Demand Distribution Research Articles

Converting Organic Municipal Solid Waste Into Volatile Fatty Acids and Biogas: Experimental Pilot and Batch Studies With Statistical Analysis.

Italy can augment its profit from biorefinery products by altering the operation of digesters or different designs to obtain more precious bioproducts like volatile fatty acids (VFAs) than biogas from organic municipal solid waste. In this context, recognizing the process stability and outputs through operational interventions and its technical and economic feasibility is a critical issue. Hence, this study involves an anaerobic digester in Treviso in northern Italy. This research compares a novel line, consisting of pretreatment, acidogenic fermentation, and anaerobic digestion, with single-step anaerobic digestion regarding financial profit and surplus energy. Therefore, a mass flow model was created and refined based on the outputs from the experimental and numerical studies. These studies examine the influence of hydraulic retention time (HRT), pretreatment, biochar addition, and fine-tuned feedstock/inoculum (FS/IN) ratio on bioproducts and operational parameters. VFA concentration, VFA weight ratio distribution, and biogas yield were quantified by gas chromatography. A t test was then conducted to analyze the significance of dissimilar HRTs in changing the VFA content. Further, a feasible biochar dosage was identified for an assumed FS/IN ratio with an adequately long HRT using the first-order rate model. Accordingly, the parameters for a mass flow model were adopted for 70,000 population equivalents to determine the payback period and surplus energy for two scenarios. We also explored the effectiveness of amendments in improving the process kinetics. Both HRTs were identical concerning the ratio of VFA/soluble chemical oxygen demand (0.88 kg/kg) and VFA weight ratio distribution: mainly, acetic acid (40%), butyric acid (24%), and caproic acid (17%). However, a significantly higher mean VFA content was confirmed for an HRT of 4.5 days than the quantity for an HRT of 3 days (30.77, SD 2.82 vs 27.66, SD 2.45 g-soluble chemical oxygen demand/L), using a t test (t8=-2.68; P=.03; CI=95%). In this research, 83% of the fermented volatile solids were converted into biogas to obtain a specific methane (CH4) production of 0.133 CH4-Nm3/kg-volatile solids. While biochar addition improved only the maximum methane content by 20% (86% volumetric basis [v/v]), the FS/IN ratio of 0.3 volatile solid basis with thermal plus fermentative pretreatment improved the hydrolysis rate substantially (0.57 vs 0.07, 1/d). Furthermore, the biochar dosage of 0.12 g-biochar/g-volatile solids with an HRT of 20 days was identified as a feasible solution. Principally, the payback period for our novel line would be almost 2 years with surplus energy of 2251 megajoules [MJ] per day compared to 45 years and 21,567 MJ per day for single-step anaerobic digestion. This research elaborates on the advantage of the refined novel line over the single-step anaerobic digestion and confirms its financial and technical feasibility. Further, changing the HRT and other amendments significantly raised the VFA concentration and the process kinetics and stability.

Bioinspired Nanochitin-Based Porous Constructs for Light-Driven Whole-Cell Biotransformations.

Solid-state photosynthetic cell factories (SSPCFs) are a new production concept that leverages the innate photosynthetic abilities of microbes to drive the production of valuable chemicals. It addresses practical challenges such as high energy and water demand and improper light distribution associated with suspension-based culturing; however, these systems often face significant challenges related to mass transfer. The approach focuses on overcoming these limitations by carefully engineering the microstructure of the immobilization matrix through freeze-induced assembly of nanochitin building blocks. The use of nanochitins with optimized size distribution enabled the formation of macropores with lamellar spatial organization, which significantly improves light transmittance and distribution, crucial for maximizing the efficiency of photosynthetic reactions. The biomimetic crosslinking strategy, leveraging specific interactions between polyphosphate anions and primary amine groups featured on chitin fibers, produced mechanically robust and wet-resilient cryogels that maintained their functionality under operational conditions. Various model biotransformation reactions leading to value-added chemicals are performed in chitin-based matrix. It demonstrates superior or comparable performance to existing state-of-the-art matrices and suspension-based systems. The findings suggest that chitin-based cryogel approach holds significant promise for advancing the development of solid-state photosynthetic cell factories, offering a scalable solution to improve the efficiency and productivity of light-driven biotransformation.

Using generic cities to assess flying ad-hoc network (FANET) performance

Abstract Flying ad-hoc networks (FANET) offer a solution to provide communication among unmanned aerial systems (UAS) without ground infrastructure and, hence, may provide redundancy if main terrestrial communication systems fail. With a strongly growing UAS market, this redundancy is of particular importance especially if the vehicles are operated over densely populated regions, such as urban areas. To further develop the FANET technology, it is, therefore, essential to understand and predict the performance requirements for such networks and the necessary systems as they arise from the different applications. However, with the diversity of cities, the problem arises that custom-made simulation models often lack generality. For this reason, in our work, we introduce an approach to generate randomized cities and to model UAS traffic for selected applications to assess different performance metrics of the FANET. This approach comprises the creation of randomized city geometries, the derivation of UAS traffic demand on these geometries, as well as the simulation of the flights of each individual vehicle. To showcase the capabilities of the approach, we generate an exemplary city and obtain characteristic datasets of the UAS traffic which are then used to assess the FANET performance for a selected FANET application using a simplified network model. We will show that FANET performance is strongly influenced by the extent of the demand, demand distribution over time, vehicle speed, and delivery network geometry.

Mapping and Assessing the Supply and Demand of Rural Recreation Services in National Parks: A Case Study of Qianjiangyuan, Zhejiang, China

National parks not only protect natural resources but also provide a variety of cultural ecosystem services, with their rural areas serving as important locations for providing rural recreation services (RRS). Spatial quantification of RRS supply and demand will contribute to ensuring the protection and promotion of human well-being in national parks. In this study, we proposed an integrated framework to map and assess the spatial distribution of RRS supply and demand in Changhong Township, located within Qianjiangyuan National Park. We used a combination of spatial analysis and the MaxEnt model as tools, which played a positive role in saving time when modeling areas providing cultural ecosystem services. Based on the findings, the study area was divided into different zones to propose spatial planning measures. The results showed that (1) the MaxEnt model was robust in mapping RRS supply. RRS supply and demand distribution had high spatial heterogeneity. (2) The proportion of areas where RRS supply exceeded demand was 72.58%, primarily distributed in areas with a high level of naturalness at the periphery of the study area. (3) This study divided Changhong Township into four types of zones: developed recreation service area, potential recreation service area, recreation service demand area, and marginal recreation service area. We proposed suggestions for the scientific utilization and management of RRS in each zone. Overall, our findings provide a scientific basis for planning rural recreation spaces within national parks, promoting the comprehensive utilization of rural cultural ecosystem services.

Enhancing the accuracy and reliability of non-online metered demand allocation in water distribution systems through dynamic spatiotemporal population distribution.

The limited penetration of smart water meters in current water distribution systems (WDS) compromises the accuracy and reliability of WDS simulations. Beyond the effectiveness of parameter calibration algorithms, the precision of demand allocation at nodes, especially for non-online metered demands, is pivotal to simulation fidelity. Traditionally, this task is addressed through top-down (TD) and bottom-up (BU) approaches. However, these methods are often constrained by outdated population data, assumptions of uniform demand distribution, and substantial initial workload. To overcome these limitations, this study proposes a novel node demand allocation method based on real-time cellular signaling (CS) data, which leverages dynamic population proportions to more accurately capture the relationship between real-time population distribution and water consumption in urban areas. A real-world WDS with three water use scenarios (weekdays, weekends, and holidays) demonstrates the utility of the proposed method, and results show that: (1) the proposed CS method achieves the lowest WDS simulation errors, with a maximum absolute error of 1.15 m at pressure sensors and a maximum absolute relative error of 3.71 % at flow sensors, outperforming the BU and TD methods; (2) the incorporation of real-time cellular signaling data allows for precise demand allocation by accurately capturing population fluctuations, particularly in high-mobility areas; and (3) the method's high accuracy and adaptability make it well-suited for complex urban water distribution systems, with seamless integration into GIS and WDS platforms, enhancing its practical implementation.

Equilibrium study of logistics demand and logistics resource allocation in Guangdong Province.

Logistics serve as a vital link between production and consumption. The balanced allocation of logistics demand and resources can promote the harmonious development of the logistics system, thereby fostering regional economic growth. As a leading region in China's reform and opening-up, Guangdong Province has experienced high economic growth. The equitable allocation of logistics demand and resources within a province is crucial for sustaining its economic development. This paper investigates the regional characteristics of logistics demand and resource allocation in Guangdong Province by analyzing the spatial distribution and evolutionary trends of logistics demand alongside the equilibrium of logistics resource allocation. First, the entropy weight method is utilized to examine the development trends of logistics demand and resource levels in Guangdong Province. Second, spatial autocorrelation analysis is applied to the spatiotemporal evolution characteristics of logistics demand across various cities in Guangdong Province for the years 2011, 2016, and 2021. Using 2021 cross-sectional data, an inconsistency index, which is based on geographic concentration, is employed to assess the mismatch between logistics demand and resource allocation across cities in Guangdong. The study reveals that logistics demand in Guangdong Province has been steadily increasing, with significant regional disparities. The spatial distribution exhibited a degree of correlation, with clustering patterns. However, logistics resource allocation remains imbalanced, with a certain degree of correspondence to logistics demand levels. Specifically, areas with higher logistics demand tend to have a higher concentration of logistics resources. The Pearl River Delta region holds the most abundant logistics resources, whereas many cities in northern and western Guangdong face severe shortages and are unable to meet the normal logistics demand.

Enhancing ‘disease x’ responsiveness: a risk-averse distributionally robust optimization approach for resource allocation under infectious disease transmission variability

Testing stands out as a crucial element in the public health response during a pandemic, serving diverse purposes pivotal for controlling the spread of the infectious agent. It enables early case detection, facilitating prompt isolation and treatment, thereby reducing the severity of individual cases and interrupting the transmission chain within communities. Recognizing the pivotal role of testing in managing and mitigating the impact of a pandemic, this paper addresses the distribution of test kits, taking into account the spatiotemporal uncertainty in demand and the ambiguity of the demand's probability distribution over a multi-period horizon. Determining decisions about location, allocation, operational distribution, and shipment is the main goal in order to guarantee equity and fairness in the distribution of resources among different populations. A two-stage distributionally robust optimisation (DRO) model is proposed to address the ambiguity in the probability distribution of demand. An equivalent reformulation is derived for this model over L 1 -norm and joint L 1 - and L ∞ -norm ambiguity sets. Additionally, a risk-averse criterion is employed to more accurately account for some of the worst realizations of random future demand scenarios. To demonstrate the proposed DRO model's practicality, a numerical analysis of COVID-19 test kit distribution in the US is carried out.

The Pasinetti Index and the Rise of Inequality in the Age of Unconventional Monetary Policy in Japan

ABSTRACT There is rising concern in Japan that unconventional monetary policy (UMP) accelerates inequality through the asset price mechanism, allowing the higher-income group to gain additional capital income. UMP has limited effectiveness in creating real wage growth and restoring demand and growth, as the overall economy has been stagnant. We revisit the issue of income inequality in Japan by using Pasinetti’s approach to measure personal income distribution and examine its effect on effective demand and functional income distribution. We implement workers’ debt-augmented Pasinetti Index (PI) as a proxy of personal income distribution, shifting from workers towards rentiers in their interpersonal lending and borrowing relations. Our empirical result with the VAR model for Japan shows that a higher PI restrains effective demand. Furthermore, higher rentier income negatively affects the wage share through decreased capacity utilization.

Impact of parameter selection on seismic loss and recovery time estimates: A variance-based sensitivity analysis

Probabilistic models in performance-based earthquake engineering propagate uncertainties from key input parameters to output performance measures. Although these models integrate important sources of uncertainty, several model parameters are deterministic and remain constant despite the difficulty in defining them with high confidence based on empirical or theoretical arguments. This study employs variance-based sensitivity analysis to investigate how uncertainty in (1) demands, (2) fragility functions, (3) building replacement consequences and (4) impeding factor delays impact seismic loss and recovery time estimates. The results indicate that the size of modeling uncertainty added to the simulated demand distribution has the most significant impact on the variance in seismic losses at all, but the highest hazard level, that is, 2475-year. At low hazard levels, that is, 100 and 475 years, the uncertainty in the capacity of structural components (e.g. slab–column connections) and nonstructural components (e.g. elevator) are the main contributors to variance in downtime to re-occupancy and functional recovery, respectively. At the 2475-year intensity level, the uncertainty in building replacement cost and replacement time becomes the primary contributor of the variance in the seismic loss and recovery time outputs due to the high probability of irreparable damage. The analyses presented in this article offer valuable insights into which parameters deserve more attention when conducting seismic loss and recovery time assessments.

"It's a good idea, but…": a qualitative evaluation of the GoldiCare intervention in Norwegian home care services.

Addressing high levels of physical strain among Norwegian home care workers is crucial if home care services are to continue to provide cost-effective and high-quality health care for people in their homes. Excessive physical demands may contribute to poor long-term musculoskeletal health and high sick leave rates among home care workers. Based on the Goldilocks Work Principle of redistributing an uneven distribution of physical demands to promote a working environment with a "just right" physical demands conducive to promoting long-term health, the GoldiCare intervention in home care services was conducted. The objective of this qualitative process evaluation study was to gain insights into how the implementation outcomes of acceptability, appropriateness, feasibility, adoption and fidelity, respectively, impacted the implementation of the GoldiCare intervention. We conducted ten individual interviews with operations managers and five focus group interviews with home care workers from the intervention units. Interviews were transcribed verbatim and a three step-content analysis was employed to analyze interview material. Our analysis identified that although the intervention was considered broadly acceptable, there were several challenges corresponding to the dimensions of appropriateness, feasibility, adoption and fidelity. Major barriers were identified in particular with regard to appropriateness, that is underlying ways of measuring physical demands; and feasibility, that is barriers to implementing the tool. Further synthesis of these findings resulted in four core issues that need to be addressed if the GoldiCare intervention is to be successfully implemented in comparable Norwegian home care settings: proxy issues; complexity and unpredictability; organization-level issues; and operational autonomy. The findings provide valuable insights for future attempts to implement GoldiCare interventions in home care settings, highlighting the need to further integrate GoldiCare and other comparable types of intervention into the political, economic, sociocultural, professional, and technological context of home care services. Performed in the right way, such integration will also allow for more participatory input from those enacting such interventions. This clinical trial was registered on 08/05/2022 under NCT05 487027.

Evaluating the Accessibility of Urban Public Open Spaces Based on an Improved 2SFCA Model: A Case Study Within Chengdu’s Second Ring Road

The rational allocation of urban public open spaces (UPOS) is critical for creating a livable urban environment. Traditional Two-Step Floating Catchment Area (2SFCA) models often lack sufficient quantitative analysis regarding the supply of urban public service facilities and population demand. This study, taking the area within Chengdu’s Second Ring Road as an example, proposes a 2SFCA model that integrates both supply and demand improvements to evaluate UPOS accessibility. The accessibility results are further analyzed using hotspot analysis, and blind zone detection. In terms of supply improvements, the model incorporates additional indicators beyond the spatial area of UPOS, including service quality and the diversity of surrounding environmental service functions, to better evaluate the overall attractiveness of UPOS to residents. On the demand side, besides population size, the model incorporates the spatial distribution of residents and differences in social characteristics affecting UPOS demand. Results indicate that the improved 2SFCA model, which considers both the attractiveness of UPOS and residents’ demand, significantly enhances the accuracy of accessibility assessments. There are substantial differences in service quality among UPOS, while the diversity of surrounding environmental service functions remains generally high. UPOS demand follows a “high in the northeast—low in the southwest” spatial pattern. The spatial distribution of UPOS accessibility shows a “high in the west—low in the east” pattern, opposite to the demand distribution, indicating a supply–demand mismatch. UPOS accessibility identifies one hotspot cluster and four cold spot clusters, with large areas showing no significant characteristics. Additionally, 10.58% of the study area remains blind zones, requiring urgent attention. This study offers a more scientific method and framework for research on the spatial layout and supply–demand matching of UPOS.

A Majority Theorem for the Uncapacitated p = 2 Median Problem and Local Spatial Autocorrelation

The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation.

Stop plan optimisation for three-pattern skip-stop schemes for urban rail transit systems

Mass rapid transit systems around the world are typically designed for all-stop operation schemes, in which train overtaking is not possible. To accelerate transit operation, the conventional A/B skip-stop scheme may be planned. This research explores alternative skip-stop schemes with three stop patterns, aiming to better match transit services with the spatial distribution of travel demand. The proposed generalised skip-stop operation model considers both the total cost of passengers and operator. A genetic algorithm is employed to solve the stop-plan optimisation problem, and a heuristic is tailored to determine an optimal dispatch headway for the respective stop plan. Based on computational experiments using synthetic data, the results suggest that skip-stop schemes have the potential to reduce total time costs by about 10%, particularly when there are structured demand concentrations, transit systems can operate safely with low time headway and short-distance demand is low. Although the total-cost saving of the best A/B skip-stop plan found is generally superior to those of other three-pattern skip-stop schemes, a three-pattern skip-stop scheme was found to offer a better total-cost saving in a scenario without short-distance travel demands. Overall, this research offers valuable insights into the potential benefits and limitations of different skip-stop schemes, contributing to a better understanding of their impact on passengers and operators.

Exploring spatiotemporal heterogeneity of urban green freight delivery parking based on new energy vehicle GPS data

To enhance the efficiency and sustainability of urban freight operations, China has initiated the Urban Green Freight Delivery (UGFD) project, which involves optimizing access control policies and introducing new energy vehicles. Identifying the parking trips of new energy vehicles and exploring the spatiotemporal patterns is crucial to actively promoting the optimal layout of temporary stops and the formulation of parking policies in the UGFD project. In this study, we aim to comprehend the spatiotemporal heterogeneity of parking for new energy vehicles both on roads (on-street) and within urban communities (off-street) for promoting the UGFD project. Its specific content includes: (1) proposing a method for identifying valid parking trips for the loading and unloading of goods based on trajectory data of UGFD new energy vehicles; and (2) mapping the identification results of valid parking trips onto communities and roads to analyze the spatiotemporal heterogeneity. Taking Suzhou, Jiangsu Province, China as an example, the identification results show that the established valid parking trips identification method can outperform state-of-the-art methods. The accuracy, precision, recall, and F1 value were found to be 0.957, 0.908, 0.937, and 0.922, respectively. Further examination of parking patterns indicates a bimodal temporal distribution of delivery demand, with peak activity occurring between 08:00–09:00 and between 14:00–17:00, with a higher delivery demand in the morning. Spatially, delivery demand was aggregated, while the parking time distribution of most delivery activities was normal. Additionally, the parking characteristics of communities and roads conformed to the ‘Rank–size rule’, suggesting that most delivery parking activities were concentrated in a few communities and roads. These findings can also be used in UGFD stop station utilization, travel time, arrival time prediction, and other related fields, all of which can further support relevant management departments in discovering abnormal delivery behaviors and reduce their negative impacts.

A data-driven newsvendor model with unknown demand and supply distribution

A data-driven newsvendor model with unknown demand and supply distribution

Use of the Baidu Index to Analyze Spatiotemporal Characteristics of Online Attention to Adult Education

Purpose: This study aims to analyze the spatiotemporal evolution of public attention to "adult education" over the past decade. Methods: Using Baidu Index data from January 1, 2014, to November 1, 2024, we examined search trends, demand distribution, and user characteristics through trend research, demand mapping, and user profiling. Results: The online search index for adult education shows a fluctuating upward trend, with peaks in April and October each year. Demand mapping indicates interest in areas such as adult college entrance exams, self-study exams, educational institutions, exam schedules, registration, major selection, tuition, and application procedures. User profiling reveals higher attention from males aged 30~39 in Guangdong Province. Conclusion: Changes in online attention to adult education correlate closely with career aspirations, policy announcements, and social contexts.

Spatiotemporal dynamic and regional differences of public attention to vaccination: An empirical study in China

Background Internet searches offer an indicator of public attention and possible demand for certain things. Studying the spatiotemporal characteristics of the public’s concern for vaccination can determine the spatiotemporal distribution of demand for vaccines in China, and capture the changes in the health awareness of the Chinese population, thus informing future vaccination strategies. Methods Based on the collection of Baidu search indices for vaccination-related keywords in 363 cities in China, This paper seeks to explore the spatiotemporal changes and regional differences in public attention toward vaccination in China by using the seasonal index, seasonal concentration index, Herfindahl index, Moran index, and Dagum Gini coefficient. Results The following findings are presented. First, there are significant seasonal fluctuations and unbalanced monthly distributions of vaccination-related public attention in China. Second, the public attention in Chinese cities shows the spatial characteristics of "leading in the east, followed by the central, western and northeastern regions". The spatial correlation of attention has been strengthened, and the high-high clusters are mainly distributed in the Beijing-Tianjin-Hebei (BTH), Yangtze River Delta (YRD), and Greater Bay Area (GBA) urban agglomerations. Third, regional differences in overall public attention narrowed in China, with intra-regional differences narrowing in seven regions (Northwest China, Central China, and so on), and intra-regional differences increasing in East China. The dominant role in the Gini coefficient changes from transvariation intensity to inter-regional differences. Conclusion Major public health emergencies stimulate the public’s attention to health topics. Although the short-term increase in vaccination-related public attention was not observed to translate into a long-term increase in public vaccine literacy, the seasonal and regional differences in vaccination-related public attention in China have significantly narrowed before and after COVID-19, suggesting that the imbalance between public health literacy levels has improved.

Is Transparency Good in a Supply Chain? The Downside of Information Acquisition Transparency

ABSTRACTIn the supply chain, retailers usually have inherent advantages over manufacturers in obtaining demand information because they are closer to the final market and can directly interact with consumers. However, manufacturers cannot make sure whether their retailers have obtained extra demand information. The retailer's information acquisition state is also an important aspect of information asymmetry among supply chain participants, besides the demand information itself. We examine two modes observed in practice regarding the transparency of the retailer's information acquisition state: non‐transparency and full transparency. By incorporating a manufacturer's information belief adjustment strategy, our study thus addresses a retailer's acquisition and ex‐post sharing of information (i.e., the decision on how to share acquired information) under the two transparency modes. The main findings show that under the non‐transparency mode, the retailer shares low‐demand information but hides high‐demand information. With respect to the interim profit (i.e., after the acquisition cost is realized), the preferences of the manufacturer, retailer, and supply chain on the two modes depend on the information acquisition cost. With respect to the ex‐ante profit (i.e., before acquisition cost is realized), surprisingly, the manufacturer and supply chain always prefer the non‐transparency mode, whereas the retailer's preference for the two modes still depends on the acquisition cost. In addition, our equilibrium outcome reveals that the retailer and the manufacturer will never sign an internal information sharing agreement (i.e., never achieve the full transparency mode), whether before or after the realization of information acquisition cost. We also find that the expected consumer surplus under the non‐transparency mode is always higher than that under the full transparency mode, which is also a counterintuitive outcome. Finally, our main findings in the core model are relatively robust when considering acquisition cost sharing, general demand distribution, general acquisition cost distribution, ex‐ante informed retailer, and imperfect information acquisition.

Demand Forecasting Model for Airline Flights Based on Historical Passenger Flow Data

This paper addresses the problem of estimating passenger demand for flights, with a particular focus on the necessity of developing precise forecasts that incorporate intricate and interdependent variables for effective resource planning within the air transport industry. The present paper focuses on the development of a model for medium-term flight demand estimation by flight destinations. This is based on the analysis of historical airline data on dates, departure times, and passenger demand, as well as the consideration of the influence of macroeconomic indicators, namely gross regional product (GRP), median per capita income, and population of departure and arrival points. This paper reviews international experience in the development of demand forecasting models and their use for resource planning in the industry. The developed model was evaluated using historical data on demand for a single turnaround flight operated by an airline. The developed model allows for the forecasting of the distribution of potential demand for airline flight destinations in the medium term, utilizing comprehensive historical data on departure times and flight demand by destination.

Capacity, Volume Flexibility, and Costs

This paper studies strategic firms' capacity choices in the presence of demand uncertainty and imperfect downside and upside volume flexibility. It provides conditions under which firms' capacity is greater or less than their expected output. It shows under certain conditions, a first-order stochastically dominant demand distribution induces higher capacity, while a mean-preserving spread of a demand distribution induces lower capacity. By endogenizing volume flexibility, it shows that firms' downside flexibility tends to be lower than their upside flexibility. This implies a firm's short-run average cost tends to be asymmetrically U-shaped, namely, the average cost increases more when output falls below capacity (the efficient scale) than when output rises above capacity by an equivalent amount.