101 Activities for Teaching Creativity and Problem Solving,Arthur B. VanGundy,Pfeiffer, J. Wiley,CA, USA (2004), p. xi + 391, £41.95, ISBN: 0-7879-7402-1

Many web sites (e.g. Hotmail, Yahoo) provide free services to the users while generating revenues from advertising. Advertising revenue is, therefore, critical for these sites. This in turn raises the question, how should advertisements at a web site be scheduled in a planning horizon to maximize revenue. Advertisements on the web are specified by geometry and display frequency and both of these factors need to be considered in developing a solution to the advertisement scheduling problem. Since this problem belongs to the class of NP-hard problems, we first develop a heuristic called LSMF to solve the problem. This heuristic is then combined with a genetic algorithm (GA) to develop a hybrid GA. The hybrid GA solution is first compared with the upper bound obtained by running CPLEX for the integer programming formulation of the problem. It is then also compared with an existing algorithm proposed in the literature. Our computational results show that the hybrid GA performs exceptionally well in the sense that it provides optimal or near optimal solution for a wide range of problem instances of realistic sizes and the improvements over existing algorithm are substantial. Finally we present a case study to illustrate how revenue could be significantly increased with a small improvement in the advertisement schedule. It is the first such study in this setup.     

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.     

A hybrid model for airline seat inventory control of the multi-leg problems

To address the discrepancy between dynamic models and industrial practice in airline revenue management, we propose a hybrid model for the multi-leg problem that integrates static and dynamic models. We formulate the problem using a stochastic dynamic program and characterize the optimal booking policy as a switching-curve (surface) type.     

Optimal dynamic pricing of inventories with stochastic demand and discounted criterion

We consider a continuous time dynamic pricing problem for selling a given number of items over a finite or infinite time horizon. The demand is price sensitive and follows a non-homogeneous Poisson process. We formulate this problem as to maximize the expected discounted revenue and obtain the structural properties of the optimal revenue function and optimal price policy by the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we study the impact of the discount rate on the optimal revenue function and the optimal price. Further, we extend the problem to the case with discounting and time-varying demand, the infinite time horizon problem. Numerical examples are used to illustrate our analytical results.     

A mathematical model for personalized advertisement in virtual reality environments

We consider a personalized advertisement assignment problem faced by the manager of a virtual reality environment. In this online environment, users log in/out, and they spend time in different virtual locations while they are online. Every time a user visits a new virtual location, the site manager can show the ad of an advertiser. At the end of a fixed time horizon, the manager collects revenues from all of the advertisers, and the total revenue depends on the number of ads of different advertisers she displays to different users. In this setup, the objective of the manager is to find an optimal dynamic ad display policy in order to maximize her expected revenue. In the current paper, we formulate this problem as a continuous time stochastic optimization problem in which the actions of users are represented with two-state Markov processes and the manager makes display decisions at the transition times of these processes. To our best knowledge, no formal stochastic model and rigorous analysis has been given for this practical problem. Such a model and its analysis are the major contributions of this paper along with an optimal solution.     

Optimal revenue management in two class pre-emptive delay dependent Markovian queues

In this paper, we present a comparative study on the total revenue generated with pre-emptive and non pre-emptive priority scheduler for a fairly generic problem of pricing the server’s surplus capacity in a single server Markovian queue. The specific problem is to optimally price the server’s surplus capacity by introducing a new class of customers (secondary class) without affecting the pre-specified service level of its current customers (primary class) when pre-emption is allowed. Pre-emptive scheduling is used in various applications. First, a finite step algorithm is proposed to obtain global optimal operating and pricing parameters for this problem. These optimal operating and pricing parameters constitute a unique Nash equilibrium in a certain two player non cooperative game. We then describe the range of service level where pre-emptive scheduling gives feasible solution and generates some revenue while non pre-emptive scheduling has infeasible solution. Further, some complementary conditions are identified to compare revenue analytically for certain range of service level where strict priority to secondary class is optimal. Our computational examples show that the complementary conditions adjust in such a way that pre-emptive scheduling always generates more revenue. Theoretical analysis is found to be intractable for the range of service level when pure dynamic policy is optimal. Hence, extensive numerical examples are presented to describe different instances. It is noted in numerical examples that pre-emptive scheduling generates at least as much revenue as non pre-emptive scheduling. A certain range of service level is identified where improvement in revenue is quite significant.     

不同易腐性农产品的委托代销方式选择研究

目前,我国农产品销售普遍采用经销模式。委托代销模式在农产品批发行业应用较广,但在零售行业还鲜有应用。针对这一问题,就单独的支付服务费方式和视同买断方式在应用上存在的不足,提出了混合式委托代销方式。在此基础上,假设代销期包含货架期和处理期,构建了生产商和代销商的序贯博弈模型并求解出最优代销期和货架期。通过需求率、变质率、保鲜成本等敏感性分析和单位时间利润的综合比较,重点分析了不同易腐性农产品的委托代销方式选择。结论表明,混合式委托代销方式具有可行性且更加适用于低易腐性农产品,而支付服务费委托代销方式更加适用于高易腐性农产品。     

Contract and product quality in platform selling

More and more e-tailers (platforms) are allowing manufacturers direct access to customers. Two common contracts are offered by platforms to manufacturers: the revenue sharing contract where a platform appropriates a portion of the manufacturer’s revenue, and the fixed fee contract where a platform charges a fixed rent for each sale. Using an analytical model, this paper studies the interrelationship between a platform’s contract choice and a manufacturer’s product quality decision. We find that if product quality is exogenously given, the platform will always adopt the revenue sharing contract. If the manufacturer endogenously decides the quality, however, the platform’s contract choice may be changed. This is because the revenue sharing contract, compared to fixed fee, leads to a lower selling price of the manufacturer, whereas the fixed fee contract can motivate a higher quality than does revenue sharing. As a result, a large (small) market heterogeneity induces the platform to adopt the revenue sharing (fixed fee) contract. We also extend the model to several directions, finding that longer product line, manufacturer competition, lower marginal production cost, and higher platform cost all tend to induce the platform to put forward a fixed fee contract; while if quality decision is less flexible than contract decision, the platform is more ready to embrace revenue sharing. Besides, when there are two platforms competing for the same market, they should differentiate their contract choices so as to mitigate competition.     

Optimal Goodwill Path to Introduce a New Product

We consider the problem of determining an optimal goodwill path for the introduction of a new product in a market, while looking for the maximum foreseen profit. The foreseen revenue depends on the product introduction time and on the goodwill level at the same time. We focus on the advertising costs associated with the goodwill evolution and assume that the cost function possesses some rather general features which are shared by the cost functions of the Nerlove-Arrow type models. The dynamic optimization problem is discussed in the calculus of variations framework. A few examples associated with special cost functions are discussed in detail.     

Analysis of seat allocation and overbooking decisions with hybrid information

We investigate a single-leg airline revenue management problem where an airline has limited demand information and uncensored no-show information. To use such hybrid information for simultaneous overbooking and booking control decisions, we combine expected overbooking cost with revenue. Then we take a robust optimization approach with a regret-based criterion. While the criterion is defined on a myriad of possible demand scenarios, we show that only a small number of them are necessary to compute the objective. We also prove that nested booking control policies are optimal among all deterministic ones. We further develop an effective computational method to find the optimal policy and compare our policy to others proposed in the literature.     

考虑炒作效应的网络视频平台商业模式选择

随着网络视频产业迅猛发展,越来越多的视频节目依赖炒作宣传吸引关注度获取丰厚的商业收益。本文考虑时间因素和炒作因素,基于用户需求不确定性建立连续时间型收益模型。应用哈密顿方法求解非线性优化问题,得到了炒作效应影响下的视频用户支付意愿变化规律,网络视频商业模式的动态演化趋势,并确立了最优的视频节目定价和营销炒作策略。研究结果表明,选择收费模式用户人数随着炒作时间的增加而增加,而选择免费模式用户人数随着炒作时间的增加而减少;随着炒作效应的提高,混合型免费—收费模式会逐渐演化为单一收费模式,且视频平台利润呈现倒“U”型变化趋势。研究结论揭示了营销炒作对视频定价、用户支付意愿和收视行为的影响,为视频平台更好的了解用户需求,制定商业策略提供决策依据。     

Dynamic Pricing via Dynamic Programming<Superscript>1</Superscript>

This article specifies an efficient numerical scheme for computing optimal dynamic prices in a setting where the demand in a given period depends on the price in that period, cumulative sales up to the current period, and remaining market potential. The problem is studied in a deterministic and monopolistic context with a general form of the demand function. While traditional approaches produce closed-form equations that are difficult to solve due to the boundary conditions, we specify a computationally tractable numerical procedure by converting the problem to an initial-value problem based on a dynamic programming formulation. We find also that the optimal price dynamics preserves certain properties over the planning horizon: the unit revenue is linearly proportional to the demand elasticity of price; the unit revenue is constant over time when the demand elasticity is constant; and the sales rate is constant over time when the demand elasticity is linear in the price. ¹We acknowledge professor robert e. kalaba for initiating this work and suggesting solution methods.     

Scheduling inspired models for two-dimensional packing problems

We propose two exact algorithms for two-dimensional orthogonal packing problems whose main components are simple mixed-integer linear programming models. Based on the different forms of time representation in scheduling formulations, we extend the concept of multiple time grids into a second dimension and propose a hybrid discrete/continuous-space formulation. By relying on events to continuously locate the rectangles along the strip height, we aim to reduce the size of the resulting mathematical problem when compared to a pure discrete-space model, with hopes of achieving a better computational performance. Through the solution of a set of 29 test instances from the literature, we show that this was mostly accomplished, primarily because the associated search strategy can quickly find good feasible solutions prior to the optimum, which may be very important in real industrial environments. We also provide a comprehensive comparison to seven other conceptually different approaches that have solved the same strip packing problems.     

Dynamic pricing model and algorithm for perishable products with fuzzy demand

This paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, α‐optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real‐world example is presented to highlight the effectiveness of the developed model and algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

易逝品价格连续下降情况下带有随机需求的供应链协调

本文研究了短生命周期产品价格随时间连续下降情况下单供应商和单销售商渠道中的供应链协调。分别建立了分散决策、集中决策和基于收入共享合同的最优订货策略模型,讨论了模型的相关性质,提出了一种基于收入共享合同的供应链协调策略,来实现整个供应链的协调。并指出该策略不仅适用于价格时变情况,能实现整个供应链的期望利润最大化,并且具有很好的适用性。最后,用实例仿真验证了本文所给出的模型和策略的有效性。     

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.     

基于Logit离散选择模型的品类优化问题综述

品类优化问题(Assortment Optimization Problem)是收益管理的经典问题.它研究零售商在满足运营约束的前提下,应如何从给定产品集合中选择一个子集提供给消费者,以最大化预期收益.该问题的核心在于如何准确地刻画消费者在面对细分产品时的选择行为、建立相应的优化模型并设计高效率的求解算法.基于Logit离散选择模型的品类优化问题:首先,介绍了基于Multinomial Logit模型的品类优化问题.然后介绍了两个更复杂的变种:第一个是基于两层以及多层Nested Logit模型的品类优化问题,这类问题可合理刻画细分产品之间的"替代效应";第二个是基于Mixtures of Multinomial Logits模型的品类优化问题,这类问题可充分考虑消费者群体的异质性.随后,介绍了数据驱动的品类优化问题的相关进展.最后,指出该问题未来可能的若干研究方向.     

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.