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Revisiting lagrange relaxation (LR) for processing large-scale mixed integer programming (MIP) problems
Lagrangean Relaxation has been successfully applied to process many well known
instances of NP-hard Mixed Integer Programming problems. In this paper we present
a Lagrangean Relaxation based generic solver for processing Mixed Integer
Programming problems. We choose the constraints, which are relaxed using a
constraint classification scheme. The tactical issue of updating the Lagrange
multiplier is addressed through sub-gradient optimisation; alternative rules for
updating their values are investigated. The Lagrangean relaxation provides a lower
bound to the original problem and the upper bound is calculated using a heuristic
technique. The bounds obtained by the Lagrangean Relaxation based generic solver
were used to warm-start the Branch and Bound algorithm; the performance of the
generic solver and the effect of the alternative control settings are reported for a wide
class of benchmark models. Finally, we present an alternative technique to calculate
the upper bound, using a genetic algorithm that benefits from the mathematical
structure of the constraints. The performance of the genetic algorithm is also
presented
Models and Algorithms for Production Planning and Scheduling in Foundries – Current State and Development Perspectives
Mathematical programming, constraint programming and computational intelligence techniques, presented in the literature in the field of operations research and production management, are generally inadequate for planning real-life production process. These methods are in fact dedicated to solving the standard problems such as shop floor scheduling or lot-sizing, or their simple combinations such as scheduling with batching. Whereas many real-world production planning problems require the simultaneous solution of several problems (in addition to task scheduling and lot-sizing, the problems such as cutting, workforce scheduling, packing and transport issues), including the problems that are difficult to structure. The article presents examples and classification of production planning and scheduling systems in the foundry industry described in the literature, and also outlines the possible development directions of models and algorithms used in such systems
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