Maximum utility product pricing models and algorithms based on reservation price

We consider a revenue management model for pricing a product line with several customer segments under the assumption that customers’ product choices are determined entirely by their reservation prices. We highlight key mathematical properties of the maximum utility model and formulate it as a mixed-integer programming problem, design heuristics and valid cuts. We further present extensions of the models to deal with various practical issues arising in applications. Our computational experiments with real data from the tourism sector as well as with the randomly generated data show the effectiveness of our approach.     

The implications of costs, capacity, and competition on product line selection

We consider a situation in which a manufacturer has to select the product(s) to sell as well as the selling price and production quantity of each selected product. There are two substitutable products in the consideration set, where product 2 has a higher quality and reservation price than that of product 1. By considering the cannibalization effect that depends on the selling price of each product, the manufacturer needs to evaluate the profit function associated with three different product line options: sell both products or only one of the 2 products. In order to examine the impact of costs, capacity, and competition on the optimal product line selection, optimal price, and optimal production quantity analytically, we present a stylized model in this paper so that we can determine the conditions under which a particular option is optimal.     

Competitive Price Equilibrium with Consumer Reservation Utility

This paper studies a competitive price equilibrium in the market of a product category where consumers are homogeneous with a reservation utility below which they will not purchase the product. The impact of the reservation utility on the price equilibrium is of particular interest, because the reservation utility may change according to the business cycle and economic environments. Using multinomial logit model to describe market response, we study the comparative statics of the prices, profits and market shares of firms, each of which produces one brand in the product category, with respect to the reservation utility in the Nash equilibrium. It is shown that, as the reservation utility increases, the prices as well as the profits at Nash equilibrium decrease. Also, in the case of duopoly market, the firm with lower cost structure will increase its market share as the reservation utility increases.     

Product line pricing for services with capacity constraints and dynamic substitution

In this paper, we address a service provider’s product line pricing problem for substitutable products in services, such as concerts, sporting events, or online advertisements. For each product, a static price is selected from a pre-defined set such that the total revenue is maximised. The products are differentiated by some of their attributes, and their availability is restricted due to individual capacity constraints. Furthermore, they are simultaneously sold during a common selling period at the end of which the service is delivered. Consumers differ from one another with respect to their willingness to pay, and, hence, their reservation prices vary depending on the product. In the event of a purchase, they choose the product that maximises their consumer surplus.     

保留效用类型依存的委托代理模型

在代理人的保留效用是类型依存的情况下,代理人的租金受外部机会成本的影响.研究表明,代理人努力负效用与成本类型的单调关系,决定了最优契约安排.相比较于非类型依存的情况,代理人都可能得到租金.高类型的租金总大于0,其租金可能仅源于保留效用,也可能受保留效用与努力负效用的综合影响.为激励其努力工作,委托人必须给予该类型代理人更高的支付;另一方面,低类型代理人的努力成本低和保留效用高,总得到比高类型更多的租金.     

基于指数效用函数的酒店可替代产品的超订模型研究

本文考虑酒店收益管理中的超订问题.在考虑可替代因素和风险偏好的前提下,我们需决定每种房型的最佳超订量.我们把这个问题归结为两阶段最优化问题:在预定阶段,需决定最佳超订量;在分房阶段,将房型按现有预定进行分配,其中可以发生替代.我们得出,期望效用收益函数关于预定上限是子模函数.也就是说,一种房型的预定上限将随着其它产品预定上限的上升而下降.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

Decision support for spare parts acquisition in post product life cycle

A major task in service management is the timely and cost efficient provision of spare parts for durable products. This especially holds good, when the regular production of the product, its components and parts has been discontinued, but customer service still has to be guaranteed for quite a long time. In such post product life cycle period, three options are available to organize the spare parts acquisition, namely (i) setting up a single large order within the final lot of regular production, (ii) performing extra production runs until the end of service and (iii) using remanufacturing to gain spare parts from used products. These three options are characterized by different cost and flexibility properties. Due to the time-variability and uncertainty of demands for spare parts and also that of the returns of used products, it is a challenging task to find out the optimal combination of these three options. In this paper we show how this problem can be modeled and solved by Decision Tree and stochastic Dynamic Programming procedure. Based on the Dynamic Programming approach a heuristic method is proposed, which can be employed to come up with a simple solution procedure for real-world spare parts acquisition problems during the post product life cycle. A numerical example is presented to demonstrate the application of the solution methods described in the paper.     

Speculative production and anticipative reservation of reactive capacity by a multi-product newsvendor

In this paper the optimal sourcing decisions of a multi-product newsvendor prior to the selling season of the products are studied. To satisfy the uncertain demands, the newsvendor can either utilize speculative production, or anticipatively reserve capacity. During the selling season when demand has become known, the newsvendor can utilize its reserved capacity and reactively satisfy demand uncovered by its speculative production. For the case where capacity for speculative production may be limited, but potential reservation of reactive capacity is unlimited two capacity reservation settings are analyzed and compared. In the first one capacity for each product has to be reserved separately, while in the second setting one joint capacity reservation for all products is permitted which can then be allocated to the different products optimally during the selling season. For the case of separate individual reservations the optimal strategies are analytically derived and structural insights concerning their existence are presented. As the model allowing for joint reservation can not be tackled analytically in general an approximation based on an LP formulation is used. Through a numerical example insights on the value of the increased flexibility induced by joint reservation, the cost-premium acceptable for joint reservation and the relative levels of capacity reservation in the two settings are given.     

Full-line or specialization strategy? The negative effect of product variety on product line strategy

This paper studies the product line decisions of firms under two consumer segments differing in their quality-sensitivity. We focus on a negative impact of the product variety on the consumers’ motivation to purchase, while each product is horizontally differentiated. In the presence of this impact and high fixed costs relative to variable costs, it is shown that when a highly quality-sensitive segment exists, it is always advantageous for the monopoly to specialize in only one product serving this segment. However, the appearance of a competitor can drastically change the product line in the market. Under the duopolistic setting where two firms sequentially determine their product lines, we show that the leader gains a better financial result by offering its product to the low segment for many cases, including the case where no product is offered to the high segment by either of the firms who are in equilibrium. Furthermore, we obtain another interesting result that indicates that the follower’s profit can exceed the leader’s profit when the quality-sensitivities between the two consumer segments are sufficiently different, even though the two firms are symmetric except for the order of their product offerings.     

Bundling decisions in supply chains

Firms often sell products in bundles to extract consumer surplus. While most bundling decisions studied in the literature are geared to integrated firms, we examine a decentralized supply chain where the suppliers retain decision rights. Using a generic distribution of customers’ reservation price we establish equilibrium solutions for three different bundling scenarios in a supply chain, and generate interesting insights for distributions with specific forms. We find that (i) in supply chain bundling the retailer’s margin equals the margin of each independent supplier, and it equals the combined margin when the suppliers are in a coalition, (ii) when the suppliers form a coalition to bundle their products the bundling gain in the supply chain is higher and retail price is lower than when the retailer bundles the products, (iii) the supply chain has more to gain from bundling relative to an integrated firm, (iv) the first-best supply chain bundling remains viable over a larger set of parameter values than those in the case of the integrated firm, (v) supplier led bundling is preferable to separate sales over a wider range of parameter values than if the retailer led the bundling, and (vi) if the reservation prices are uniformly distributed bundling can be profitable when the variable costs are low and valuations of the products are not significantly different from one another. For normally distributed reservation prices, we show that the bundling set is larger and the bundling gain is higher than that for a uniform distribution.     

Optimal Product Line Design: Genetic Algorithm Approach to Mitigate Cannibalization

In this marketing-oriented era where manufacturers maximize profits through customer satisfaction, there is an increasing need to design a product line rather than a single product. By offering a product line, the manufacturer can customize his or her products to the needs of a variety of segments in order to maximize profits by satisfying more customers than a single product would. When the amount of data on customer preferences or possible product configurations is large and no analytical relations can be established, the problem of an optimal product line design becomes very difficult and there are no traditional methods to solve it. In this paper, we show that the usage of genetic algorithms, a mathematical heuristics mimicking the process of biological evolution, can solve efficiently the problem. Special domain operators were developed to help the genetic algorithm mitigate cannibalization and enhance the algorithm’s local search abilities. Using manufacturer’s profits as the criteria for fitness in evaluating chromosomes, the usage of domain specific operators was found to be highly beneficial with better final results. Also, we have hybridized the genetic algorithm with a linear programming postprocessing step to fine tune the prices of products in the product line. Attacking the core difficulty of cannibalization in the algorithm, the operators introduced in this work are unique.     

Product line selection and pricing under a share-of-surplus choice model

Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today’s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs.We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer’s surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment’s surplus from this particular product to the segment’s total surplus across all offered products with positive surplus for that segment.We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities.     

搜寻成本下可替代产品的定价策略与库存决策

为探寻存在搜寻成本情况下消费者购买可替代产品时的定价与库存问题,从消费者效用出发,对厂商收益构建了基于马尔可夫决策过程的优化模型。在消费者方面,分析了其购买与继续搜寻的条件,并分别在搜寻成本不变和搜寻成本边际递减的情况下研究了消费者保留效用的变化情况以及购买相应产品的概率。此外,与很多相关文献不同的是,由于搜寻成本的存在,该情形下的消费者并不一定会在完成购买之前搜寻完所有的产品。在厂商方面,根据实际情况构建不同搜寻顺序下的收益模型并求解出最优定价策略与库存策略,并将定价模型与库存策略扩展到了动态的环境,为厂商制定价格及库存方案提供相应的决策支持。     

Profitability in product line pricing and composition with manufacturing commonalities

When pricing and composing a product line for optimal profitability, it is important to consider the fixed cost associated with offering each product. However, when similar products are offered, as in most product lines, manufacturing can often utilize common resources for the production of several products. In this paper, we investigate the profitability impact of including these common fixed manufacturing costs in product line pricing and composition decisions. A variable pricing product line model from research by Dobson and Kalish [Dobson, Gregory, Kalish, Shlomo, 1993. Heuristics for pricing and positioning a product-line using conjoint and cost data. Management Science 39 (2), 160–175] is integrated with manufacturing classes set forth by Morgan et al. [Morgan, Leslie Olin, Daniels, Richard L., Kouvelis, Panos, 2001. Marketing/manufacturing trade-offs in product line management. IIE Transactions 33, 949–962] to develop the new model. This new model introduces an improved method for assessing segment choice in a competitive environment of substitute products. Finally, a new solution methodology using a linear discrete reduction model is compared to two generalized genetic algorithms.     

Optimal media planning for multi-products in segmented market

Promotion is an essential stage of any product life cycle. All firms either concerned with single or multiple products promote their products. Advertising is the most dominated form of promotion for most of the products. Our research focuses on firms which produces a multiple range of products and advertise them using available media options. The budget constraint forms the major restriction. The existing research in media allocation of multiple products ignores the market segmentation and formulates the media plan assuming all segments alike. In this paper we formulate a media planning problem for allocating the available budget in multiple media that are found suitable for the advertising of multiple products considering marketing segmentation aspect of advertising. The objective is to maximize the total reach in all the segments. Goal programming technique is used to solve the problem. A case study is presented to show the real life application of the model.     

Operationalizing technology improvements in product development decision-making

Achieving competitive advantage and price premiums in many technology-based markets requires the incorporation of current technology in new products. To do so, firms in hyper-competitive environments increasingly plan and design their products concurrent with the independent development and validation of underlying technologies. Simultaneous validation of a core technology has important implications for a company’s product positioning and launch sequence decisions making these traditional marketing decisions relevant to operations managers. Prior research has shown that to minimize cannibalization in the absence of such improvements in technology, a firm should not launch low-end products before high-end products. However, concurrent evolution of technology can make it desirable and even necessary to introduce low-end products before high-end products. This is because in technology-based industries, improvements in technology delay the introduction of a high-end product, and a firm must trade-off the benefit of launching the low-end product earlier (greater discounted profits) against the cost of cannibalization of high-end product sales. High-end product cannibalization can be further reduced by offering the customer an option to upgrade from the low-end to high-end product, with important implications for the firm’s product positioning and introduction sequence decisions. Based on our study in the high technology industry, we model the product positioning and introduction sequence decisions under the simultaneous evolution of technology. Our analysis indicates that it may be optimal in a variety of circumstances for a firm to launch products in an increasing order of performance, even in the absence of network externalities. Besides presenting analytical results for product positioning and profit from different introduction sequences, the paper also makes a contribution to managerial practice by providing insights in the form of a conceptual framework.     

Product variety and channel structure strategy for a retailer-Stackelberg supply chain

Motivated by the observations that the direct sales channel is increasingly used for customized products and that retailers wield leadership, we develop in this paper a retailer-Stackelberg pricing model to investigate the product variety and channel structure strategies of manufacturer in a circular spatial market. To avoid channel conflict, we consider the commonly observed case where the indirect channel sells standard products whereas the direct channel offers custom products. Our analytical results indicate that if the reservation price in the indirect channel is sufficiently low, adding the direct channel raises the unit wholesale price and retail price in the indirect channel due to customization in the direct channel. Despite the fact that dual channels for the retailer may dominate the single indirect channel, we find that the motivation for the manufacturer to use dual channels decreases with the unit production cost, while increases with (i) the marginal cost of variety, (ii) the retailer’s marginal selling cost, and (iii) the customer’s fit cost. Interestingly, our equilibrium analysis demonstrates that it is more likely for the manufacturer to use dual channels under the retailer Stackelberg channel leadership scenario than under the manufacturer Stackelberg scenario if offering a greater variety is very expensive. When offering a greater variety is inexpensive, the decentralization of the indirect channel may invert the manufacturer’s channel structure decision. Furthermore, endogenization of product variety will also invert the channel structure decision if the standard product’s reservation price is sufficiently low.     

A dynamic pricing approach for returned products in integrated forward/reverse logistics network design

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics network. In this paper, we address the problem of designing and planning a multi-echelon, multi-period, multi-commodity and capacitated integrated forward/reverse logistics network. Returned products are categorized with respect to their quality levels, and a different acquisition price is offered for each return type. Furthermore, the reservation incentive of customers, the expected price of customers for one unit of used product described by uniform distribution, is applied to model the customers’ return willingness. Due to the fact that the remaining worthwhile value in the used products is the corporation’s key motivation for buying them from customers, a dynamic pricing approach is developed to determine the acquisition price for these products and based on it determine the percentage of returned products collected from customer zones. The used products’ acquisition prices at each time period are determined based on the customers’ return willingness by each collection center.     

The optimal sequential information acquisition structure: A rational utility-maximizing perspective

We consider a rational utility maximizer decision maker (DM) who must gather two pieces of information from a set of multidimensional products before making a choice. We analyze the resulting sequential information acquisition process where the DM tries to find the best possible product subject to his information acquisition constraint. In addition, we introduce publicly observable signals that allow the DM to update his expected utility functions following a standard Bayesian learning rule. Even though it seems intuitively plausible to assume that the transmission of positive and credible information may lead DMs to accept any product signaled more eagerly, this paper illustrates how transmitting credible positive information is not sufficient to decrease the rejection probability faced by the information sender on its set of products. A significant difference in product rejection probabilities arises depending on the characteristic on which signals are issued, as will be illustrated numerically for both risk-neutral and risk-averse DMs.