Algorithm for optimal allocation of a continuous resource varying over time

2014 ◽  
Author(s):  
Marek Mika ◽  
Rafal Rozycki ◽  
Grzegorz Waligora
Keyword(s):  
Optimal Allocation ◽  
Over Time

Intertemporal Content Variation with Customer Learning

2021 ◽  
Author(s):  
Fernando Bernstein ◽  
Soudipta Chakraborty ◽  
Robert Swinney
Keyword(s):  
Lower Bound ◽  
Dynamic Pricing ◽  
Business Models ◽  
Optimal Allocation ◽  
Planning Horizon ◽  
Problem Definition ◽  
Allocation Policy ◽  
Content Variation ◽  
Managerial Implications ◽  
Over Time

Problem definition: We analyze a firm that sells repeatedly to a customer population over multiple periods. Although this setting has been studied extensively in the context of dynamic pricing—selling the same product in each period at a varying price—we consider intertemporal content variation, wherein the price is the same in every period, but the firm varies the content available over time. Customers learn their utility on purchasing and decide whether to purchase again in subsequent periods. The firm faces a budget for the total amount of content available during a finite planning horizon, and allocates content to maximize revenue. Academic/practical relevance: A number of new business models, including video streaming services and curated subscription boxes, face the situation we model. Our results show how such firms can use content variation to increase their revenues. Methodology: We employ an analytical model in which customers decide to purchase in multiple successive periods and a firm determines a content allocation policy to maximize revenue. Results: Using a lower bound approximation to the problem for a horizon of general length T, we show that, although the optimal allocation policy is not, in general, constant over time, it is monotone: content value increases over time if customer heterogeneity is low and decreases otherwise. We demonstrate that the optimal policy for this lower bound problem is either optimal or very close to optimal for the general T period problem. Furthermore, for the case of T = 2 periods, we show how two critical factors—the fraction of “new” versus “repeat” customers in the population and the size of the content budget—affect the optimal allocation policy and the importance of varying content value over time. Managerial implications: We show how firms that sell at a fixed price over multiple periods can vary content value over time to increase revenues.

EXPRESS: A New Livestream Retail Analytics Framework to Assess the Sales Impact of Emotional Displays

2021 ◽  
pp. 002224292110130
Author(s):  
Neeraj Bharadwaj ◽  
Michel Ballings ◽  
Prasad A. Naik ◽  
Miller Moore ◽  
Mustafa Murat Arat
Keyword(s):  
Closed Form ◽  
Optimal Allocation ◽  
Performance Appraisals ◽  
Emotional Displays ◽  
Emotional Display ◽  
Managerial Implications ◽  
Over Time ◽  
Retail Analytics

At the intersection of technology and marketing, the authors develop a framework to unobtrusively detect salespersons’ faces and simultaneously extract six emotions: happiness, sadness, surprise, anger, fear, and disgust. They analyze 99,451 sales pitches on a livestream retailing platform and match them with actual sales transactions. Results reveal that each emotional display, including happiness, uniformly exhibits a negative U-shaped effect on sales over time. The maximum sales resistance appears in the middle rather than at the beginning or the end of sales pitches. Taken together, in one-to-many screen-mediated communications, salespersons should sell with a straight face. In addition, the authors derive closed-form formulae for the optimal allocation of the presence of a face and emotional displays over the presentation span. In contrast to the U-shaped effects, the optimal face presence wanes at the start, gradually builds to a crescendo, and eventually ebbs. Finally, they show how to objectively rank salespeople and circumvent biases in performance appraisals, thereby making novel contributions to people analytics. This research integrates new types of data and methods, key theoretical insights, and important managerial implications to inform the expanding opportunity that livestreaming presents to marketers to create, communicate, deliver, and capture value.

Variation in mass and nutrient concentration of leaf litter across years and sites in a northern hardwood forest

2012 ◽  
Vol 42 (8) ◽  
pp. 1597-1610 ◽  
Author(s):  
Ruth D. Yanai ◽  
Mary A. Arthur ◽  
Marty Acker ◽  
Carrie R. Levine ◽  
Byung Bae Park
Keyword(s):  
Leaf Litter ◽  
Nutrient Concentration ◽  
Optimal Allocation ◽  
Research Effort ◽  
Phosphorus Concentration ◽  
Nutrient Analysis ◽  
Northern Hardwood ◽  
Leaf Litterfall ◽  
Species Specific ◽  
Over Time

Leaf litterfall represents an important nutrient flux in forests, but separating leaves by species and collecting fresh litter annually for nutrient analysis is time-consuming and expensive. To quantify the sources of variation in litterfall nutrient estimates and guide optimal allocation of research effort, we analyzed nutrient concentration (5 years) and mass (6 years) of leaf litter for nine tree species in 13 northern hardwood sites. Coefficients of variation (CVs) in nutrient concentration were higher across sites than over time within sites for most elements; phosphorus was especially variable across sites (56% CV). Thus, to estimate litterfall nutrient fluxes accurately in forests of this type, nutrient analyses should be site-specific as well as species-specific but may not need to be repeated annually (CVs over time averaged 17% for calcium, 21% for magnesium, 28% for potassium, and 32% for phosphorus concentration). Total leaf litterfall mass varied considerably from year to year, ranging from 234 to 370 g·m–2 averaged over 13 sites. We recommend that litter collectors be elevated above the ground to avoid oversampling during extreme wind events. Use of species-specific allometric equations, or even basal area, to estimate the species composition of total litter mass may obviate the need to sort litter by species.

Social transmission bias and the cultural evolution of folk-economic beliefs

2018 ◽  
Vol 41 ◽  
Author(s):  
David Hirshleifer ◽  
Siew Hong Teoh
Keyword(s):  
Cultural Evolution ◽  
Social Transmission ◽  
Cognitive Approach ◽  
Economic Problems ◽  
Economic Attitudes ◽  
The Social ◽  
Economic Beliefs ◽  
Over Time

AbstractEvolved dispositions influence, but do not determine, how people think about economic problems. The evolutionary cognitive approach offers important insights but underweights the social transmission of ideas as a level of explanation. The need for asocialexplanation for the evolution of economic attitudes is evidenced, for example, by immense variations in folk-economic beliefs over time and across individuals.

Articulatory Generalization in Two Word-Medial, Ambisyllabic Contexts

1988 ◽  
Vol 19 (3) ◽  
pp. 251-258 ◽  
Author(s):  
Virginia I. Wolfe ◽  
Suzanne D. Blocker ◽  
Norma J. Prater
Keyword(s):  
Common View ◽  
Perceptual Salience ◽  
The Common ◽  
Unitary Concept ◽  
Over Time

Articulatory generalization of velar cognates /k/, /g/ in two phonologically disordered children was studied over time as a function of sequential word-morpheme position training. Although patterns of contextual acquisition differed, correct responses to the word-medial, inflected context (e.g., "picking," "hugging") occurred earlier and exceeded those to the word-medial, noninflected context (e.g., "bacon," "wagon"). This finding indicates that the common view of the word-medial position as a unitary concept is an oversimplification. Possible explanations for superior generalization to the word-medial, inflected position are discussed in terms of coarticulation, perceptual salience, and the representational integrity of the word.

Treatment Fidelity Procedures for an Aphasia Intervention Within a Randomized Controlled Trial: Design, Feasibility, and Results

2020 ◽  
Vol 29 (1S) ◽  
pp. 412-424
Author(s):  
Elissa L. Conlon ◽  
Emily J. Braun ◽  
Edna M. Babbitt ◽  
Leora R. Cherney
Keyword(s):  
Randomized Controlled Trial ◽  
Controlled Trial ◽  
Treatment Protocol ◽  
Treatment Fidelity ◽  
Protocol Adherence ◽  
Study Condition ◽  
Randomized Controlled ◽  
Aphasia Therapy ◽  
Percent Accuracy ◽  
Over Time

Purpose This study reports on the treatment fidelity procedures implemented during a 5-year randomized controlled trial comparing intensive and distributed comprehensive aphasia therapy. Specifically, the results of 1 treatment, verb network strengthening treatment (VNeST), are examined. Method Eight participants were recruited for each of 7 consecutive cohorts for a total of 56 participants. Participants completed 60 hr of aphasia therapy, including 15 hr of VNeST. Two experienced speech-language pathologists delivered the treatment. To promote treatment fidelity, the study team developed a detailed manual of procedures and fidelity checklists, completed role plays to standardize treatment administration, and video-recorded all treatment sessions for review. To assess protocol adherence during treatment delivery, trained research assistants not involved in the treatment reviewed video recordings of a subset of randomly selected VNeST treatment sessions and completed the fidelity checklists. This process was completed for 32 participants representing 2 early cohorts and 2 later cohorts, which allowed for measurement of protocol adherence over time. Percent accuracy of protocol adherence was calculated across clinicians, cohorts, and study condition (intensive vs. distributed therapy). Results The fidelity procedures were sufficient to promote and verify a high level of adherence to the treatment protocol across clinicians, cohorts, and study condition. Conclusion Treatment fidelity strategies and monitoring are feasible when incorporated into the study design. Treatment fidelity monitoring should be completed at regular intervals during the course of a study to ensure that high levels of protocol adherence are maintained over time and across conditions.

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