Optimal allocation of stratified samples with several variance constraints and equal workloads over time by geometric programming

1989 ◽  
Vol 18 (4) ◽  
pp. 1507-1520
Author(s):  
Miles Davis ◽  
Robert H. Finch
Author(s):  
Fernando Bernstein ◽  
Soudipta Chakraborty ◽  
Robert Swinney

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.


2021 ◽  
pp. 002224292110130
Author(s):  
Neeraj Bharadwaj ◽  
Michel Ballings ◽  
Prasad A. Naik ◽  
Miller Moore ◽  
Mustafa Murat Arat

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.


2012 ◽  
Vol 42 (8) ◽  
pp. 1597-1610 ◽  
Author(s):  
Ruth D. Yanai ◽  
Mary A. Arthur ◽  
Marty Acker ◽  
Carrie R. Levine ◽  
Byung Bae Park

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.


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