Strategic Capacity Management When Customers Have Boundedly Rational Expectations

In retailing industries, such as apparel, sporting goods, customer electronics, and appliances, many firms deploy sophisticated modeling and optimization software to conduct dynamic pricing in response to uncertain and fluctuating market conditions. However, the possibility of markdown pricing creates an incentive for customers to strategize over the timing of their purchases. How should a retailing firm optimally account for customer behavior when making its pricing and stocking/capacity decisions? For example, is it optimal for a firm to create rationing risk by deliberately under stocking products? In this study, we develop a stylized modeling framework to answer these questions. In our model, customers strategize over the timing of their purchases. However, customers have boundedly rational expectations in the sense of anecdotal reasoning about the firm's fill rate, i.e., they have to rely on anecdotes, past experiences, or word‐of‐mouth to infer the firm's fill rate. In our modeling framework, we distinguish two settings: (i) capacity commitment, where the firm commits to its capacity level in the long run, or (ii) the firm dynamically changes it in each season. For both settings, within the simplest form of anecdotal reasoning, we prove that strategic capacity rationing is not optimal independent of customer risk preferences. Then, using a general form of anecdotal reasoning, we provide sufficient conditions for capacity rationing to be optimal for both settings, respectively. We show that the result of strategic capacity rationing being suboptimal is fairly robust to different valuation distributions and utility functions, heterogeneous sample size, and price optimization.     

Dynamic pricing and revenue management process in Internet retailing under uncertainty: An integrated real options approach

Competition and demand volatility often cause modern enterprises to be confronted by uncertain environments. When a firm manages revenue in such competitive and risky environments, the optimization of pricing and capacity allocation, subject to a fixed time and capacity, becomes a complicated problem. Many previous papers concerning revenue management (RM) and pricing require that the firm possesses the ability to know the demand curve (or demand distribution) and set prices on it to maximize profits. However, this assumption may not be the case in some industries. Therefore, this paper focuses on the dynamic lead indicators rather than assumptive lag indicators to establish a concise and flexible decision model for practical use. This paper provides an integrated real options (IRO) approach with analytic hierarchy process (AHP) for the auction RM problem under competitive/dynamic pricing and revenue uncertainty in Internet retailing. A numerical example is also presented to illustrate that the IRO approach can generate better decisions than the naı¨ve (or risk unawareness) approach in revenue quality of safety and profitability. The new perspective and approach proposed by this paper can be extended to other RM fields whenever both profitability and risk are critical to decision making.     

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.     

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.     

Responsive Pricing Newsvendor Networks with Discretionary Commonality

Discretionary commonality is a form of operational flexibility used in multi‐product manufacturing environments. Consider a case where a firm produces and sells two products. Without discretionary commonality, each product is made through a unique combination of input and production capacity. With discretionary commonality, one of the inputs could be used for producing both products, and one of the production capacities could be used to process different inputs for producing one of the products. In the latter case, the manager can decide, upon the realization of uncertainty, not only the quantities for different products (outputs) but also the means of transforming inputs into outputs. The objective of this study is to understand how the firm's value, its inventory levels for inputs and capacity levels for resources are affected by the demand characteristics and market conditions. In pursuing this research, we extend Van Mieghem and Rudi ( 2002 )'s newsvendor network model to allow for the modeling of product interdependence, demand functions, random shocks, and firm's ex post pricing decision. Applying the general framework to the network with discretionary commonality, we discover that inventory and capacity management can be quite different compared to a network where commonality is non‐discretionary. Among other results, we find that as the degree of product substitution increases, the relative need for discretionary commonality increases; as the market correlation increases, while the firm's value may increase for complementary products, the discretionary common input decreases but the dedicated input increases. Numerical study shows that discretionary flexibility and responsive pricing are strategic substitutes.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

Investment in Facility Changeover Flexibility for Early Entry into High‐Tech Markets

A model is introduced to analyze the manufacturing‐marketing interface for a firm in a high‐tech industry that produces a series of high‐volume products with short product life cycles on a single facility. The one‐time strategic decision regarding the firm's investment in changeover flexibility establishes the link between market opportunities and manufacturing capabilities. Specifically, the optimal changeover flexibility decision is determined in the context of the firm's market entry strategy for successive product generations, the changeover cost between generations, and the production efficiency of the facility. Moreover, the dynamic pricing policy for each product generation is obtained as a function of the firm's market entry strategy and manufacturing efficiency. Our findings provide insights linking internal manufacturing capabilities with external market forces for the high‐tech and high‐volume manufacturer of products with short life cycles. We show the impact of manufacturing efficiency and a firm's ability to benefit from volume‐based learning on the dynamic pricing policy for each product generation. The results demonstrate the benefits realized by a firm that works with its manufacturing equipment suppliers to develop more efficient and flexible technology. In addition, we explore how opportunities afforded by pioneer advantage enable a firm operating a less efficient facility to realize long term competitive advantage by deploying an earlier market entry strategy.     

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.     

Capacity Planning with Financial and Operational Hedging in Low‐Cost Countries

The authors of this article outline a capacity planning problem in which a risk‐averse firm reserves capacities with potential suppliers that are located in multiple low‐cost countries. While demand is uncertain, the firm also faces multi‐country foreign currency exposures. This study develops a mean‐variance model that maximizes the firm's optimal utility and derives optimal utility and optimal decisions in capacity and financial hedging size. The authors show that when demand and exchange rate risks are perfectly correlated, a risk‐averse firm, by using financial hedging, will achieve the same optimal utility as a risk‐neutral firm. In this study as well, a special case is examined regarding two suppliers in China and Vietnam. The results show that if a single supplier is contracted, financial hedging most benefits the highly risk‐averse firm when the demand and exchange rate are highly negatively related. When only one hedge is used, financial hedging dominates operational hedging only when the firm is very risk averse and the correlation between the two exchange rates have become positive. With both theoretical and numerical results, this study concludes that the two hedges are strategic tools and interact each other to maximize the optimal utility.     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

Multi‐Product Quality Competition: Impact of Resource Constraints

We study a multi‐product firm with limited capacity where the products are vertically (quality) differentiated and the customer base is heterogeneous in their valuation of quality. While the demand structure creates opportunities through proliferation, the firm should avoid cannibalization between its own products. Moreover, the oligopolistic market structure puts competitive pressure and limits the firm's market share. On the other hand, the firm has limited resources that cause a supply‐side fight for adequate and profitable production. We explicitly characterize the conditions where each force dominates. Our focus is on understanding how capacity constraints and competition affect a firm's product‐mix decisions. We find that considering capacity constraints could significantly change traditional insights (that ignore capacity) related to product‐line design and the role of competition therein. In particular, we show that when the resources are limited, the firm should offer only the product that has the highest margin per unit capacity. We find that this product could be the diametrically opposite product suggested by the existing literature. In addition, we show that for intermediate capacity levels, whereas the margin per unit capacity effect dominates in a less competitive market, proliferation and cannibalization effects dominate in a more competitive market.     

Product Portfolio Strategies: The Case of Multifunction Products

Motivated by the proliferation of multifunction products, we investigate product portfolio decisions of a single firm by analyzing the impact of three major factors. First, because multifunction products provide complete or partial functionalities of single‐function products, we incorporate substitution or cannibalization effects between the potential products. Second, we explicitly model the variable costs of manufacturing the single‐function and multifunction products. Third, we examine the firm's pricing decisions because of their impact on the degree of cannibalization between the multifunction product and one or more single‐function products. Using an economic model, we first characterize the firm's optimal product portfolio (through a quantity‐based decision), which in turn determines the market equilibrium prices for each product in its portfolio. Some of the unique insights stemming from our analysis are: (a) the optimal product portfolio choice is driven primarily by maximum profit margins for the single‐function products weighted by the demand substitution effects; and (b) from a product design perspective, the complete functionality of the base single‐function product is always included in the optimal product offering, but this is not necessarily the case with the complete functionality of the nonbase single‐function product.     

Production and Sales Planning in Capacitated New Product Introductions

How should a firm with limited capacity introduce a new product? Should it introduce the product as soon as possible or delay introduction to build up inventory? How do the product and market characteristics affect the firm's decisions? To answer such questions, we analyze new product introductions under capacity restrictions using a two‐period model with diffusion‐type demand. Combining marketing and operations management decisions in a stylized model, we optimize the production and sales plans of the firm for a single product. We identify four different introduction policies and show that when the holding cost is low and the capacity is low to moderate, a (partial) build‐up policy is indeed optimal if consumers are sensitive to delay. Under such a policy, the firm (partially) delays the introduction of its product and incurs short‐term backlog costs to manage its future demand and total costs more effectively. However, as either the holding cost or the capacity increases, or consumer sensitivity to delay decreases, the build‐up policy starts to lose its appeal, and instead, the firm prefers an immediate product introduction. We extend our analysis by studying the optimal capacity decision of the firm and show that capacity shortages may be intentional.     

The Design and Introduction of Product Lines When Consumer Valuations are Uncertain

This article presents a model of the design and introduction of a product line when the firm is uncertain about consumer valuations for the products. We find that product line introduction strategy depends on this uncertainty. Specifically, under low levels of uncertainty the firm introduces both models during the first period; under higher levels of uncertainty, the firm prefers sequential introduction and delays design of the second product until the second period. Under intermediate levels of uncertainty the firm's first product should be of lower quality than one produced by a myopic firm that does not take product line effects into consideration. We find that when the firm introduces a product sequentially, the strategy might depend on realized demand. For example, if realized demand is high, the firm's second product should be a higher‐end model; if demand turns out to be low, the firm's second product should be a lower‐end model or replace the first product with a lower‐end model.     

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.     

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.     

Sourcing Decisions with Stochastic Supplier Reliability and Stochastic Demand

Supplier sourcing strategies are a crucial factor driving supply chain success. In this paper, we investigate the implications of uncertain supplier reliability on a firm's sourcing decisions in an environment with stochastic demand. In particular, we characterize specific conditions under which a firm should choose a single versus multiple supplier sourcing strategy. In an environment with both uncertain demand and supply, we characterize the total order quantity, the number of suppliers selected for order placement, and the allocation of the total order quantity among these selected suppliers. For deeper managerial insight, we also examine the sensitivity of the optimal sourcing decisions to interactions between uncertainties in product demand and supply reliability. We show that sourcing from a single supplier is an optimal strategy for environments characterized by high levels of demand uncertainty or high salvage values. A numerical analysis based on data obtained from an office products retailer further reinforces our analytical results. In addition, we also find that when minimal order quantities are imposed, there are situations where it is not optimal to place an order with the lowest cost supplier.     

Managing Technology Selection and Development Risk in Competitive Environments

Managing development decisions for new products based on dynamically evolving technologies is a complex task, especially in highly competitive industries. Product managers often have to choose between introducing an incrementally better, safe new product early and a superior, yet highly risky, product later. Recommendations for managing such performance vs. time‐to‐market trade‐offs often ignore competitive reactions to development decisions. In this paper, we study how a firm could incorporate the presence of a strategic competitor in making technology selection and investment decisions regarding new products. We consider a model in which an innovating firm and its rival can introduce a new product immediately or pursue a more advanced product for later launch. Further, the firm can reduce the uncertainty surrounding product development by dedicating more resources; the effectiveness of this investment depends on the firm's innovative capacity. Our model generates two sets of insights. First, in highly competitive industries, firms can adopt different technologies and effectively use introduction timing to mitigate the effects of price competition. More importantly, the firm could strategically invest in the advanced product to influence its rival's technology choice. We characterize equilibrium development and investment decisions of the firms, and derive innovative capacity hurdles that govern a firm's choice between the risky and safe alternatives. The effects of development flexibility—where firms might have the option to revert to the safe product if the advanced product fails—are also considered.     

Manufacturing network configuration in supply chains with product recovery

Efficient implementation of product recovery requires appropriate network structures. In this paper, we study the network design problem of a firm that manufactures new products and remanufactures returned products in its facilities. We examine the capacity decisions and expected performance of two alternative manufacturing network configurations when demand and return flows are both uncertain.     

Mitigating Supply Uncertainty: The Interplay Between Diversification and Pricing

We consider a firm's sourcing problem from one reliable supplier and one unreliable supplier in two price‐setting scenarios. In the committed pricing scenario, the firm makes the pricing decision before the supply uncertainty is resolved. In the responsive pricing scenario, the firm's pricing decision is made after the supply uncertainty is resolved. For the committed pricing scenario, we develop a condition on supply uncertainty that guarantees the unimodality of the firm's objective function. By comparing the firm's optimal diversification decisions in the two pricing scenarios, we examine the interplay of supply diversification strategy and responsive pricing strategy in mitigating supply uncertainty. While both strategies are effective in mitigating supply uncertainty, we show that they are not necessarily substitutes. The relationship between these two strategies depends on two adverse effects caused by supply uncertainty: the lost‐revenue effect and the lost‐goodwill effect. More specifically, when the lost‐revenue effect dominates the lost‐goodwill effect, these two strategies are complements; otherwise, they are substitutes. Furthermore, we examine the impact of market size, price sensitivity, supplier reliability, and failure rebate on the interplay between these two strategies, and discuss the implications of our results. Finally, we extend our analysis to the case of two unreliable suppliers and show that the insights regarding the interplay between diversification and pricing continue to hold.