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We consider parallel-machine job scheduling problems with precedence constraints. Job processing times are variable and depend on positions of jobs in a schedule. The objective is to minimize the maximum completion time or the total weighted completion time. We specify certain conditions under which the problem can be solved by scheduling algorithms applied earlier for fixed job processing times.

This study addresses the social impact of the popularity of recreational running (called: running boom). Four dimensions are classified: (1) economic, (2) health and psychological well-being, (3) environmental and (4) social (in narrow sense). The first three of these were included in the analysis performed. The analysis relates to Polish society in 2018 and is based on a thought experiment assuming that 3.4 million recreational runners engage in leisure activities as passive and indifferent to their surroundings as possible instead of running. What economic, health, and environmental consequences would this have? The interdisciplinary analysis uses and combines existing scientific findings. The economic effects of the running boom include at least PLN 1.7 billion spent annually on the purchase of running equipment (not including effects related to employee health, development of running tourism, etc.). The health effects include at least a 30% reduction in the risk of death in the next 15 years for the population of runners. Finally, the carbon footprint of Polish amateur runners can be estimated at 2.9 million tons of CO2.

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