We present new lower bounds for the Capacitated Lot Sizing Problem with Set Up Times. We improve the lower bound obtained by the textbook Dantzig-Wolfe decomposition where the capacity constraints are the linking constraints. In our approach, Dantzig-Wolfe decomposition is applied to the network...

A new smoothing approach based on entropic perturbationis proposed for solving mathematical programs withequilibrium constraints. Some of the desirableproperties of the smoothing function are shown. Theviability of the proposed approach is supported by acomputationalstudy on a set of well-known...

Many practical optimization problems are characterized by some flexibility in the problem constraints, where this flexibility can be exploited for additional trade-off between improving the objective function and satisfying the constraints. Especially in decision making, this type of flexibility...

In this technical note we give a short proof based on standard results in convex analysis of some important characterization results listed in Theorem 3 and 4 of [1]. Actually our result is slightly general since we do not specify the convex set X. For clarity we use the same notation for the...

Although the possibility to combine column generation and Lagrangian relaxation has been known for quite some time, it has only recently been exploited in algorithms. In this paper, we discuss ways of combining these techniques. We focus on solving the LP relaxation of the Dantzig-Wolfe master...

We present a mathematical analysis of the long-run behavior of genetic algorithms that are used for modeling social phenomena. The analysis relies on commonly used mathematical techniques in evolutionary game theory. Assuming a positive but infinitely small mutation rate, we derive results that...

Advanced Planning and Scheduling (APS) systems have gained renewed interest from academics and practitioners. However, literature on APS adoption is scant. This study explores the impact of organizational and innovation related factors on the adoption of APS systems from a factors approach. The...

By using a smooth entropy function to approximate the non-smooth max-type function, a verticallinear complementarity problem (VLCP) can be treated as a family of parameterized smoothequations. A Newton-type method with a testing procedure is proposed to solve sucha system. We show that the...

We consider generalized monotone functions f: X -- {0,1}defined for an arbitrary binary relation = on X by theproperty x = y implies f(x) = f(y). These include thestandard monotone (or positive) Boolean functions, regular Booleanfunctions and other interesting functions as special cases. It...