Abstract. The best exact algorithms for the Capacitated Vehicle Routing Problem (CVRP) have been based on either branch-and-cut or Lagrangean relaxation/column generation. This paper presents an algorithm that combines both approaches: it works over the intersection of two polytopes, one associated with a traditional Lagrangean relaxation over q-routes, the other defined by bound, degree and ca...

We consider a capacitated plant location problem with multi-commodity flow on a two-level network including plants and transshipment points. The objective is to locate plants and determine commodities movement while satisfying customers’ demand and minimizing costs. We present a new and effective hybrid method, composed from Lagrangean Relaxation and UB Creating Method to solve the problem. We ...

Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual subgradient scheme does not automatically produce primal feasible solutions; there is an abundance of techniques for computing such solutions (via penalty functions, tangential app...

This paper proposes an admission control algorithm for CDMA networks, from which a revenue optimization problem is formulated as a mixed integer problem. The objective of the optimization problem is to maximizing total system revenue subject to capacity as well as QoS constraints. The approach for solving revenue optimization problem is Lagrangean relaxation in conjunction with a heuristic. The...

We consider the Retail Planning Problem in which the retailer chooses suppliers, and determines the production, distribution and inventory planning for products with uncertain demand in order to minimize total expected costs. This problem is often faced by large retail chains that carry private label products. We formulate this problem as a convex mixed integer program and show that it is stron...

This paper investigates a model for pricing the demand for a set of goods when multiple suppliers operate discount schedules based on total business value. We formulate the buyers’s decision problem as a mixed binary integer program (MIP) which is a generalization of the capacitated facility location problem (CFLP) and can be solved using Lagrangean heuristics. We have investigated commercially...

A Lagrangean for the dynamics of an electromagnetic field in a dispersive and dissipative material is constructed (adapting some ideas by Bekenstein and Hannay) and an expression for the energy density that is positive is obtained from it. The expression contains extra (sink) degrees of freedom that represent dissipating modes. In simplified cases the sink modes can be eliminated to yield an en...

In this paper, we attempt to solve the problem of constructing a minimum cost multicast tree with the consideration of dynamic user membership. Unlike the other minimum cost multicast tree algorithms, this problem consists of one multicast group of fixed members and each destination member is dynamic and has a probability of being active as which was gathered by observation over some period of ...

The Capacitated p-median problem (CPMP) seeks to solve the optimal location of p facilities, considering distances and capacities for the service to be given by each median. In this paper we present a column generation approach to CPMP. The identified restricted master problem optimizes the covering of 1-median clusters satisfying the capacity constraints, and new columns are generated consider...

This paper studies a single machine scheduling problem whose objective is to minimize a regular step total cost function. Lower and upper bounds, obtained from linear and Lagrangean relaxations of different Integer Linear Programming formulations, are compared. A dedicated exact approach is presented, based on a Lagrangean relaxation. It consists of finding a Constrained Shortest Path in a spec...