This paper investigated a multistage sustainable production–inventory model for deteriorating items (i.e., raw materials and finished goods) with price-dependent demand and collaborative carbon reduction technology investment under carbon tax regulation. The model was developed by first defining the total profit of the supply chain members under carbon tax regulation and, second, considering a manufacturer (leader)–retailer (follower) Stackelberg game. The optimal equilibrium solutions that maximize the manufacturer’s and retailer’s total profits were determined through the method analysis. An algorithm complemented the model to determine the optimal equilibrium solutions, which were then treated with sensitivity analyses for the major parameters. Based on the numerical analysis, (a) carbon tax policies help reduce carbon emissions for both the manufacturer and retailer; (b) most carbon emissions from supply chain operations negatively impact the total profits of both members; (c) the retailer may increase the optimal equilibrium selling price to respond to an increase in carbon emissions from supply chain operations or carbon tax; and (d) autonomous consumption positively affects both members’ optimal equilibrium policies and total profits, whereas induced consumption does the opposite. These findings are very managerial and instructive for companies seeking profits and fulfilling environmental responsibility and governments.

Background: The relationship between sleep duration and physical fitness is one aspect of sleep health. Potential factors associated with sleep duration interfere with physical fitness performance, but the impact trends on physical fitness indicators remain unclear. Methods: This study examined associations between sleep duration and physical fitness among young to middle-aged adults in Taiwan. A total of 42,781 Taiwanese adults aged 23–45 participated in the National Physical Fitness Examination Survey 2013 (NPFES-2013) in Taiwan between October 2013 and March 2014. A standardized structural questionnaire was used to record participants’ sleep duration, which was stratified as short (< 6 h/day (h/d)), moderate (6–7 h/d; 7–8 h/d; 8-9 h), and long (≥ 9 h/d) sleep duration groups. Physical fitness was assessed based on four components: body composition (body mass index [BMI], waist-to-height ratio [WHtR], and waist-to-hip ratio [WHR]), muscle strength and endurance (1-min bent-leg sit-up test [BS]), flexibility (sit-and-reach test [SR]), and cardiorespiratory endurance index (3-min step test [CEI]). Results: By using analysis of covariance (ANCOVA), after sex grouping and age adjustment, we observed that sleep duration was significantly associated with obesity, functional fitness, and self-perception of health. The sleep duration for low obesity-related values (BMI, WHtR, and WHR) for men was 7–9 h/d, and that for women was 7–8 h/d. Sleeping more than 8 h/d showed poor functional fitness performances (BS and SR). For both sexes, sleep duration of 8–9 h/d was the optimal sleep duration for self-perceptions of health. Conclusions: Our research found that there were wide and different associations of sleep duration with physical fitness and self-perception of health among Taiwanese adults aged 23–45, and there were differences in these associated manifestations between men and women. This study could be of great importance in regional public health management in Taiwan, and provide inspirations for clinical research on physical fitness.