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In the single-processor scheduling problem with time restrictions there is one main processor and B resources that are used to execute the jobs. A perfect schedule has no idle times or gaps on the main processor and the makespan is therefore equal to the sum of the processing times. In general, more resources result in smaller makespans, and as it is in practical applications often more economic not to mobilize resources that will be unnecessary and expensive, we investigate in this paper the problem to find the smallest number B of resources that make a perfect schedule possible. We show that the decision version of this problem is NP-complete, derive new structural properties of perfect schedules, and we describe a Mixed Integer Linear Programming (MIP) formulation to solve the problem. A large number of computational tests show that (for our randomly chosen problem instances) only B=3 or B=4 resources are sufficient for a perfect schedule.
Research integrity (RI) has been a focus of society in recent years as a means to create and to keep trust in science. Higher education institutions (HEIs) play a key role in promoting a culture of RI and responsible conduct of research (RCR). The understanding and practice of RI can vary across cultures. This article aims to outline initial insights into university students’ RI mindsets based on five RI facets: understanding, importance, value-action gap, enforcement approaches, and training. A qualitative exploratory cross-cultural study was conducted with participants from Germany and Bulgaria via semi-structured guided group interviews. An explicit transcultural agreement regarding the significance of RI was categorically indicated. Intercultural differences between the two European countries were revealed and discussed in reference to understanding RI, the value-action gap, enforcement approaches, and training preferences.