We consider a variant of no-wait flowshop scheduling that is motivated by continuous casting in the multistage production process in steel manufacturing. The task is to find a feasible schedule with a minimum number of interruptions, i.e., continuous idle time intervals on the last production stage. Based on an interpretation as Eulerian Extension Problems, we fully settle the complexity status of any particular problem case: We give a very intuitive optimal algorithm for scheduling on two processing stages with one machine in the first stage, and we show that all other problem variants are strongly NP-hard. We also discuss alternative idle time related scheduling models and their justification in the considered steel manufacturing environment. Here, we derive constant factor approximations.

We consider the problem of scheduling jobs on a single machine. Given some continuous cost function, we aim to compute a schedule minimizing the weighted total cost, where the cost of each individual job is determined by the cost function value at the job's completion time. This problem is closely related to scheduling a single machine with nonuniform processing speed. We show that for piecewise linear cost functions it is strongly NP-hard. The main contribution of this article is a tight analysis of the approximation factor of Smith's rule under any particular convex or concave cost function. More specifically, for these wide classes of cost functions we reduce the task of determining a worst case problem instance to a continuous optimization problem, which can be solved by standard algebraic or numerical methods. For polynomial cost functions with positive coefficients it turns out that the tight approximation ratio can be calculated as the root of a univariate polynomial. To overcome unrealistic worst case instances, we also give tight bounds that are parameterized by the minimum, maximum, and total processing time.

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We present the first experimental study of online packet buffering algorithms for network switches. We consider a basic scenario in which m queues of size B have to be maintained so as to maximize the packet throughput. For this model various online algorithms with competitive factors ranging between 2 and 1.5 were developed in the literature. We first develop a new 2-competitive online algorithm, called HSFOD, which is especially designed to perform well under real-world conditions. In our experimental study we have implemented all the proposed algorithms, including HSFOD, and tested them on packet traces from benchmark libraries. We have evaluated the experimentally observed competitiveness, the running times, memory requirements and actual packet throughput of the strategies. The tests were executed for varying values of m and B as well as varying switch speeds. It shows that greedylike strategies and HSFOD perform best in practice.