This contribution deals with dynamic, capacitated, multi-level lot sizing and scheduling. The basic assumption is that for each item there is exactly one machine that this item can be manufactured on but no two items share a common machine. Finding an optimal solution with a greedy algorithm...

This contribution acquaints the reader with a model for multi-level single-machine proportional lot sizing and scheduling problems (PLSPs) that appear in the scope of short-term production planning. It is one of the first papers that deals with dynamic capacitated multi-level lot sizing and...

The paper develops a version of Pontryagin's maximum principle for optimal control problems with monotonicity constraints on control variables. Whereas the literature handles such constraints by imposing an assumption of piecewise smoothness on the control variable and treating the slope of this...

This paper presents a mixed-integer program for the dynamic lot sizing and scheduling problem in a multi-level, single-machine environment. It turns out that in contrast to single-level problems the integration of initial inventory is a crucial aspect if generality should not be lost. It is...

Cellular automata were used to model and to simulate phenomena in the area of physics, biology and medicine. In this paper it is now shown how the idea of cellular automata can be applied to optimization problems as well. As an example a cellular automaton is used as a basis for solving...

This contribution presents two heuristic approaches for multi-level, single-machine lot sizing and scheduling. The first one is a variant of a so-called randomized regret based heuristic which is assumed to be the fastest available method for this particular class of problems. The second...

Three types of multi-item capacitated dynamic lotsizing and scheduling models are well established until now: The capacitated lotsizing problem, the discrete lotsizing and scheduling problem as well as the continuous setup lotsizing problem. An analysis of the underlying fundamental assumptions...

This paper explores a single-item capacitated lot sizing problem with minimum order quantity, which plays the role of minor set-up cost. We work out the necessary and suffcient solvability conditions and apply the general dynamic programming technique to develop an O(T³) exact algorithm that is...

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. A feature that makes this family particularly desirable for econometric applications is that it possesses closed-form expressions for its anti-derivatives (e.g., the...

The literature on electoral cycles has developed in two distinct phases. The first one considered the existence of non-rational (naive) voters whereas the second one considered fully rational voters. In our perspective, an intermediate approach is more interesting, i.e. one that considers...