We consider on-line scheduling of unit time jobs on a single machine with job-dependent penalties. The jobs arrive on-line (one by one) and can be either accepted and scheduled, or be rejected at the cost of a penalty. The objective is to minimize the total completion time of the accepted jobs plus the sum of the penalties of the rejected jobs. We give an on-line algorithm for this problem with...

In this paper we consider an important order completion, the rounded-ideal completion, that has arisen in the modern theory of continuous domains. We show that it can be alternately viewed as a special case of a more general topo­ logical method of completion, namely taking the sobrification of a topological space. A number of important special caSes and examples are in­ cluded.

We consider a single machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time and the machine is subject to an availability constraint. We consider the non-resumable case. The objectives are to minimize the makespan and the total completion time. We show that both problems are NP-hard and present pseudo-polynomial time optimal ...

We study academic integrity in a final exam of compulsory course with almost 500 undergraduate students at major Spanish university. Confinement and university closure due to Covid-19 took place by the end last lecture week. As consequence, usual classroom was turned into an unproctored on-line multiple-choice without backtracking. exploit different orders problems detailed data timestamps stud...