Presence Of Demand Uncertainty Research Articles

Price Regulation under Demand Uncertainty

In this paper we provide a taxonomy of price cap regulation in oligopoly under demand uncertainty. We show that independently of the nature of uncertainty high price caps always increase production and welfare as compared to setting no price cap. We also derive conditions on the demand distribution under which a price cap close to marginal cost can be optimal and when it is not. For demand distributions with an increasing hazard rate we show that price regulation under demand uncertainty can be viewed as a well behaved extension of the analysis for deterministic demand. For this class of distributions we characterize the optimal price cap, which is unique and may or may not be close to marginal cost. Our general framework nests the limit case of deterministic demand as well as results by Earle et al. (2007), who have shown that standard arguments supporting the imposition of price caps may break down in the presence of demand uncertainty.

Dynamic Pricing and Inventory Control: Uncertainty and Competition

In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition (in particular a duopoly setting) together with the presence of demand uncertainty. We consider a dynamic setting where multiple products share production capacity. We introduce a demand-based fluid model where the demand is a linear function of the price of the supplier and of her competitor, the inventory and production costs are quadratic, and all coefficients are time dependent. A key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitor's strategy. First, we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a Nash equilibrium in continuous time. We then discuss issues of uniqueness and address how to compute a particular Nash equilibrium, i.e., the normalized Nash equilibrium.

Bargaining in competing supply chains with uncertainty

Substantial literature has been devoted to supply chain coordination. The majority of this literature ignores competition between supply chains. Moreover, a significant part of this literature focuses on coordination that induce the supply chain members to follow strategies that produce the equilibria chosen by a vertically integrated supply chain. This paper investigates the equilibrium behavior of two competing supply chains in the presence of demand uncertainty. We consider joint pricing and quantity decisions and competition under three possible supply chain strategies: Vertical Integration (VI), Manufacturer’s Stackelberg (MS), and Bargaining on the Wholesale price (BW( α ), α is the bargaining parameter) over a single or infinitely many periods. We show that, in contrast to earlier literature, using VIVI (VI in both chains) is the unique Nash Equilibrium over one period decision, while using MSMS or BW( α )BW( α ) may be Nash Equilibrium over infinitely many periods.

A procurement model using capacity reservation

Abstract In this paper we model a scenario where a buyer reserves capacity from one or more suppliers in the presence of demand uncertainty. We explicitly derive suppliers’ capacity reservation price, which is a function of their capacity, amount of capacity reserved by the buyer and other parameters. The buyer operates in a “built-to-order” environment and needs to decide how much capacity to reserve and from how many suppliers. For a strategy of equal allocation of capacity among the selected suppliers we develop closed form solutions and show that the model is robust to the number of suppliers from whom capacity is procured through reservation. When the parameters of demand distribution changes the supply base is likely to remain more or less the same. Our analysis further shows that increasing the number of pre-qualified suppliers does not provide significant advantages to the buyer. On the other hand, a pre-qualified supply base with greater capacity heterogeneity will benefit the buyer.

Freight Transportation Network Design Problem for Maximizing throughput under Uncertainty

A mathematical programming formulation is developed to determine the throughput of a freight transportation network. The impact of demand and capacity uncertainty on the throughput is systematically studied. Mathematical proofs are provided to show that accounting for capacity uncertainty by using a single-point expected value can lead to systematic overestimation of network throughput. This result is also valid for other measures, such as system capacity. Two sampling-based methodologies–independent random number and common random number–are provided to determine network design decisions in the presence of demand uncertainty. The sampling-based solution methods provide an approximate estimate of optimal solution and provide probabilistic bounds on the optimality gap. The presented methodologies are generic and can be applied even if different functional forms (nonlinear, nonconvex) are used to model various aspects of the freight transportation network. The numerical tests demonstrate that not accounting for capacity uncertainty can result in overestimation of system throughput of up to 40%. A common random number-based sampling strategy was found to significantly outperform the independent random number strategy for all the scenarios tested.

Suitable application situations of different postponement approaches: Standardization vs. modularization

Although postponement benefits manufacturers by increasing flexibility and reducing inventory and product complexity, this strategy may not be suitable for all situations faced by manufacturers. This paper builds a cost model to examine the value of postponement for a firm with two products made in N stages and compares two different postponement approaches (that is, standardization and modularization) in terms of their costs in the presence of demand uncertainty. The considered trade-offs include processing costs, inventory costs, and the cost of product/process redesign. The analytical results provide two optimal decisions, the static decision and the dynamic decision, and suggest how firms choose a suitable postponement decision according their business environments. In addition, case studies with numerical examples are provided to illustrate the effectiveness of the model. The main contributions of this paper are: (1) the explanation of the effect of environment uncertainty on the decision to use a postponement strategy, (2) the definitions of some environmental circumstances that make postponement economical, and (3) the illustration of the cost structures under different postponement strategies.

Design of responsive supply chains under demand uncertainty

This paper addresses the optimization of supply chain design and planning under responsive criterion and economic criterion with the presence of demand uncertainty. The supply chain consists of multi-site processing facilities and corresponds to a multi-echelon production network with both dedicated and multiproduct plants. The economic criterion is measured in terms of net present value, while the criterion for responsiveness accounts for transportation times, residence times, cyclic schedules in multiproduct plants and inventory management. By using a probabilistic model for stock-out, the expected lead time is proposed as the quantitative measure of supply chain responsiveness. The probabilistic model can also predict the safety stock levels by integrating stock-out probability with demand uncertainty. These are all incorporated into a multi-period mixed-integer nonlinear programming (MINLP) model, which takes into account the selection of manufacturing sites and distribution centers, process technology, production levels, scheduling and inventory levels. The problem is formulated as a bi-criterion optimization model that maximizes the net present value and minimizes the expected lead time. The model is solved with the ɛ-constraint method and produces a Pareto-optimal curve that reveals how the optimal net present value, supply chain network structure and safety stock levels change with different values of the expected lead time. A hierarchical algorithm is also proposed based on the decoupling of different decision-making levels (strategic and operational) in the problem. The application of this model and the proposed algorithm are illustrated with two examples of polystyrene supply chains.

On Price Caps Under Uncertainty

This paper shows how standard arguments supporting the impo- sition of price caps break down in the presence of demand uncertainty. In particular, though in the deterministic case the introduction or lowering of a price cap (above marginal cost) results in increased production, increased total welfare, decreased prices, and increased consumer welfare, we show that all of the above comparative statics predictions fail for generic uncertain demand functions. For example, for price caps su-ciently close to marginal cost, a decrease in the price cap always leads to a decrease in production and total welfare under certain mild conditions. Under stronger regularity assumptions, all of the monotone comparative statics predictions from the deterministic case also do not hold for a generic uncertain demand if we restrict attention to price caps in an arbitrary flxed interval (as long as the price caps are binding for some values in that interval).

On Price Caps Under Uncertainty

This paper shows how standard arguments supporting the imposition of price caps break down in the presence of demand uncertainty. In particular, though in the deterministic case the introduction or lowering of a price cap (above marginal cost) results in increased production, increased total welfare, decreased prices, and increased consumer welfare, we show that all of the above comparative statics predictions fail for generic uncertain demand functions. For example, for price caps su ciently close to marginal cost, a decrease in the price cap always leads to a decrease in production and total welfare under certain mild conditions. Under stronger regularity assumptions, all of the monotone comparative statics predictions from the deterministic case also do not hold or a generic uncertain demand if we restrict attention to price caps in an arbitrary fixed interval (as long as the price caps are binding for some values in that interval).

Control of Dividends, Capital Subscriptions, and Physical Inventories

Business organizations are faced with the financial and physical task of managing interrelated flows of material and cash. Material needs capital, and on the other hand, when finished goods are sold, they contribute to cash reserves. In this paper, we present and study a dynamic model in which inventory and financial decisions are made simultaneously and interact directly with each other in the presence of demand uncertainty and financial constraints. The criterion is to maximize the expected present value of dividends net of capital subscriptions. We establish conditions which imply that the optimal values of dividends, capital subscriptions, material procurement, and short term borrowing are nondecreasing functions of the levels of inventory and retained earnings. We establish that the optimal policy is myopic and explicitly characterized for a special and important case where both inventory costs and default penalties are linear. As a consequence, the optimal base-stock inventory level should be lower in a dividend-maximizing firm than in a profit-maximizing firm.

Joint Production and Financing Decisions: Modeling and Analysis

This paper develops models to make production and financing decisions simultaneously in the presence of demand uncertainty and market imperfections. While the Modigliani and Miller propositions demonstrate that a firm's investment and financing decisions can be made independently in a perfect capital market, our models illustrate how a firm's production decisions are affected by the existence of financial constraints. We analyze the interactions between a firm's production and financing decisions as a tradeoff between the tax benefits of debt and financial distress costs. Our numerical examples illustrate that a traditional all-equity manufacturing company can improve its performance significantly by making real and financial decisions together. The results illustrate greater firm value sensitivity to production decisions than to financing decisions and that low-margin producers face significant risk in not coordinating production and financing decisions.

Stackelberg leadership with demand uncertainty

We consider a simple Stackelberg model with demand uncertainty only for the first mover in order to compare the advantages of leadership and flexibility, and use an example to provide some discussion about the endogenous order of moves in the presence of demand uncertainty. We find that only when the realized demand is in an intermediate zone does the first mover preserve its advantage; when the realized demand is far from its expected value, the second mover obtains higher profit than the leading firm, as the leadership advantage is dominated by the benefit of flexibility when demand fluctuation is significant. Even with this risk of losing flexibility under significant demand variation, for some parameter values in our model the first firm still has incentive to choose Stackelberg rather than Cournot competition. Copyright © 2005 John Wiley & Sons, Ltd.

Reply to “Do Returns Policies Intensify Retail Competition?”

Returns policies are common in many sectors of retail distribution. Padmanabhan and Png (1997) showed that with demand uncertainty, a returns policy could improve manufacturer profitability under certain conditions. Wang (2004) showed that returns policies do not change manufacturer profitability when demand is certain and retailing is competitive. We show that returns policies do increase manufacturer profitability by attenuating retailer price competition when demand is low and intensifying competition when demand is high. Importantly, this effect holds only in the presence of demand uncertainty. Further, the conditions under which a returns policy raises the manufacturer's profit are weaker when retailing is a duopoly than when retailing is a monopoly. This suggests that returns policies serve both to manage competition and mitigate demand uncertainty.

Foreign Direct Investment and Exports with Growing Demand

We explore entry into a foreign market with uncertain demand growth. A multinational can serve the foreign demand by two modes, or by a combination thereof: it can export its products, or it can create productive capacityvia foreign direct investment (FDI). The advantage of FDI is that it allows for lower marginal cost than exporting does. The disadvantage is that FDI is irreversible and, hence, entails the risk of creating under-utilized capacity in the case that the market turns out to be small. The presence of demand uncertainty and irreversibility gives rise to an interior solution, where the multinational, under certain conditions, both exports its products and does FDI.

Semicollusion vs. Full Collusion: The Role of Demand Uncertainty and Product Substitutability

We examine the profitability of two different cartel organizational forms: full collusion, under which firms collude on both price and quality, and semicollusion, under which firms collude on price only. We show that, in the presence of demand uncertainty that cannot be contracted upon in the cartel agreement, firms may be better off limiting their collusive agreement to price only. However, a positive relationship between demand uncertainty and the relative profitability of semicollusion exists only for low levels of demand substitutability. The converse is true for high levels of demand substitutability. Therefore, if demand substitutability is sufficiently high, no level of demand uncertainty will make semicollusion the optimal organizational form. In contrast, semicollusion is guaranteed to be optimal for a sufficiently low level of demand substitutability. The market structure described is motivated by and closely parallels that of shipping cartels.

Product Variety, Supply Chain Structure, and Firm Performance: Analysis of the U.S. Bicycle Industry

Using data from the U.S. bicycle industry, we examine the relation among product variety, supply chain structure, and firm performance. Variety imposes two types of costs on a supply chain: production costs and market mediation costs. Production costs include, among other costs, the incremental fixed investments associated with providing additional product variants. Market mediation costs arise because of uncertainty in product demand created by variety. In the presence of demand uncertainty, precisely matching supply with demand is difficult. Market mediation costs include the variety-related inventory holding costs, product mark-down costs occurring when supply exceeds demand, and the costs of lost sales occurring when demand exceeds supply. We analyze product variety at the product attribute level, noting that the relative impact of variety on production and market mediation costs depends to a large extent on the attribute underlying the variety. That is, some types of variety incur high production costs and some types of variety incur high market mediation costs. We characterize supply chain structure by the degree to which production facilities are scale-efficient and by the distance of the production facility from the target market. We hypothesize that firms with scale-efficient production (i.e., high-volume firms) will offer types of variety associated with high production costs, and firms with local production will offer types of variety associated with high market mediation costs. This hypothesis implies that there is a coherent way to match product variety with supply chain structure. Empirical results suggest that firms which match supply chain structure to the type of product variety they offer outperform firms which fail to match such choices.

Endogenously Asynchronous Entries into an Uncertain Industry

In the presence of demand uncertainty, a priori identical firms may voluntarily choose asynchronous timing of entries. We formulate a duopoly model where two firms compete during many marketing periods. To enter the market, each firm is required to make a long-term supply contract with retailers, which stipulates that the firm must supply a constant quantity each period. The state of demand is ex ante uncertain, and becomes observable a period after at least one firm's entry.

Entry, financing, and bankruptcy decisions: The limited liability effect

A firm, which has a privileged right to undertake an irreversible investment project, simultaneously determines whether to exercise this project and also how many bonds to issue in the presence of demand uncertainty. The firm will not exercise the project until its net value from investing immediately equals its option value from delaying investment. The firm’s choice of debt levels balances the tax advantage of debt against a cost associated with the event of bankruptcy. The effects of uncertainty, asset specificity, and the costs to purchase capital later on a firm’s entry, financing, and bankruptcy decisions are examined and compared with those in the literature.

Divisionalization and strategic managerial incentives in oligopoly under uncertainty

This paper argues that divisionalization and incentive contracting are complementary rent shifting tools in the presence of demand uncertainty. The role for divisionalization arises if managers know the state of demand prior to making output decisions and if incentive contracts are linear and non-state contingent. In this context incentive contracts achieve expected Stackelberg outcomes but have no impact on the firm's responsiveness to demand shocks. Divisionalization, on the other hand has the strategically beneficial effect of making the firm more responsive to demand shocks.

Simple regulatory policies in the presence of demand and cost uncertainty

We analyze the design of regulatory policy in the presence of demand uncertainty when the regulated firm has superior knowledge of its cost structure. The presence of demand uncertainty introduces important new considerations for the regulator. We show that by limiting the regulated firm's obligation to serve and by protecting the firm against stranded investment, the regulator can enhance consumer welfare relative to the case where the regulator can only set a single price for the regulated product before demand is realized.