We study a single machine scheduling problem with batch setup time and batch delivery cost. In this problem, n jobs have to be scheduled on a single machine and delivered to a customer. Each job has a due date, a processing time and a weight. To save delivery cost, several jobs can be delivered together as a batch including the late jobs. The completion (delivery) time of each job in the same b...

In many computational fluid dynamics (CFD) studies of stented vessel haemodynamics, the geometry of the stented vessel is described using non-deformed (NDF) geometrical models. These NDF models neglect complex physical features, such as stent and vessel deformation, which may have a major impact on the haemodynamic environment in stented coronary arteries. In this study, CFD analyses were carri...

There has been recent success in using polyhedral formulations of scheduling problems not only to obtain good lower bounds in practice but also to develop provably good approximation algorithms. Most of these formulations rely on binary decision variables that are a kind of assignment variables. We present quite simple polynomial-time approximation algorithms that are based on linear programmin...

There has been recent success in using polyhedral formulations of scheduling problems not only to obtain good lower bounds in practice but also to develop provably good approximation algorithms. Most of these formulations rely on binary decision variables that are a kind of assignment variables. We present quite simple polynomial{ time approximation algorithms that are based on linear programmi...

In this paper we introduce a new scheduling model with learning effects in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the job’s scheduled position. We show that the single-machine problems to minimize makespan and total completion time are polynomially solvable. In addition, we show that the problems to minim...

Estimation of haplotype sequences from DNA sequencing samples is a challenging task whose mathematical formulation leads to an NP-hard problem. Also, accuracy the estimates plays essential role in providing required information for personalized medicine. In order fully incorporate available quality measurements with higher into estimates, this paper, we propose new optimization design using wei...

In this paper we study the average distance in weighted graphs. More precisely, we consider assignments of families of non-negative weights to the edges. The aim is to maximise (minimise, respectively) the average distance in the resulting weighted graph. Two variants of the problem are considered depending on whether the collection of weights is fixed or not. The main results of this paper are...