A specialized branch & bound & cut for Single-Allocation Ordered Median Hub Location problems

The Single-Allocation Ordered Median Hub Location problem is a recent hub model introduced by Puerto et al. (2011) [32] that provides a unifying analysis of the class of hub location models. Indeed, considering ordered objective functions in hub location models is a powerful tool in modeling classic and alternative location paradigms, that can be applied with success to a large variety of problems providing new distribution patterns induced by the different users’ roles within the supply chain network. In this paper, we present a new formulation for the Single-Allocation Ordered Median Hub Location problem and a branch-and-bound-and-cut (B&B&Cut) based algorithm to solve optimally this model. A simple illustrative example is discussed to demonstrate the technique, and then a battery of test problems with data taken from the AP library are solved. The paper concludes that the proposed B&B&Cut approach performs well for small to medium sized problems.     

Synthesis of aqueous ferrofluids of ZnxFe3−xO4 nanoparticles by citric acid assisted hydrothermal-reduction route for magnetic hyperthermia applications

Superparamagnetic and monodispersed aqueous ferrofluids of Zn substituted magnetite nanoparticles (Zn_xFe_3−xO₄, x=0, 0.25, 0.3, 0.37 and 0.4) were synthesized via hydrothermal-reduction route in the presence of citric acid, which is a facile, low energy and environmental friendly method. The synthesized nanoparticles were characterized by X ray diffraction (XRD) analysis, Fourier transform infrared (FTIR) spectroscopy, scanning and transmission electron microscopy (SEM and TEM) and the dynamic light scattering (DLS) method. The results showed that a certain amount of citric acid was required to obtain single phase Zn substituted magnetite nanoparticles. Citric acid acted as a modulator and reducing agent in the formation of spinel structure and controlled nanoparticle size and crystallinity. Mean particle sizes of the prepared nanoparticles were around 10 nm. The results that are obtained from XRD, magnetic and power loss measurements showed that the crystallinity, saturation magnetization (M_S) and loss power of the synthesized ferrofluids were all influenced by the substitution of Zn in the structure of magnetite. The Zn substituted magnetite nanoparticles obtained by this route showed a good stability in aqueous medium (pH 7) and hydrodynamic sizes below 100 nm and polydispersity indexes below 0.2. The calculated intrinsic loss power (ILP) for the sample x=0.3 (e.g. 2.36 nH m²/kg) was comparable to ILP of commercial ferrofluids with similar hydrodynamic sizes.     

The geometry of optimal partitions in location problems

Given the position of some facilities, we study the shape of optimal partitions of the customers’ area in a general planar demand region minimizing total average cost that depends on a set up cost plus some function of the travelling distances. By taking into account different norms, according to the considered situation of the location problem, we characterize optimal consumers’ partitions and describe their geometry. The case of dimensional facilities is also investigated.     

A model and two heuristic approaches for a forage harvester planning problem: a case study

This work considers a decision problem about orders of owners and routes of smallholdings for a harvester in an agricultural cooperative in which each owner has a proposal about the instant time in which he would like that the machine starts the activity in his land and the different smallholdings of each owner should be processed as a block. A binary linear programming model is introduced in order to reducing costs. Solving the model for actual size instances is computationally burdensome. Hence, we introduce and implement two heuristic algorithms to reduce the computational time. The heuristics are applied to the real case of the cooperative “Os Irmandiños” with a large number of owners and smallholdings. The numerical results show that the heuristics can solve large instances effectively with reasonable computational effort.     

Revisiting <Emphasis Type="Italic">k</Emphasis>-sum optimization

In this paper, we address continuous, integer and combinatorial k-sum optimization problems. We analyze different formulations of this problem that allow to solve it through the minimization of a relatively small number of minisum optimization problems. This approach provides a general tool for solving a variety of k-sum optimization problems and at the same time, improves the complexity bounds of many ad-hoc algorithms previously reported in the literature for particular versions of this problem. Moreover, the results developed for k-sum optimization have been extended to the more general case of the convex ordered median problem, improving upon existing solution approaches.     

Modeling cooperation on a class of distribution problems

In this paper we study models of cooperation between the nodes of a network that represents a distribution problem. The distribution problem we propose arises when, over a graph, a group of nodes offers certain commodity, some other nodes require it and a third group of nodes neither need this material nor offer it but they are strategically relevant to the distribution plan. The delivery of one unit of material to a demand node generates a fixed profit, and the shipping of the material through the arcs has an associated cost. We show that in such a framework cooperation is beneficial for the different parties. We prove that the cooperative situation arising from this distribution problem is totally balanced by finding a set of stable allocations (in the core of an associated cooperative game). In order to overcome certain fairness problems of these solutions, we introduce two new solution concepts and study their properties.     

On discrete optimization with ordering

This paper studies discrete optimization problems with ordering requirements. These problems are formulated on general discrete sets in which there exists an ordering on their elements together with a cost function that evaluates each element of a given subset depending on its ordering relative to the remaining elements in the set. It is proven that ordered sequences over the original ground set define an independence system. The simplest such ordering problem, that consists of finding the ordered sequence of maximum weight, and its restriction to sets of a fixed cardinality are studied. In both cases, the polyhedral structure of the corresponding feasible sets is analyzed.     

The minimum cost shortest-path tree game

A minimum cost shortest-path tree is a tree that connects the source with every node of the network by a shortest path such that the sum of the cost (as a proxy for length) of all arcs is minimum. In this paper, we adapt the algorithm of Hansen and Zheng (Discrete Appl. Math. 65:275?C284, 1996) to the case of acyclic directed graphs to find a minimum cost shortest-path tree in order to be applied to the cost allocation problem associated with a cooperative minimum cost shortest-path tree game. In addition, we analyze a non-cooperative game based on the connection problem that arises in the above situation. We prove that the cost allocation given by an ??à la?? Bird rule provides a core solution in the former game and that the strategies that induce those payoffs in the latter game are Nash equilibrium.     

Olga Nikolajevna Bondareva 1937–1991

Obituary

Olga Nikolajevna Bondareva 1937–1991     

Center location problems on tree graphs with subtree-shaped customers

We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler’s classical linear time algorithms for unweighted 1- and 2-center problems with respect to point customers, linearly solves the unweighted 1- and 2-center problems with addends of the above subtree customer model. We also develop polynomial time algorithms for the p-center problems based on solving covering problems and searching over special domains.