Modular decomposition is a thoroughly investigated topic inmany areas such as switching theory, reliability theory, game theory andgraph theory. We propose an O(mn)-algorithm for the recognition of amodular set of a monotone Boolean function f with m prime implicantsand n variables. Using this...

The textbook Dantzig-Wolfe decomposition for the Capacitated Lot Sizing Problem (CLSP),as already proposed by Manne in 1958, has an important structural deficiency. Imposingintegrality constraints on the variables in the full blown master will not necessarily give theoptimal IP solution as only...

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...

The present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we...

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 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...

In a recent paper, Fisher et al. (2001) present a method tomitigate end-effects in lot sizing by including a valuation term for end-of-horizon inventory in the objective function of the short-horizon model. Computational tests show that the proposed method outperforms the Wagner-Whitin algorithm...

We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic...