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.     

The Use of Flexible Manufacturing Capacity in Pharmaceutical Product Introductions*

This work considers the value of the flexibility offered by production facilities that can easily be configured to produce new products. We focus on technical uncertainty as the driver of this value, while prior works focused only on demand uncertainty. Specifically, we evaluate the use of process flexibility in the context of risky new product development in the pharmaceutical industry. Flexibility has value in this setting due to the time required to build dedicated capacity, the finite duration of patent protection, and the probability that the new product will not reach the market due to technical or regulatory reasons. Having flexible capacity generates real options, which enables firms to delay the decision about constructing product‐specific capacity until the technical uncertainty is resolved. In addition, initiating production in a flexible facility can enable the firm to optimize production processes in dedicated facilities. The stochastic dynamic optimization problem is formulated to analyze the optimal capacity and allocation decisions for a flexible facility, using data from existing literature. A solution to this problem is obtained using linear programming. The result of this analysis shows both the value of flexible capacity and the optimal capacity allocation. Due to the substantial costs involved with flexibility in this context, the optimal level of flexible capacity is relatively small, suggesting products be produced for only short periods before initiating construction of dedicated facilities.     

Design of Flexible Multi‐Stage Processes

Faced with demand uncertainty across multiple product lines, many companies have recourse to flexible capacities which can process different products in order to better balance the trade‐off between capacity utilization and cost efficiency. Many studies demonstrated the potential benefit of using flexible capacity at the aggregate level by treating a whole plant or a whole process as a single stage. This paper extends these analyses by studying the benefits of flexible capacity while considering the multi‐stage structure of processes and consequently determining which stages should be flexible, which should be dedicated, and how much capacity to assign to each stage. We consider a two‐product firm which operates in a process‐to‐order environment and faces uncertain demand. Each stage of the process can be designed as dedicated or flexible. Dedicated resources are highly cost efficient but limited to the single product they are exclusively designed for, whereas flexible resources are versatile to handle several products but are more expensive. Using a general mathematical formulation our analysis shows that the optimal design may have some dedicated and some flexible stages along the process. Interestingly, this decision should be decoupled from the chronological order of the stages along the process.     

Joint Ordering and Pricing Strategies for Managing Substitutable Products

Starr and Rubinson (1978) develop a model to establish the relationship between product demand and relative prices. The notion of relative prices motivates us to consider a situation in which a retailer would either charge the same retail price for all products if he adopts a ‘fixed’ pricing strategy or charge different prices for different products if he adopts a ‘variable’ pricing strategy. In this paper, we develop a base model with deterministic demand that is intended to examine how a retailer should jointly determine the order quantity and the retail price of two substitutable products under the fixed and variable pricing strategies. Our analysis indicates that the optimal retail price under the variable pricing strategy is equal to the optimal retail price under the fixed pricing strategy plus or minus an adjustment term. This adjustment term depends on product substitutability and price sensitivity. We also present two different extensions of our base model. In the first extension, our analysis indicates that the underlying structure of the optimal retail price and order quantity is preserved when there is a limit on the total order quantity. The second extension deals with the issue of retail competition. Relative to the base case, we show that the underlying structure of the optimal retail price and order quantity is preserved in a duopolistic environment. Moreover, our analysis suggests that both retailers would adopt the variable pricing strategy at the equilibrium.     

面向产品生命周期的部分柔性技术选择

本文研究随机需求下产品生命周期不同阶段的部分柔性技术选择与生产能力规划问题。部分柔性技术是相对于完全柔性技术而言的,一种生产技术的柔性程度定义为能生产一产品类中产品个数多少的能力。不同柔性强度的生产技术,其投资成本和运行成本不同。本文首先建立了以计划期上总成本最小为目标的技术选择和生产能力规划模型,然后根据产品在其生命周期不同阶段的特点与市场需求的特点,应用所建立的模型进行仿真并总结产品导入期和成熟期技术选择的特点。     

An Analysis of Monopolistic and Competitive Take‐Back Schemes for WEEE Recycling

We study two prevailing types of take‐back schemes for electrical and electronic equipment waste recycling: monopolistic and competitive. We address key market and operating factors that make one scheme preferable to the other from the viewpoints of recyclers, manufacturers, and consumers. To this end, we model competitive decision making in both take‐back schemes as two‐stage sequential games between competing manufacturers and recyclers. Deriving and computing equilibria, we find that the competitive take‐back scheme often accomplishes a win–win situation, that is, lower product prices, and higher recycler and manufacturer profits. Exceptionally, recyclers prefer the monopolistic scheme when the substitutability level between the manufacturers' original products is high or economies of scale in recycling are very strong. We show that consolidation of the recycling industry could benefit all stakeholders when the economies of scale in recycling are strong, provided that manufacturer's products are not highly substitutable. Higher collection rates also render recycler consolidation desirable for all stakeholders. We also identify a potential free rider problem in the monopolistic scheme when recyclers differ in operational efficiency, and propose mechanisms to eliminate the discrepancy. We show that our results and insights are robust to the degree of competition within the recycling industry.     

The price-setting newsvendor with service and loss constraints

Current performance measurement systems consider not only financial measures, like costs and profits, but also non-financial indicators with respect to customer service, quality and flexibility. Using the newsvendor model, we analyse the respective influence of these possibly conflicting performance measures on important operations and marketing decisions, for instance the order quantity and the selling price of a product. As in the classical newsvendor model for price-independent as well as price-dependent demand distribution, the objective of the firm is to maximise expected profit. In this paper, we also consider a service constraint—a lower bound for the level of product availability—and a loss constraint—an upper bound for the probability of a loss occurring. For both models, we provide conditions for the existence of solutions. We then analyse the influence of demand variability using a set of conditions specifying the quantiles of the predetermined performance measures: a higher variability of demand implies a smaller admissible region of the decision variables. In the price-independent case, the optimal solution has a control-limit structure: the optimal order quantity is thus given either by the classical newsvendor solution or by the control-limits corresponding to the constraints. In the price-setting model with multiplicative demand, this structure is used to check whether small admissible prices are determined by the service constraint or by the loss constraint. Using these structural results, a procedure is developed to more easily enable the computation of the optimal values of the order quantity, selling price and expected profit.     

Optimal procurement of long-term contracts in the presence of imperfect spot market

B2B spot market has grown rapidly and become an effective trading channel for commodity products. Besides long-term contract procurement from conventional suppliers (forward and option), a buyer can procure or sell commodities at any time in B2B spot market to adjust her inventory level. However, spot prices are generally volatile and the market is imperfect in the sense that spot trading may be realized with uncertainty in a given period of time and often comes with extra transaction cost. This paper considers a commodity buyer who can order forward and option contracts in advance and trade in a B2B spot market when spot price and demand are observed stochastically. Based on a single-period newsvendor model, we discuss three optimal order strategies and derive respective expected profits when the buyer is risk-neutral. The sensitivity of purchase costs, market liquidity and transaction cost is investigated. We also compare the optimal expected profits for different strategies to illustrate the effects of the two long-term contracts in the presence of the B2B spot market. We then extend our model to a multi-period setting and derive the optimal strategy. Finally, we numerically compute the optimal order strategy for a risk-averse buyer and analyze the impact of spot market, risk aversion, as well as the correlation between customer demand and spot price.     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

Optimal Dynamic Order Scheduling under Capacity Constraints Given Demand‐Forecast Evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand‐forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single‐product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead‐time reduction a better alternative than capacity expansion. We then extend the model to a multi‐product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two‐product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.     

Strategic Outsourcing Decisions for Manufacturers that Produce Partially Substitutable Products in a Quantity‐Setting Duopoly Situation*

This article examines production and outsourcing decisions for two manufacturers that produce partially substitutable products and play a strategic game with quantity competition. When both manufacturers outsource key components to the same upstream supplier, their products become more substitutable due to the increased commonality of the products. In addition, outsourcing may create better consumer perception about the product if the manufacturers choose reputable suppliers with better brand or quality. We explicitly model the substitutability change and the brand/quality effect and provide conditions under which the manufacturers should outsource the components to a supplier. We present the subgame perfect Nash equilibriums for the situation in which there is only one supplier and the case in which two suppliers compete with each other in the upstream supply chain. Numerical examples are presented to illustrate the findings.     

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.     

基于需求转移的易逝性产品最优动态定价策略

本文针对易逝性产品中新产品对老产品需求的转移作用,应用收入管理方法得出老产品的最优动态定价策略,并应用最大凹向包络理论给出了简化算法的方法.数值算例表明在存在需求转移的情况下,应更早的提供较低的价格.最后作者给出了包含生产和定价的综合模型.     

Flexible Capacity Investments and Product Mix: Optimal Decisions and Value of Postponement Options

In this article, we study a firm's interdependent decisions in investing in flexible capacity, capacity allocation to individual products, and eventual production quantities and pricing in meeting uncertain demand. We propose a three‐stage sequential decision model to analyze the firm's decisions, with the firm being a value maximizer owned by risk‐averse investors. At the beginning of the time horizon, the firm sets the flexible capacity level using an aggregate demand forecast on the envelope of products its flexible resources can accommodate. The aggregate demand forecast evolves as a Geometric Brownian Motion process. The potential market share of each product is determined by the Multinomial Logit model. At a later time and before the end of the time horizon, the firm makes a capacity commitment decision on the allocation of the flexible capacity to each product. Finally, at the end of the time horizon, the firm observes the demand and makes the production quantity and pricing decisions for end products. We obtain the optimal solutions at each decision stage and investigate their optimal properties. Our numerical study investigates the value of the postponed capacity commitment option in supplying uncertain operation environments.     

制造柔性的期权特征及其经济价值度量方法

本文分析了制造柔性的内涵,对其从生产状态变化的目标和产生来源进行了分类,并对制造柔性从期权的视角重新加以了表述.然后提出当存在市场需求、产品价格和可变成本三种不确定源的情形下制造柔性的多阶段期权定价模型,最后结合蒙特卡洛法实现了对项目投资决策阶段柔性经济价值的度量.     

Pricing of flexible products

The pricing of flexible products is a new price discrimination practice that can enable firms to increase revenues under capacity considerations. A flexible product is defined as a good or service with at least one product attribute not fully specified at the time of the purchase, leaving the seller with at least two alternatives for the final product design and the ability to assign consumers to one of these alternatives at a later date. Flexible products enable sellers to better utilized capacity, as well as, to segment consumers and price discriminate according to different levels of flexibility. We empirically analyze consumer purchase behavior for flexible products based on a large field study of a low-cost airline. At this low-cost airline, consumers can select the level of flexibility of the flexible product. We identify the drivers of purchase behavior by analyzing the impact of consumers?? flexibility and search behavior and the price discount of the flexible ticket. Further, we estimate the revenue and profit effects of flexible products.     

两级供应链产品质量控制契约模型分析

基于博弈论和委托代理理论,研究在两级供应链中如何进行质量控制契约设计的问题。建立生产商和购买商的期望收益函数模型,生产商对其生产过程投资水平进行决策并确定其产品质量预防水平;购买商进行质量评价决策并确定其产品质量检验水平。生产商存在降低其生产过程投资水平的道德风险问题,在生产过程中将"削减投资",购买商为激励生产商提高其生产过程投资水平将支付"信息租金"的成本。购买商在进行产品质量检验决策时,存在夸大产品质量缺陷率的道德风险问题,在产品质量检验过程中将"过度检验"。运用最优化原理,求解生产商的最优生产过程投资水平、产品质量预防水平和价格折扣额与购买商的最优质量检验水平和外部损失分摊比例,并进行了算例分析,结果表明:当生产商提高其生产过程投资水平时,其质量预防水平将显著增加,购买商的质量检验水平将显著下降;随着购买商质量检验水平的提高,生产商所提供的价格折扣额先增大后减少,生产商所承担的外部损失分摊比例将会下降,其期望收益增加,购买商的期望收益将会减少,供应链联合期望收益将呈现"倒U"型,求解了期望收益的最大值及各契约参数的值,结果证明所提出的质量控制契约模型是可行的。     

需求不确定环境下多个零售商竞争的鲁棒随机优化模型

在需求不确定环境下构建了由一个制造商和多个零售商组成的供应链系统,考虑不同产品的可替代性,建立了多个零售商竞争的随机优化模型。利用鲁棒优化方法研究了需求不确定环境下多个零售商竞争的绝对鲁棒优化问题、偏差鲁棒优化问题和相对鲁棒优化问题。最后通过数值算例比较分析了不同产品替代率下的绝对鲁棒优化解、偏差鲁棒优化解及相对鲁棒优化解。     

考虑交易安全风险控制投入的在线旅游供应链网络均衡模型

基于包括供应商、平台和消费市场的三层供应链网络结构，利用变分不等式刻画均衡态时在线旅游供应链网络各成员的最优经济行为，以及平台交易安全风险控制投入对供应链平台企业、供应链整体的风险水平和期望收益的影响。研究发现，在平台企业风险控制投入相同情况下，平台和消费市场的产品交易数量和价格大致相同，验证了模型的合理性和有效性。其次，随着交易安全风险控制投入的增加，平台自身交易安全风险下降，供应链网络整体的交易安全水平和交易数量上升，但平台自身的期望收益下降。最后，随着更多的平台加入，平台的期望收益下降，市场需求价格下降，消费者获利。但部分平台企业的搭便车行为，会导致供应链整体的交易安全风险水平上升。     

Updating Inventories of Substitutable Resources in Response to Forecast Updates

We show simple yet optimal results to update the inventory/capacity levels, expected profit, fill rates, and service levels of substitutable resources in response to an updating of the mean demand forecasts for the resources. We find that a change in the mean demand of one resource does not affect the optimal inventory level of any other resource. The results are obtained for demands with location‐scale distribution, and for a revenue structure satisfying a triangle property such that the manager will always use the inventory of a resource to meet her own demand first before using it for substitution. The results for updating the performance measures also extend to managers who maintain non‐optimal inventory/capacity levels. Implications for procurement, sales and operational planning, and multi‐store operations are discussed.