No abstract

Water distribution systems (WDSs) require high-quality water for safe consumption. To achieve this, disinfectants such as chlorine are often added to the water in the system. However, it is important to regulate the levels of chlorine to ensure they fall within acceptable limits. The higher limit is to control disinfection by-products, while the lower limit is established to guarantee that the water is free of organic contaminants. The rate at which chlorine reacts within the pipes is affected by various factors, such as the type of pipe, its age, the pH level of the water, the temperature, and others. This variability makes it challenging to accurately model water quality in WDSs, which can impact the optimal rate of booster injection. To address the uncertainty in the chlorine reaction rate, the current research proposes a robust counterpart reformulation of the booster chlorination scheduling problem, which considers the chlorination reaction rate as uncertain. The proposed reformulation was tested on two benchmark WDSs and analyzed with a thorough sensitivity analysis. The results showed that as the size of the uncertainty set increased, the injection mass also increased. This reformulated approach can be applied to any WDS and provides a way to obtain optimal scheduling within the desired protection levels.

No abstract

No abstract

We consider the non-preemptive scheduling problem on identical machines where there is a parameter B and each machine in every unit length time interval can process up to B different jobs. The goal function we consider is the makespan minimization and we develop an EPTAS for this problem. Prior to our work a PTAS was known only for the case of one machine and constant values of B, and even the case of non-constant values of B on one machine was not known to admit a PTAS.