Pre-emptive scheduling problems with controllable processing times

We consider a range of single machine and identical parallel machine pre-emptive scheduling models with controllable processing times. For each model we study a single criterion problem to minimize the compression cost of the processing times subject to the constraint that all due dates should be met. We demonstrate that each single criterion problem can be formulated in terms of minimizing a linear function over a polymatroid, and this justifies the greedy approach to its solution. A unified technique allows us to develop fast algorithms for solving both single criterion problems and bicriteria counterparts.

The use of a mathematical multicriteria decision-making model for selecting the fire origin room

Over the last three decades, the fire safety codes have been changing from a prescriptive approach to a performance-based one. Some countries, such as the USA, Sweden, New Zealand, Australia and the UK, are in an advanced stage of development and implementation of the performance-based codes. However, there are some difficulties in this process. Most of them are due to the uncertainties associated with fire design. For instance, one of the questions that need to be answered is how to select the most probable fire origin room (FOR)? On the other hand, to know where the FOR is located is also an important aspect in terms of forensic issues. Given that, to address this question is an important step for the establishment of fire designs (i.e., pre-fire phases) and also for fire investigations (i.e., post-fire phases). This paper proposes a methodology for selecting the FOR through the use of a mathematical multicriteria decision-making model: the analytical hierarchy process (AHP). The proposed method is then applied to a hypothetical study case. The results are presented and discussed in this paper.