We develop a model to determine the optimal structure and size of a rail car fleet at a chemical company under uncertainty in demand and travel times as well as substitution between rail car types. First, we formulate an MILP model that accounts for the substitution relations between the types...

A set of ellipses, with given semi-major and semi-minor axes, is to be cut from a rectangular design plate, while minimizing the area of the design rectangle. The design plate is subject to lower and upper bounds of its widths and lengths; the ellipses are free of any orientation restrictions....

For univariate functions, we compute optimal breakpoint systems subject to the condition that the piecewise linear approximation (or, under- and overestimator) never deviates more than a given δ-tolerance from the original function, over a given finite interval. The linear approximators, under-...

Following up on Rebennack and Kallrath (2012), in this paper, for functions depending on two variables, using refinement heuristics, we automatically construct triangulations subject to the condition that the continuous, piecewise linear approximation, under- or overestimation never deviates...

We discuss cutting stock problems (CSPs) from the perspective of the paper industry and the financial impact they make. Exact solution approaches and heuristics have been used for decades to support cutting stock decisions in that industry. We have developed polylithic solution techniques...