they consider to purchase. In most problem instances, our heuristic policy results in significant revenue gains over some currently available alternatives at low computational cost.     

A pricing model for clearing end-of-season retail inventory

The problem of setting prices for clearing retail inventories of fashion goods is a difficult task that is further exacerbated by the fact that markdowns enacted near the end of the selling season have a smaller impact on demand. In this article, we present discrete-time models for setting clearance prices in such an environment. When demand is deterministic, we compute optimal prices and show that decreasing reservation prices lead to declining optimal prices. When demand is stochastic and arbitrarily correlated across planning periods, we obtain bounds on the optimal expected revenue and on optimal prices. We also develop a heuristic procedure for finding near-optimal prices and test its accuracy through numerical experiments. These experiments reveal new insights for practitioners. For example, the penalty for choosing clearance price once and keeping it unchanged for the remainder of the selling season is found to be small when either the mean reservation prices do not change appreciably over time or when they drop sharply after the first period.     

Channel coordination through a revenue sharing contract in a two-period newsboy problem

This paper studies channel coordination through revenue sharing contract between a single retailer and a single wholesaler in a two-period newsboy problem. Two models are discussed, a single-buying-opportunity model and a two-buying-opportunity model. We discuss how the revenue sharing ratio and the wholesale prices are to be determined in order to achieve channel coordination and a win–win outcome. We find that the wholesale prices are set to be lower than the retail prices and the optimal revenue sharing ratio is linearly increasing in the wholesale prices. The proposed revenue sharing contract has more flexibility than price protection, in that the optimal revenue sharing ratio can be settled reasonably through negotiation between the retailer and wholesaler.     

Dynamic simultaneous fare proration for large-scale network revenue management

Network revenue management is concerned with managing demand for products that require inventory from one or several resources by controlling product availability and/or prices in order to maximize expected revenues subject to the available resource capacities. One can tackle this problem by decomposing it into resource-level subproblems that can be solved efficiently, for example by dynamic programming. We propose a new dynamic fare proration method specifically having large-scale applications in mind. It decomposes the network problem by fare proration and solves the resource-level dynamic programs simultaneously using simple, endogenously obtained dynamic marginal capacity value estimates to update fare prorations over time. An extensive numerical simulation study demonstrates that the method results in tightened upper bounds on the optimal expected revenue, and that the obtained policies are very effective with regard to achieved revenues and required runtime.     

Optimal pricing for service facilities with self-optimizing customers

Many service industries (e.g., walk-in clinics, vehicle inspection facilities, and data-processing centers) have customers who choose among congested facilities, and select the facility with the lowest combination of travel cost plus congestion cost at the facility. In general, customers over-utilize attractive facilities, causing higher costs than if customers were assigned to facilities to minimize total costs. Optimal facility prices induce customers to select facilities that minimize total cost. We find optimal facility prices and show they equal charging customers for the impact (net costs and benefits) they cause for others. We explore a rich flexibility that allows a range of optimal prices, useful when negotiating the implementation of facility fees. Facility prices can be positive or negative (price discounts), and can be adjusted to be all positive, or to provide net subsidy or net revenue. We contribute to unifying and generalizing several disparate streams of research.     

Network revenue management with inventory-sensitive bid prices and customer choice

We develop an approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a non-linear function which is separable across resource inventory levels. This approximation can exhibit significantly improved accuracy compared to currently available methods. It further allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach can outperform some recently proposed alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.     

On the asymptotic optimality of the randomized linear program for network revenue management

For network revenue management problems, it is known that the bid prices computed through the so-called deterministic linear program are asymptotically optimal as the capacities on the flight legs and the expected numbers of product requests increase linearly with the same rate. In this paper, we show that the same asymptotic optimality result holds for the bid prices computed through the so-called randomized linear program. We computationally investigate how the performance of the randomized linear program changes with different problem parameters and with the number of samples. The hope is that our asymptotic optimality result and computational experiments will raise awareness for the randomized linear program, which has yet not been popular in the research community or industry.     

The impact of delivery lags on irreversible investment under uncertainty

We consider the valuation and rational exercise of irreversible investment opportunities in the presence of revenue uncertainty and delivery lags. In order to capture supply side market imperfections in the markets for investment goods, we assume that the lag depends on the revenue process faced by the investor. We show that such imperfections have a pronounced decelerating impact on rational investment demand as they may increase the value of waiting in excess of the exercise payoff even for projects which otherwise would be perceived as highly remunerative. We also consider the comparative static properties of the optimal investment policy and its value, and demonstrate that typically increased uncertainty decreases the investment incentives by increasing the value of waiting.     

考虑盗版容忍度的软件产品动态定价模型

基于收益管理理论,对产品瞬态扩散模型进行拓展,选择盗版容忍度、价格和创新改进作为控制变量,扩散速度和创新水平作为状态变量,构建收益最大化的动态定价模型,依据最优化控制理论,建立哈密尔顿方程进行求解,探讨了三个控制变量的联合优化策略和相关特性,通过算例仿真验证其结论。结论显示:应采取撇脂定价策略;当由盗版引起边际收益增加的价值量与损失价值相等时,盗版容忍度达到最优;与产品生命周期的成长阶段相比较,在成熟阶段,应逐渐增加盗版容忍度,同时,减缓创新改进的速度;当损失结构降低时,应提高盗版容忍度,并且可采用创新与保护监管相互互补的策略。动态建模能够拓展静态模型中关于网络外部性的概念,分析连续状态下的变量,与自适应学习机制相一致,对实践具有更好的借鉴作用。     

Integration of pricing and capacity allocation for perishable products

For years pricing and capacity allocation decisions in most revenue management models have been carried out independently. This article presents a comprehensive model to integrate these two decisions for perishable products. We assume that the supplier sells the same products to different micro-markets at distinct prices. Throughout the sales season, the supplier faces decisions as to which micro-markets or customer classes should be served and at what prices. We show that (i) at any time, a customer class is active (being served) if and only if the price offered is over a threshold level, but the optimal price may not be the highest one of the supplier’s choice; (ii) when the price decision is made in conjunction with inventory, it is similar to the procedure shown in pure pricing models, i.e., the optimal price comes from a subset of prices that forms a maximum increasing concave envelope; (iii) because of dynamic changes in the optimal prices, the nested-price structure does not necessarily hold in general and needs to be redefined; and (iv) the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory, price and demand intensity. Numerical examples are provided.     

基于航段需求计算网络竞价的近似动态规划方法

竞价控制是收益管理中广泛应用的一种存量控制方法.将网络存量控制问题描述为一个动态规划模型,通过状态向量的一个仿射函数近似动态规划的最优值函数,并且在航段水平上考虑随机需求,最终得到一个计算网络竞价所需的确定性线性规划(DLP),相对于标准的DLP,这个DLP得到了更接近于动态规划最优值的上界.给出了一个列生成算法用于求解这个DLP,并提供了模拟算例,计算结果表明可获得比标准的DLP方法更好的收益.     

销售商出售看跌期权的供应链优化研究

在由一个供应商和一个销售商组成的单期两级供应链中,处于主导地位的销售商以其卖场所具有的销售能力参与供应链合作,并从销售的每一个产品中获取既定收益。同时,销售商还向供应商出售建立在产品销售量保障基础上的看跌期权,以激励供应商参与供应链合作。论文对上述情形的销售商出售看跌期权的供应链合作问题进行了研究,通过建模与优化分析,证明了在销售商提供看跌期权的供应链合作中,供应商存在唯一的最优生产批量和看跌期权采购量,以及销售商存在最优的从每一单位产品销售中获取的既定收益。论文还揭示了销售商提供看跌期权,虽然无法实现供应链协调,但可以实现供应链参与企业所获得的收益与其所承担的风险相匹配。最后,论文论证了在销售商出售看跌期权机制下,供应链存在收益损失较小的理想合作区域。     

Formation of a strategic manufacturing and distribution network with transfer prices

We propose a profit maximization model for the decision support system of a firm that wishes to establish or rationalize a multinational manufacturing and distribution network to produce and deliver finished goods from sources to consumers. The model simultaneously evaluates all traditional location factors in a manufacturing and distribution network design problem and sets intra-firm transfer prices that take account of tax and exchange rate differentials between countries. Utilizing the generalized Benders decomposition approach, we exploit the partition between the product flow and the cash allocation (i.e., the pricing and revenue assignment) decisions in the supply chain to find near optimal model solutions. Our proposed profit maximizing strategic planning model produces intuitive results. We offer computational experiments to illustrate the potential valuable guidance the model can provide to a firm's supply chain design strategic planning process.     

A continuous-time dynamic pricing model knowing the competitor’s pricing strategy

In this paper we consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy. We establish a continuous time model to analyze the effect of dynamic pricing on the improvement in expected revenue in the duopoly. We assume that customers arrive to purchase tickets in accordance with a geometric Brownian motion. We derive an explicit closed-form expression for an optimal pricing policy to maximize the expected revenue. It is shown that when the competitor adopts a static pricing policy, dynamic pricing is not always effective in terms of maximizing expected revenue compared to a fixed pricing strategy. Moreover, we show that the size of the reduction in the expected revenue depends on the competitor’s pricing strategy. Numerical results are presented to illustrate the dynamic pricing policy.     

不同价格模式下考虑需求波动性和差异化服务的网约车平台定价决策

针对单个平台两种品牌网约车的最优定价问题,考虑平台服务质量的差异化和市场需求波动性,分别建立动态价格、差异化价格和静态价格模式下的网约车动态服务模型,运用多元函数和泛函的条件极值求得两种品牌网约车的最优定价策略。研究发现,平台最优动态价格和差异化价格均随需求波动时长单调变化,而最优静态价格并非单调。此外,平台提高差异化服务时,两种品牌网约车的最优价格均提高,但高服务质量的网约车会有更高的提价幅度;固定佣金报酬率增大时,平台最优价格均提高,但边际损失成本较大的网约车会有更高的提价幅度。最后,通过数值仿真对不同价格模式下的平台利润进行比较和灵敏度分析,并发现平台利润在市场需求稳定时差异不大。     

Revenue management for a supply chain with two streams of customers

In this paper, we consider revenue management for a service supply chain with one supplier and one retailer. The supplier has a limited capacity of a perishable product and both the supplier and the retailer face customers. Each customer may choose to buy a product from either the supplier or the retailer by considering prices and the cost associated with switching. For the centralized model, the supplier determines the selling prices for both herself and the retailer, and the retailer simply collects a commission fee for each product sold. We derive monotone properties for the revenue functions and pricing strategies. Further, we show that the commission fee increases the retailer’s price while decreasing the supplier’s and leads to efficiency loss of the chain. For the decentralized decision-making model, the supplier and the retailer compete in price over time. Two models are considered. In the first, the retailer buys products from the supplier before the selling season and in the second the retailer shares products with the supplier in retailing. For both models, we discuss the existence of the equilibrium and characterize the optimal decisions. Numerical results are presented to illustrate properties of the models and to compare the supply chain performance between the centralized and the decentralized models.     

Strategic new product pricing when demand obeys saturation effects

We analyze dynamic pricing strategies for new products over an infinite planning horizon in a duopolistic market. The sales dynamic is modelled as a linear demand function with saturation effects, marginal costs are assumed to be constant. The optimal pricing strategies are obtained as (degenerate) closed-loop Nash solutions. It is shown that the optimal dynamic prices are greater than the static ones. In the case of no discounting there is in addition to the constant solution also an equilibrium with monotonically increasing prices.     

An examination of the role of price insurance products in stimulating investment in agriculture supply chains for sustained productivity

This study examines how managing risk by introducing commodity price insurances may improve the likelihood of increased investment in agri-food supply chains. A model is introduced which shows how insurance products on index prices can reduce the uncertainty of the impact of investment, and also how lower investment can generate the same impact as a higher investment. To show our results, we use two different frameworks which include total profit (Pareto optimal) and Stackelberg game setups. The results demonstrate that in both frameworks the investment will have a greater impact when an insurance product is present. By implication, the study presents an encouraging message to the insurance industry to introduce products to secure supply chain actors’ revenue leading to an increase in investment rate. Consequently, the study offers insight into how the role of traditional government subsidies for protecting farmers, particularly the small to medium-sized farms, may be revisited by replacing some of the existing subsidisation policies with revenue insurance.     

A Note on Shadow Prices in Linear Programming

Using convex analysis and a characterization of the entire family of optimal solutions to an L.P., we show that in order to obtain shadow prices, one has to solve a much smaller L.P. derived from any optimal tableau. We then show that positive as well as negative shadow prices for any constraint or for any combination of constraints can easily be computed by parametric linear programming. Some examples exhibiting the method are also included.     

Dynamic bidding strategies in search-based advertising

Search-based advertising allows the advertisers to run special campaigns targeted to different groups of potential consumers at low costs. Google, Yahoo and Microsoft advertising programs allow the advertisers to bid for an ad position on the result page of a user’s query when the user searches for a keyword that the advertiser relates to its products or services. The expected revenue generated by the ad depends on the ad position, and the ad positions of the advertisers are concurrently determined after an instantaneous auction based on the bids of the advertisers. The advertisers are charged only when their ads are clicked by the users. To avoid excessive ad expenditures due to sudden surges in the keyword-search activities, each advertiser reserves a fixed finite daily budget, and the ads are not shown in the remainder of the day when the budget is depleted. Arrival times of keyword-search instances, ad positions, ad selections, and sales generated by the ads are random. Therefore, an advertiser faces a dynamic stochastic total net revenue optimization problem subject to a strict budget constraint. Here we formulate and solve this problem using dynamic programming. We show that there is always an optimal dynamic bidding policy. We describe an iterative numerical approximation algorithm that uniformly converges to the optimal solution at an exponential rate of the number of iterations. We illustrate the algorithm on numerical examples. Because dynamic programing calculations of the optimal bidding policies are computationally demanding, we also propose both static and dynamic alternative bidding policies. We numerically compare the performances of optimal and alternative bidding policies by systematically changing each input parameter. The relative percentage total net revenue losses of the alternative bidding policies increases with the budget loading, but were never more than 3.5 % of maximum expected total net revenue. The best alternative to the optimal bidding policy turned out to be a static greedy bidding policy. Finally, statistical estimation of the model parameters is visited.