Presence Of Demand Uncertainty Research Articles

A note on the uniqueness of Nash–Cournot equilibria in an oligopolistic energy market with renewable generation and demand uncertainty

This work explores the uniqueness of Nash–Cournot equilibria in wholesale electricity markets with both thermal and renewable generation in the presence of demand uncertainty. Criteria guaranteeing a unique equilibrium are derived for an energy market where each firm owns a share of renewable generation. This work expands upon the uniqueness results proven by Lagerlöf (2006) to incorporate the presence of renewable generation into the market in the manner of Acemoglu et al. (2017). A numerical case study is used to illustrate the potential impacts of increasing renewable generation on equilibrium uniqueness and directions for future research are discussed.

Quality, Shelf Life, and Demand Uncertainty

Abstract This paper studies a monopolist’s choices of quality and shelf life of a perishable good in the presence of demand uncertainty and sunk production cost. It shows that, in response to demand uncertainty, the firm typically produces multiple products which differ in quality and shelf life; under certain conditions, products with a longer shelf life are of lower quality; a probability distribution of demand which first-order (second-order) stochastically dominates another induces more (more or fewer) product varieties. It also provides conditions under which a higher quality product has a higher absolute profit margin but a lower percentage margin.

Estimating the cost efficiency of public service providers in the presence of demand uncertainty

Public service managers generally make input choices in the face of uncertainty about future demands for service. This is generally not taken into account when estimating cost efficiency. In the operations research literature, for example, the standard approach to estimating cost efficiency is based on the assumption that managers choose inputs to minimise the cost of producing realised (i.e., observed) outputs. However, when outputs are unknown at the time input decisions are made, most managers will instead choose inputs to minimise the cost of producing output targets (e.g., minimum service levels, predicted maximum demands). In this paper, we explain how data envelopment analysis (DEA) estimators can be used to estimate cost, technical and allocative efficiency in these situations. The methodology is applied to Australian data on hospital and health service providers. We obtain estimates of efficiency that are quite different from estimates obtained using a standard approach that ignores uncertainty. Our work has important implications for performance evaluation and improvement programs in many public service settings.

Research on energy performance contracting with shared savings under stochastic market demand

In practice, the market risk caused by stochastic market demand is a main risk affecting the shared savings contract implementation in energy performance contracting. We develop a game-theoretic model to characterize the strategic interaction between the manufacturer’s ex-ante capacity decision and the energy service company (ESCO)’s investment decision on digitization and intellectualization to save energy, through which we unfold the impact of stochastic market demand upon all the stakeholders, the supply chain efficiency and the total energy consumption. The results show that the demand uncertainty can significantly affect the decisions of the ESCO and the manufacturer. Specifically, when there is no demand uncertainty, the manufacturer’s capacity decision is independent of the ESCO’s decision on energy-saving effort. By contrast, under stochastic demand there exists a complementary relationship between the manufacturer’s capacity investment and the ESCO’s energy-saving effort. Moreover, by comparing the optimal equilibria in shared savings with that under centralized supply chain, we find that decentralization causes inefficiencies in the form of lower energy-saving effort, underinvestment or overinvestment in capacity, and lower supply chain profit. In addition, it is more valuable for the supply chain to coordinate the ESCO and the manufacturer when the market demand is more stochastic. Furthermore, though always cutting the manufacturer’s total energy consumption without demand uncertainty, implementing the ESCO’s energy-saving service can increase the manufacturer’s total energy consumption and carbon emission in the society in the presence of demand uncertainty. Hence, governmental agencies should not ignore the impact of stochastic demand upon the total energy consumption with the interplay between the endogenous capacity setup decision and energy-saving service, and to reduce the carbon emission in the society governmental policies should be designed by taking into account such an increase of the total energy consumption.

Design of a two-echelon last-mile delivery model

Due to high congestion in cities and growing demand for last-mile delivery services, several companies have been implementing two-echelon distribution strategies over the past few years. Notably, the installation of urban transshipment points has gained increasing attention, used by logistics operators to transfer goods from large freight trucks to smaller and more agile vehicles for last-mile delivery. Nevertheless, the main challenge is how to decide the number and location of these facilities under the presence of demand uncertainty. In this paper, we develop a two-stage stochastic program to design two-echelon last-mile delivery networks under demand uncertainty. This approach decomposes the problem into strategic decisions (facility location) and operational decisions (daily distribution of goods). To address large-scale instances, we solve the model through the sample average approximation (SAA) technique and estimate the optimal routing costs (of the SAA counterpart) using a continuous approximation method. Using a real-world case study with more than 1300 customers from New York City, our results provide several managerial insights regarding the mix of transportation modes, facility location, and the impact of allowing the outsourcing of customer demand. We provide extensive validation of the two-stage stochastic program results through a simulation-based approach and the calculation of the value of the stochastic solutions. • We develop a two-stage stochastic program to design two-echelon last-mile delivery networks under demand uncertainty. • We use sample average approximation and continuum approximation of route cost to address large-scale instances. • For a real-world case study, we provide managerial insights regarding the mix of transportation modes, facility locations, and the benefits of outsourcing deliveries. • We extensively validate our results using a simulation-based approach and assess the value of accounting for stochasticity.

Multi-stage strategic trade policy in a differentiated duopoly

We consider a three-stage, non-cooperative game between two countries and two firms (duopoly) under a “reciprocal market model” to identify the optimal trade policy in the presence of tariffs and subsidies, but also allowing each country to commit to free trade. Even in the presence of demand uncertainty and horizontal product differentiation, it is established that there always exists a subgame perfect equilibrium in which one of the countries chooses protection while the other country chooses free trade.

Dynamic pricing with finite price sets: a non-parametric approach

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected demand corresponding to each price is unknown to the seller, whose objective is to maximize cumulative expected revenue. We propose an algorithm that estimates the unknown parameters in a learning phase, and in each subsequent season applies a policy determined as the solution to a sample dynamic program, which modifies the underlying dynamic program by replacing the unknown parameters by the estimate. Revenue performance is measured by the regret: the expected revenue loss relative to the optimal attainable revenue under full information. For a given number of seasons n, we show that if the number of seasons allocated to learning is asymptotic to (n^2log n)^{1/3}, then the regret is of the same order, uniformly over all unknown demand parameters. An extensive numerical study that compares our algorithm to six benchmarks adapted from the literature demonstrates the effectiveness of our approach.

Labor market reform and innovation: Evidence from Spain

We analyze the effect of a labor market reform on firms’ product innovation. The reform, which amounts to a natural experiment, differentially reduced firing costs for some firms, thereby lowering adjustment costs in the presence of demand uncertainty. Using a difference-in-differences framework, we show that the reform increased product innovations. We also provide evidence that the reform induced upgrading of product quality and enabled firms to grow faster and enter new markets. The effects are concentrated in industries with high levels of demand volatility and R&D intensity, where flexible adjustments to unexpected shocks are important.

Dual-Sourcing, Dual-Mode Dynamic Stochastic Inventory Models: A Review

We review academic research on dual-sourcing (or dual-mode) dynamic stochastic inventory models, which study the replenishment of inventory from two sources (or two transportation modes) in the presence of demand uncertainty. The classic assumption, also adopted here, is that the two sources (modes) differ by replenishment leadtimes and costs. We cover both discrete and continuous-time models. A distinguish feature of our review from others is that our review is more technically detailed and provides self-contained proofs of several fundamental results in the dual-sourcing literature. We also highlight theory advanced recently by using asymptotic analysis.

Financing a risk‐averse manufacturer in a pull contract: early payment versus retailer investment

AbstractThis work focuses on a two‐level supply chain with a pull contract, where the retailer acts as a leader and the capital‐constrained manufacturer as a follower who undertakes the inventory risk. In the presence of demand uncertainty, the manufacturer is risk‐averse, and the risk is measured by the semideviation method. To finance the capital‐constrained manufacturer, we investigate two collaborative supply chain finance schemes: retailer's early payment (EP) financing and retailer investment (RI) financing. We characterize the manufacturer's optimal production quantity and the retailer's wholesale price under EP and RI. Under the two financing schemes, the manufacturer obtains a higher utility when his risk aversion degree is moderate, while the retailer is worse off in the presence of a higher risk aversion degree. Under RI, both optimal production quantity and wholesale price decrease in the proportion of dividends shared by the manufacturer. For the manufacturer (or the retailer or the total supply chain), we derive the associated parameter region in which RI achieves a higher performance than EP. When RI and EP are available, there exists a common parameter region in which RI is preferred by the manufacturer, retailer, and total supply chain.

The value of physical distribution flexibility in serving dense and uncertain urban markets

Abstract Urban last-mile distribution in emerging economies suffers from unique levels of operational complexity, largely due to the prevailing dominance of the highly fragmented traditional retail channel. To support companies in strategically designing efficient urban distribution networks in such uncertain market environments, we propose a large-scale stochastic mixed integer linear programming model that incorporates three commonly deployed measures of physical distribution flexibility. Being able to flexibly adjust transportation capacities, facility capacities, and demand allocations may enable companies to serve urban markets more efficiently, especially in the presence of demand uncertainty. The model supports strategic network design decisions by optimizing the number, type, and capacity of distribution facilities as well as the composition of corresponding vehicle fleets. We apply the model to two large-scale, real-world case studies based on real data from Coca-Cola Femsa’s last-mile operations in Bogota and Cali, Colombia. These case studies are representative for many last-mile distribution problems in emerging market megacities. Our numerical results demonstrate how considering stochasticity and incorporating physical distribution flexibility in the strategic design of urban last-mile distribution networks jointly and independently affect the resulting network design and improve its commercial and operational performance. The stochastic design approach outperforms the deterministic design approach on every instance in terms of expected cost and performance risk. In most cases, physical distribution flexibility improves performance. However, we show that in some cases, if strategic decisions are based on deterministic assumptions, allowing for operational flexibility may result in a deterioration in network performance.

Evaluating Manufacturer's Wholesale Price Policy Under Order Postponement With Buyback Option

In this article, a decentralized newsvendor model is analyzed in the presence of demand uncertainty, where the retailer wishes to postpone his ordering decision by few days until the most accurate demand information is available. The impact of such order postponement on the equilibrium profits of both manufacturer and retailer with and without a buyback contract is subsequently examined to obtain a range of wholesale prices within which the marginal profits for both manufacturer and retailer which are non-negative. Furthermore, it is observed that the possibility of implementing order postponement is higher when it is done in the presence of a buyback contract as it increases the marginal profits for both manufacturer and the retailer and expands the feasible region of wholesale price, which leads to a provision of higher flexibility for negotiation between the manufacturer and the retailer.

Risk averse sourcing in a stochastic supply chain: A simulation-optimization approach

A growing need for global sourcing has forced firms to manage more complex supply chains with increasing risks of supply disruptions. Multi sourcing is a common method to hedge against these risks. In the presence of demand uncertainties and supply disruptions, minimizing the downside risk is necessary. Hence, in this paper a new multi-period and scenario based supply chain model consists of a number of unreliable suppliers and a number of retailers is developed in the form of a multi-period newsvendor problem with a risk averse objective function. In the model, there are two types of retailers both faced uncertain demands: risk sensitive and risk neutral. Retailers have three choices to respond to the customer demand: a forward contract, and two option contracts include reserving a certain capacity in the secondary supplier and buying from the spot market. The problem has also developed as an agent-based system. As a solution approach in the large scale problem instances, a simulation-optimization algorithm is developed. Two kinds of heuristics are compared in order to optimize the simulation procedure: genetic algorithm and q-learning. Results showed the efficiency of the q-learning algorithm.

Online Scheduling: Understanding the Impact of Uncertainty

Abstract We present a framework to study quality of schedules obtained iteratively and online (real-time) in the presence of demand uncertainty Using this framework, we carry out a computational study, and make interesting observations. First, we find that uncertainty plays a less important role as a manufacturing facility is operated close to capacity. Second, the choice of the horizon for the online iterations, is dependent on the mean load, but independent of the accuracy of the forecasts. Finally, feedback, in the form of re-optimization, plays a very important role in mitigating the impact of uncertainty. Thus, through the analysis presented in this work, we gain insights that are applicable to all general rescheduling approaches.

A Trade Credit Model with Asymmetric Competing Retailers

We study a supply chain of a manufacturer selling to two asymmetric retailers engaged in inventory (order quantity) competition in the presence of demand uncertainty and an exogenously given retail price. The effective demand of each retailer includes its primary demand and reallocated demand from its competitor. We model two salient features causing asymmetry: (i) the weak retailer is capital‐constrained and (ii) the bargaining power of the dominant retailer implies that it enjoys a lower wholesale price. The manufacturer offers trade credit to the weak, capital‐constrained retailer. We show that such trade credit can be used by the manufacturer as a strategic response to the bargaining power of its dominant retailer. Computational examples reveal that under inventory competition, the capital‐constrained retailer benefits from the trade credit, leaving the dominant retailer worse off. We show that demand substitution increases the profit of the dominant retailer and the manufacturer but, somewhat surprisingly, decreases the weak retailer's profit. When both bank and trade credit are available, we show conditions under which trade credit is preferred over bank credit by the manufacturer. Compared with a trade credit with an endogenous interest rate (and an exogenously given wholesale price), a trade credit with an endogenous wholesale price (and an exogenously given interest rate) is preferred by the manufacturer, but is only preferred by the system when the weak retailer's initial working capital is small.

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.

Horizontal Subcontracting From Competitors: When and What?

We investigate horizontal subcontracting between two firms that compete in selling to uncertain markets. Each firm manages resources to make a key component indispensable for final assembly by both firms. A horizontal subcontract stipulates that one of them prepares key component or even produces final product for the other. The subcontract can be signed before or after resource preparation, which we refer to as forward and spot subcontracting, respectively. With the presence of demand uncertainty, the subcontract is signed before (after, resp.) demand realization in forward (spot, resp.) subcontracting, while resources are always prepared in advance. Forward subcontracting enables the firms to achieve the maximum overall cost saving by concentrating all production activities in the more cost‐efficient firm. Spot subcontracting draws the firms to unilateral undertaking to prepare resources and cooperative resource allocation. This gives rise to an efficiency effect by balancing production and market selling between the firms, and a pooling effect that enables them to profit from synergies between markets. The subcontracting subject is crucial to the contribution of total cost saving relative to total revenue gain to the efficiency effect, but is inconsequential on the scale of the pooling effect. We conduct a comparative investigation into forward and spot subcontracting, with the subject playing a differentiating role, and explore the impacts of the means and variances of demand intercepts and the firms’ costs on system performance under various horizontal subcontracting modes differentiated by timing and subject.

Surface vs. Air Shipment of Humanitarian Goods under Demand Uncertainty

The combination of insufficient funds and limited information regarding the demand in regions of desperate need presents a great challenge to many humanitarian organizations. This study examines how a humanitarian organization can minimize the expected shortage in delivering relief aid to regions of need, either though surface or air transportation, in the presence of demand uncertainty with a budget constraint. The study makes four contributions. First, we show that when there is reserved supply for air transportation, it is optimal to provide a higher service level through surface shipment to regions with greater demand uncertainty. Second, we show that the demand variation plays a significant role in the allocation of funds between surface and air shipments. The reaction of the humanitarian organization to higher degrees of demand uncertainty can be determined by the optimal level of inventory purchased for surface shipment. If the optimal inventory for surface shipment is less than the mean demand, then we show that increasing degrees of demand uncertainty leads to increasing reliance on the air shipment option with greater levels of inventory reserved for air transportation and decreasing levels of inventory reserved for surface shipment. Third, when there are opportunities to invest in better forecasting, we find that a humanitarian organization should focus its resources on improving the demand forecast in one region as opposed to evenly allocating resources to all regions. Fourth, we show that the expected amount of shortages reduces with a higher number of regions to serve due to a risk‐pooling effect.

A Note on the Desirability of the Supply Function Competition with Demand Uncertainty

In this paper, we formalize a prediction of Klemperer and Meyer (1989) arguing that the expected profits of oligopolistic firms may be higher under the supply function competition than under the stochastic Cournot competition in the presence of demand uncertainty, and investigate how this prediction is affected by certain attributes of a oligopolistic industry, such as the number of firms, the cost of producing a unit output, and the slope of the demand curve.

Dynamic Pricing of Experience Goods in Markets with Demand Uncertainty

This paper studies a firm’s optimal dynamic pricing strategies for its experience goods in markets, where the distribution of consumers’ valuations is ex ante unknown. We find several interesting findings. First, a high-quality firm can signal its quality with either a skimming-pricing strategy or a penetration-pricing strategy in the early period. Second, though a firm with higher quality benefits more from learning market demand, in equilibrium the low-quality firm not the high-quality firm will learn demand if consumers have very different willingness to pay. This is because the high-quality firm may forgo the benefit of learning demand to convince consumers of its high quality. Third, although consumers have higher willingness to pay for the high-quality product, in the first period the high-quality firm may actually charge a lower price than the low-quality firm. Lastly, the firm may earn higher profits when its initial pricing decision is made under demand uncertainty than under no demand uncertainty. The underlying reason is that the presence of demand uncertainty can sufficiently lower the high-quality firm’s signaling cost, leading to a separating outcome and allowing it to make higher profits by setting future prices based on its high quality.