Consumer Value-Maximizing Sweepstakes & Contests: A Theoretical and Experimental Investigation

Sweepstakes and contests are an extremely common promotional strategy used by firms. The sweepstakes and contests often differ significantly in the design of reward structure. For example, in 1999, Godiva Chocolates conducted a sweepstakes where one box of chocolates contained a diamond jewellery. The chance of winning was 1 in 320,000. In 2000, M&M conducted a contest where the Grand Prize of a 1,000,000 had winning odds of 1 in 380,000,000 and a million second prizes of a coupon redeemable for a M&M packet had the odds of 1 in 380. In a contest conducted by Planters in 2000, the first prize too was a 1 m (odds 1 in 5,000,000) but there were only 100 second prizes of a NFL football jacket with odds of 1 in 50,000. In 1999, Old Navy conducted a sweepstake where there were 4,552 first prize winners who got $100 gift cards with the odds of winning 1 in 1,000, the 9,105 second prize of$ 20 gift certificates had odds of 1 in 500 and the 13,660 third prizes of $10 certificates and 883,476 fourth prizes of$5 had winning odds of 1 in 333 and 1 in 50 respectively. These examples raise the issue of how reward structure would affect consumer valuation and participation. The objective of this paper is to obtain an understanding of how consumers' valuation of sweepstakes varies on the basis of differing consumer segments and the characteristics of the consumers. Our paper focuses on the decisions pertaining to the reward structure. We examine some commonly used sweepstakes and provide insights on how consumer valuations depend on the number of winners, the number of levels of prizes, and the difference in the awards between the levels (reward spread). We follow the Cumulative Prospect Theory to develop a model for consumer valuations of alternative formats of sweepstakes. The model applies a S-shaped probability weighting function and a loss-aversion framework for the consumers who switched to less preferred brands for sweepstakes but eventually did not win any prizes. We analytically derive our theoretical results and experimentally test some of the key implications. The results of the model show that the sweepstakes reward structure should be based on three factors: the objectives of the firm, the risk aversion of the customers, and the level of sub-additivity of probability weighting. The results of the model prescribes that the firm should begin by setting sweepstake objectives in terms of either attracting switchers or targeting current users. If the objective is to target current users, then the number of prizes awarded should be lower than in the case where the targets are switchers. If the current users are risk neutral, then the consumer value-maximizing award is a single grand prize. If the current users are risk averse, then the award should consist of multiple "large" prizes. When the firm's objective is to draw sales away from competitors, the value-maximizing strategy is to distribute the award money over more prizes. If the non-current user segment is risk neutral with respect to gains but sufficiently risk averse in the domain of losses, then the prescribed reward structure is to have a single grand prize but also include several small prizes which ideally should be close to the opportunity cost of the customers. If the non-loyal customers are risk averse in gain and loss averse, then the best prize allocation is to have both multiple large prizes as well as several small prizes.Another recommendation from the model analysis is that the firm should minimize the number of prizes at each level. In practice, the costs of implementing and communicating such a prize structure could be high. To trade-off between the logistical and communication costs and the theoretically value-maximizing approach, firms could increase the number of prizes at each level for easier implementation. A trade-off is involved between increasing the attractiveness of the sweepstake and the implementation costs of administering several levels of prizes. Often, when the prizes are products rather than cash, the firm may obtain quantity discounts for the products but the value of the products will be the same for the sweepstake participants.Sales promotion, prospect theory, customer loyalty ,

A Conceptualized Groundwater Flow Model Development for Integration with Surface Hydrology Model

A groundwater system model was developed and calibrated in the study area of Lehman Creek watershed, eastern Nevada. The model development aims for integrating the surface hydrologic model - precipitation runoff modeling system (PRMS) model - with the three-dimensional (3D) finite-difference model MODFLOW. A two-layer groundwater model was developed with spatial discretization of 100 x 100 m grid. The water balance was estimated with inflows of gravity drainage and initial streamflow estimated from a calibrated PRMS model, and with outflows of spring discharges, boundary fluxes, and stream base flow. A steady-state model calibration was performed to estimate the hydraulic properties. The modeling results were able to represent the geographic relieves, simulate water balance components, and capture the hydrogeologic features. The preliminary results presented in this study provide insights into the local groundwater flow system and lay groundwork for future study of interactive influences of surface hydrologic variation

A Conceptual Framework for Integration Development of GSFLOW Model: Concerns and Issues Identified and Addressed for Model Development Efficiency

In Coupled Groundwater and Surface-Water Flow (GSFLOW) model, the three-dimensional finite-difference groundwater model (MODFLOW) plays a critical role of groundwater flow simulation, together with which the Precipitation-Runoff Modeling System (PRMS) simulates the surface hydrologic processes. While the model development of each individual PRMS and MODFLOW model requires tremendous time and efforts, further integration development of these two models exerts additional concerns and issues due to different simulation realm, data communication, and computation algorithms. To address these concerns and issues in GSFLOW, the present paper proposes a conceptual framework from perspectives of: Model Conceptualization, Data Linkages and Transference, Model Calibration, and Sensitivity Analysis. As a demonstration, a MODFLOW groundwater flow system was developed and coupled with the PRMS model in the Lehman Creek watershed, eastern Nevada, resulting in a smooth and efficient integration as the hydrogeologic features were well captured and represented. The proposed conceptual integration framework with techniques and concerns identified substantially improves GSFLOW model development efficiency and help better model result interpretations. This may also find applications in other integrated hydrologic modelings

Relationship between Ocean-Atmospheric Climate Variables and Regional Streamflow of the Conterminous United States

Understanding the interconnections between oceanic-atmospheric climate variables and regional streamflow of the conterminous United States may aid in improving regional long lead-time streamflow forecasting. The current research evaluates the time-lagged relationship between streamflow of six geographical regions defined from National Climate Assessment and sea surface temperature (SST), 500-mbar geopotential height (Z500), 500-mbar specific humidity (SH500), and 500-mbar east-west wind (U500) of the Pacific and the Atlantic Ocean using singular value decomposition (SVD). The spatio-temporal correlation between streamflow and SST was developed first from SVD and thus obtained correlation was later associated with Z500, SH500, and U500 separately to evaluate the coupled interconnections between the climate variables. Furthermore, the associations between regional streamflow and the El Niño Southern Oscillation (ENSO), Pacific Decadal Oscillation, and Atlantic Multidecadal Oscillation were evaluated using the derivatives of continuous wavelet transform. Regional SVD analysis revealed significant teleconnection between several regions and climate variables. The warm phase of equatorial SST had shown a stronger correlation with the majority of streamflow. Both SVD and wavelet analyses concluded that the streamflow variability of the regions in close proximity to the Pacific Ocean was strongly associated with the ENSO. Improved knowledge of teleconnection of climate variables with regional streamflow variability may help in regional water management and streamflow prediction studies

Ice-Cover and Jamming Effects on Inline Structures and Upstream Water Levels

River ice cover is a reoccurring phenomenon in the Northern United States every year. Sheets and layers of ice result in a rise of water surface elevation and may lead to ice jams in a river. This research explains the modeling of a river reach through Northern Illinois containing a structural weir and how the water profile is effected during ice cover and ice jam events. The Hydraulic Engineering Center’s River Analysis System was used in conjunction with Esri ArcMap software to model a portion of the river for analysis. The study area of the Rock River flowing through Oregon, IL is known to freeze and ice over during the winter months in Northern Illinois. Data from the United States Geological Survey and National Oceanic and Atmospheric Administration were utilized to obtain cross-section and discharge measurements. The impacts of an ice jam occurring upstream of the weir and downstream of the weir were studied. The effects of the ice jam on the upstream water levels were also evaluated to observe if any flooding may occur inside the town or even farther upstream. Results of the ice cover and ice jam data were then compared to those of the Rock River under normal open flow conditions thus observing the change in water level, Froude number, and flow velocity. Results from this study help to point out the significance of ice jam occurrences and their effects on inline structures and future flooding concerns in the surrounding area

Management of an Urban Stormwater System Using Projected Future Scenarios of Climate Models: A Watershed-Based Modeling Approach

Anticipating a proper management needs for urban stormwater due to climate change is becoming a critical concern to water resources managers. In an effort to identify best management practices and understand the probable future climate scenarios, this study used high-resolution climate model data in conjunction with advanced statistical methods and computer simulation. Climate model data from the North American Regional Climate Change Assessment Program (NARCCAP) were used to calculate the design storm depths for the Gowan Watershed of Las Vegas Valley, Nevada. The Storm Water Management Model (SWMM), developed by the Environmental Protection Agency (EPA), was used for hydrological modeling. Two low-impact development techniques – Permeable Pavement and Green Roof – were implemented in the EPA SWMM hydrological modeling to attenuate excess surface runoff that was induced by climate change. The method adopted in this study was effective in mitigating the challenges in managing changes in urban stormwater amounts due to climate change

Evaluating changes and estimating seasonal precipitation for Colorado River Basin using stochastic non-parametric disaggregation technique

Precipitation estimation is an important and challenging task in hydrology because of high variability and changing climate. This research involves (1) analyzing changes (trend and step) in seasonal precipitation and (2) estimating seasonal precipitation by disaggregating water year precipitation using a k-nearest neighbor (KNN) nonparametric technique for 29 climate divisions encompassing the Colorado River Basin. Water year precipitation data from 1900 to 2008 are subdivided into four seasons (i.e., autumn, winter, spring, and summer). Two statistical tests (Mann-Kendall and Spearman’s rho) are used to evaluate trend changes, and a rank sum test is used to identify the step change in seasonal precipitation. The results indicate a decrease in the upper basin and an increase in the lower basin winter precipitation resulting from an abrupt step change. The effect of El Niño–Southern Oscillations in relation to seasonal precipitation is also evaluated by removing the historic El Niño events. Decreasing winter and spring season precipitation trends for the upper basin are not linked to El Niño. Corroborating evidence of changes in seasonal precipitation is established by analyzing the trends in snow telemetry (SNOTEL) data and streamflow at the Lees Ferry gauge. KNN disaggregation results indicate satisfactory seasonal precipitation estimates during winter and spring seasons compared to autumn and summer seasons, and the superiority of KNN results is established when compared with the first-order periodic autoregressive parametric approach. The analysis of seasonal changes and estimates of precipitation can help water managers to better manage the water resources in the Colorado River Basin

Estimating annual precipitation for the Colorado River Basin using oceanic-atmospheric oscillations

Estimating long-lead time precipitation under the stress of increased climatic variability is a challenging task in the field of hydrology. A modified Support Vector Machine (SVM) based framework is proposed to estimate annual precipitation using oceanic-atmospheric oscillations. Oceanic-atmospheric oscillations, consisting of Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), Atlantic Multidecadal Oscillation (AMO), and El Niño–Southern Oscillation (ENSO) for a period of 1900–2008, are used to generate annual precipitation estimates with a 1 year lead time. The SVM model is applied to 17 climate divisions encompassing the Colorado River Basin in the western United States. The overall results revealed that the annual precipitation in the Colorado River Basin is significantly influenced by oceanic-atmospheric oscillations. The long-term precipitation predictions for the Upper Colorado River Basin can be successfully obtained using a combination of PDO, NAO, and AMO indices, whereas coupling AMO and ENSO results in improved precipitation predictions for the Lower Colorado River Basin. The results also show that the SVM model provides better precipitation estimates compared to the Artificial Neural Network and Multivariate Linear Regression models. The annual precipitation estimates obtained using the modified SVM modeling framework may assist water managers in statistically understanding the hydrologic response in relation to large scale climate patterns within the Colorado River Basin

Modeling of GRACE-Derived Groundwater Information in the Colorado River Basin

Groundwater depletion has been one of the major challenges in recent years. Analysis of groundwater levels can be beneficial for groundwater management. The National Aeronautics and Space Administration’s twin satellite, Gravity Recovery and Climate Experiment (GRACE), serves in monitoring terrestrial water storage. Increasing freshwater demand amidst recent drought (2000–2014) posed a significant groundwater level decline within the Colorado River Basin (CRB). In the current study, a non-parametric technique was utilized to analyze historical groundwater variability. Additionally, a stochastic Autoregressive Integrated Moving Average (ARIMA) model was developed and tested to forecast the GRACE-derived groundwater anomalies within the CRB. The ARIMA model was trained with the GRACE data from January 2003 to December of 2013 and validated with GRACE data from January 2014 to December of 2016. Groundwater anomaly from January 2017 to December of 2019 was forecasted with the tested model. Autocorrelation and partial autocorrelation plots were drawn to identify and construct the seasonal ARIMA models. ARIMA order for each grid was evaluated based on Akaike’s and Bayesian information criterion. The error analysis showed the reasonable numerical accuracy of selected seasonal ARIMA models. The proposed models can be used to forecast groundwater variability for sustainable groundwater planning and management

Using Wavelet to Analyze Periodicities in Hydrologic Variables

The trend and shift in the seasonal temperature, precipitation and streamflow time series across the Midwest have been analyzed, for the period 1960-2013, using the statistical analyses (Mann- Kendall test with and without considering short term persistence (MK2 and MK1, respectively) and Pettitt test). The paper also utilizes a relatively new approach, wavelet analysis, for testing the existence of trend and shift in the time series. The method has the ability to decompose a time series in to lower (trend) and higher frequency components (noise). Discrete wavelet transform (DWT) has been employed in the present study with an aim to find which periodicities are mainly responsible for trend in the original data. The combination of MK1, MK2, and DWT along with Pettitt test hasn’t been extensively used up to this time, especially in detecting trend and shift in the Midwest. The analysis of climate division temperature and precipitation data and USGS naturalized streamflow data revealed the presence of periodicity in the time series data. All the incorporated time series data were seasonal to analyze the trends and shifts for four seasons-winter, spring, summer and fall independently. D3 component of DWT were observed to be influential in detecting real trend in temperature, precipitation and streamflow data, however unlike temperature, precipitation and streamflow showed decreasing trend as well. Shift was relatively observed more than trend in the region with dominance of D3 component in the data. The result indicate the significant warming trend which agrees with the “increasing temperature” observations in the past two decades, however a clear explanation for precipitation and streamflow is not obvious