Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

RELIABILITY-CONSTRAINED PRICING,CAPACITY, AND QUALITY: AN ILLUSTRATION OF ECONOMIC CONCEPTS TO POSTAL SERVICES

A model is developed from which welfare-optimal prices, capacities, and reliabilities for a service provider are simultaneously determined. Solutions are determined under conditions of stochastic demand subject to a reliability constraint on service quality. Both quality of service provided, as well as price, impact on demand for services rendered. Results indicate that (i) optimal prices are equated to the reliability-constrained marginal costs, (ii) optimal reliabilities require that the marginal benefits of increasing reliability are equated to the marginal costs of doing so, and (iii) optimal capacity allocation involves minimizing the system's expected costs subject to meeting the prespecified reliability constraint for service quality. The model is applied to postal delivery services in light of the growing competition that has emerged in this industry.     

Analyzing the Effect of Express Orders on Supply Chain Costs and Delivery Times

Delivery time differentiation is a supply chain concept that has been implemented in various industries, but not yet in the automotive industry. One reason is that the effects of delivery time differentiation on the supply chain are not well understood. The BMW Group, for instance, has considered offering an express order option, where express orders bypass standard orders in the supply chain processes to achieve short delivery times. Express orders distort planning processes, increase operations cost, and increase the delivery times of standard orders, however the effects have not been quantified yet. This study analyzes the impact of express orders on the supply chain, when express orders are built‐to‐order. To understand the supply chain consequences of express orders better, we analyzed the relevant supply chain processes at BMW Group. We determine the effect that built‐to‐order express orders have on delivery times and on component demand. To analyze the effect of introducing express orders on expected delivery times and expected cost, we use queuing theory and derive expressions for the transient behavior of a discrete time batch queue. Our analyses indicate that many supply chain processes are only marginally affected. However, the orders to the suppliers become considerably more uncertain, which must be compensated by additional safety stock. Our results indicate that express orders can be an attractive option for BMW and other automotive companies. If the fraction of express orders stays at a reasonable level, express orders can be delivered within about two weeks.     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

Prices,Markups, and Trade Reform

This paper examines how prices, markups, and marginal costs respond to trade liberalization. We develop a framework to estimate markups from production data with multi‐product firms. This approach does not require assumptions on the market structure or demand curves faced by firms, nor assumptions on how firms allocate their inputs across products. We exploit quantity and price information to disentangle markups from quantity‐based productivity, and then compute marginal costs by dividing observed prices by the estimated markups. We use India's trade liberalization episode to examine how firms adjust these performance measures. Not surprisingly, we find that trade liberalization lowers factory‐gate prices and that output tariff declines have the expected pro‐competitive effects. However, the price declines are small relative to the declines in marginal costs, which fall predominantly because of the input tariff liberalization. The reason for this incomplete cost pass‐through to prices is that firms offset their reductions in marginal costs by raising markups. Our results demonstrate substantial heterogeneity and variability in markups across firms and time and suggest that producers benefited relative to consumers, at least immediately after the reforms.     

PRODUCT OFFERING,PRICING, AND MAKE‐TO‐STOCK/MAKE‐TO‐ORDER DECISIONS WITH SHARED CAPACITY

In an era of mass customization, many firms continue to expand their product lines to remain competitive. These broader product lines may help to increase market share and may allow higher prices to be charged, but they also cause challenges associated with diseconomies of scope. To investigate this tradeoff, we considered a monopolist who faces demand curves, which for each of its potential products, decline with both price and response time (time to deliver the product). The firm must decide which products to offer, how to price them, whether each should be make‐to‐stock (mts) or make‐to‐order (mto), and how often to produce them. The offered products share a single manufacturing facility. Setup times introduce disceonomies of scope and setup costs introduce economies of scale. We provide motivating problem scenarios, model the monopolist's problem as a non‐linear, integer programming problem, characterize of the optimal policy, develop near‐optimal procedures, and discuss managerial insights.     

Lead Time and Price Quotation Mode Selection: Uniform or Differentiated?

Firms in service and make‐to‐order manufacturing industries often quote lead times and prices to customers. We define uniform quotation mode (UQM) as the strategy where a firm offers a single lead time and price quotation, and differentiated quotation mode (DQM) is where a firm offers a menu of lead times and prices for customers to choose from. Both modes are followed in practice. Firms should determine which is more profitable. We classify customers into two groups: lead time sensitive (LS) and price sensitive (PS). LS customers value lead time reduction more than PS customers. We develop mathematical models of both quotation modes and analyze them to determine the most profitable mode under specified situations as well as the best lead time and price quotations within each mode. We find that DQM is dominated by UQM whenever PS customers have positive utilities from UQM or LS customers have positive utilities from DQM. Otherwise, which quotation mode is better depends on multiple factors, such as customer characteristics (including lead time reduction valuation and product valuation of a customer, and the proportion of LS customers) and production characteristics (including the desired service level and service or production cost).     

Competing on Time: An Integrated Framework to Optimize Dynamic Time‐to‐Market and Production Decisions

This study develops a comprehensive framework to optimize new product introduction timing and subsequent production decisions faced by a component supplier. Prior to market entry, the supplier performs process design activities, which improve manufacturing yield and the chances of getting qualified for the customer's product. However, a long delay in market entry allows competitors to enter the market and pass the customer's qualification process before the supplier, reducing the supplier's share of the customer's business. After entering the market and if qualified, the supplier also needs to decide how much to produce for a finite planning horizon by considering several factors such as manufacturing yield and stochastic demand, both of which depend on the earlier time‐to‐market decision. To capture this dependency, we develop a sequential, nested, two‐stage decision framework to optimize the time‐to‐market and production decisions in relation to each other. We show that the supplier's optimal market entry and qualification timing decision need to be revised in real time based on the number of qualified competitors at the time of market‐entry decision. We establish the optimality of a threshold policy. Following this policy, at the beginning of each decision epoch, the supplier should optimally stop preparing for qualification and decide whether to enter the market if her order among qualified competitors exceeds a predetermined threshold. We also prove that the supplier's optimal production policy is a state‐dependent, base‐stock policy, which depends on the time‐to‐market and qualification decisions. The proposed framework also enables a firm to quantify how market conditions (such as price and competitor entry behavior) and operating conditions (such as the rate of learning and inventory/production‐related costs) affect time‐to‐market strategy and post‐entry production decisions.     

消费者导向类型与电商全渠道决策研究

从现实出发，基于不同消费者导向类型研究了电商的全渠道决策问题。首先建立电商单渠道销售的基础模型，并得出最优产品组合、价格和交付时间。在此基础上，给出了消费者为产品导向型和渠道导向型情况下电商采取全渠道决策的条件，得出双渠道产品组合、价格及交付时间的最优决策；并进行了数值验证。研究发现，同一渠道提供的产品其最优价格相同，最优交付时间只和消费者耐心程度及交付成本函数有关。若消费者为产品导向型，仅当双渠道运营成本之差较小且消费者耐心程度较低时，电商进入线下渠道才有利可图，且在线下渠道提供最受欢迎的产品，线上渠道提供剩余产品。若消费者为渠道导向型，电商进入线下渠道必然有利可图，且在线下渠道提供最受欢迎的产品，线上渠道提供所有产品。     

Coordinating Service‐Sensitive Demand and Capacity by Adaptive Decision Making: An Application of Case‐Based Decision Theory*

The subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry. The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

Impact of Price Postponement on Capacity and Flexibility Investment Decisions

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

Exploring the Impact of Delivery Performance on Customer Transaction Volume and Unit Price: Evidence from an Assembly Manufacturing Supply Chain

This study examines the effect of delivery performance on customer transactions. We propose that different delivery performance dimensions (on‐time delivery rate, early delivery inaccuracy, late delivery inaccuracy, and delivery speed) have varying impacts on future customer transaction quantities and unit prices. We further explore the effect of customer types on the proposed relationships. Trade customers (resellers) and Original Equipment Manufacturer (OEM) customers generally have different operational needs for deliveries and therefore may value these metrics differently. Using instrumental variable regression, we analyze a proprietary transaction‐level dataset. The information was compiled by a Fortune 500 manufacturer from its Heating, Ventilation and Air Conditioning (HVAC) control product supply chain, consisting of the manufacturer and its customers. The results indicate that measures of delivery performance affect customer transaction quantity and unit price differently. Furthermore, these impacts can differ significantly between trade customers and OEM customers. These findings provide fine‐grained insights about tuning delivery capabilities to increase sales volume or boost price.     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.     

An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

A Choice‐Based Dynamic Programming Approach for Setting Opaque Prices

Opaque pricing is a form of pricing where certain characteristics of the product or service are hidden from the consumer until after purchase. In essence, opaque selling transforms a differentiated good into a commodity. Opaque pricing has become popular in service pricing as it allows firms to sell their differentiated product at higher prices to regular brand loyal customers while simultaneously selling to non‐brand loyal customers at discounted prices. We use a nested logit model in combination with logistic regression and dynamic programming to illustrate how a service firm can optimally set prices on an opaque sales channel. The choice model allows the characterization of consumer trade‐offs when purchasing opaque products while the dynamic programming approach allows the characterization of the optimal pricing policy as a function of inventory and time remaining. We compare optimal prices and expected revenues when dynamic pricing is restricted to daily price changes. We provide an illustrative example using data from an opaque selling mechanism ( Hotwire.com ) and a Washington DC‐based hotel.     

Mass Customization and Guardrails: “You Can Not Be All Things to All People”

A mass customization strategy enables a firm to match its product designs to unique consumer tastes. In a classic horizontal product‐differentiation framework, a consumer's utility is a decreasing function of the distance between their ideal taste and the taste defined by the most closely aligned product the firm offers. A consumer thus considers the taste mismatch associated with their purchased product, but otherwise the positioning of the firm's product portfolio (or, “brand image”) is immaterial. In contrast, self‐congruency theory suggests that consumers assess how well both the purchased product and its overall brand image match with their ideal taste. Therefore, we incorporate within the consumer utility function both product‐specific and brand‐level components. Mass customization has the potential to improve taste alignment with regard to a specific purchased product, but at the risk of increasing brand dilution. Absent brand dilution concerns, a firm will optimally serve all consumers’ ideal tastes at a single price. In contrast, by endogenizing dilution costs within the consumer utility model, we prove that a mass‐customizing firm optimally uses differential pricing. Moreover, we show that the firm offers reduced prices to consumers with extreme tastes (to stimulate consumer “travel”), with a higher and fixed price being offered to those consumers having more central (mainstream) tastes. Given that a continuous spectrum of prices will likely not be practical in application, we also consider the more pragmatic approach of augmenting the uniformly priced mass customization range with preset (non‐customized) outlying designs, which serve customers at the taste extremes. We prove this practical approach performs close to optimal.     

Managing Supply Risk for Vertically Differentiated Co‐Products

The manufacturing complexity of many high‐tech products results in a substantial variation in the quality of the units produced. After manufacturing, the units are classified into vertically differentiated products. These products are typically obtained in uncontrollable fractions, leading to mismatches between their demand and supply. We focus on product stockouts due to the supply–demand mismatches. Existing literature suggests that when faced with product stockouts, firms should satisfy all unmet demand of a low‐end product by downgrading excess units of a high‐end product (downward substitution). However, this policy may be suboptimal if it is likely that low‐end customers will substitute with a higher quality product and pay the higher price (upward substitution). In this study, we investigate whether and how much downward substitution firms should perform. We also investigate whether and how much low‐end inventory firms should withhold to strategically divert some low‐end demand to the high‐end product. We first establish the existence of regions of co‐production technology and willingness of customers to substitute upward where firms adopt different substitution/withholding strategies. Then, we develop a managerial framework to determine the optimal selling strategy during the life cycle of technology products as profit margins shrink, manufacturing technology improves, and more capacity becomes available. Consistent trends exist for exogenous and endogenous prices.     

基于价格调整的长寿风险自然对冲策略

在长寿风险对冲框架下,通过引入外生的产品价格,构建了基于价格调整的自然对冲模型。首先运用最优化理论得到了模型最优产品配比的解析式,然后在实际的销售配比与模型的最优配比相等的约束下,推导出了寿险产品和年金产品的最优定价。该定价能够使得模型的最优配比真正被实现,即销售的配比刚好是使产品组合长寿风险最小化的最优配比。最后通过数值算例,阐述了基于价格调整的自然对冲策略的效果,并进一步分析了利率、承保年龄、性别等因素对自然对冲策略的影响。