This paper deals with the ring star problem that consists in designing a ring that pass through a central depot, and then assigning each non visited customer to a node of the ring. The objective is to minimize the total routing and assignment costs. A new chain based formulation is proposed. Valid inequalities are proposed … Read more
In this work, we consider a classification problem where the objects to be classified are bags of instances which are vectors measuring d different attributes. The classification rule is defined in terms of a ball, whose center and radius are the parameters to be computed. Given a bag, it is assigned to the positive class … Read more
Intensity–modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {a,ß}–relaxation, meaning that no more than a percent of the inequalities are violated by no more than ß … Read more
We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints … Read more
This paper considers packing problems with balancing conditions and items consisting of clusters of parallelepipeds (mutually orthogonal, i.e. tetris-like items). This issue is quite frequent in space engineering and a real-world application deals with the Automated Transfer Vehicle project (funded by the European Space Agency), at present under development. A Mixed Integer Programming (MIP) approach … Read more
In this paper, we introduce an operation that creates families of facet-defining inequalities for high-dimensional infinite group problems using facet-defining inequalities of lower-dimensional group problems. We call this family sequential-merge inequalities because they are produced by applying two group cuts one after the other and because the resultant inequality depends on the order of the … Read more
We consider a revenue management model for pricing a product line with several customer segments under the assumption that customers’ product choices are determined entirely by their reservation prices. We highlight key mathematical properties of the maximum utility model and formulate it as a mixed-integer programming problem, design heuristics and valid cuts. We further present … Read more
In this paper we address the following probabilistic version (PSC) of the set covering problem: min { cx | P (Ax>= xi) >= p, x_{j} in {0,1} j in N} where A is a 0-1 matrix, xi is a random 0-1 vector and p in (0,1] is the threshold probability level. In a recent development … Read more
The block layout problem for a multi-floor facility is an important sub class of the facility layout problem with practical applications when the price of land is high or when a compact building allows for more efficient environmental control. Several alternative formulations for the block layout problem of a multi-floor facility are presented, where the … Read more
In this paper we address the following probabilistic version (PSC) of the set covering problem: $min \{ cx \ |\ {\mathbb P} (Ax\ge \xi) \ge p,\ x_{j}\in \{0,1\}^N\}$ where $A$ is a 0-1 matrix, $\xi$ is a random 0-1 vector and $p\in (0,1]$ is the threshold probability level. We formulate (PSC) as a mixed integer … Read more