A simple and robust Monte Carlo hybrid local search algorithm for the facility location problem

In this article, a new Monte Carlo hybrid local search algorithm (Hyb-LS) is proposed for solving the uncapacitated facility location problem. Hyb-LS is based on repeated sampling using two local search strategies based on best improvement and randomized neighbourhood search. A major advantage of Hyb-LS for its practical use is that the number of restarts is its only parameter to tune. The algorithm is also simple to reimplement, scalable and robust to changes in coefficients within a problem instance. The stopping criterion for local search is learned automatically. Experimental results are presented for four representative and contrasting cost and distance models. The results obtained by Hyb-LS are compared to the optimal or near-optimal solutions found by a mixed integer linear programming (MILP) solver with a generous time limit. For three out of the four models, Hyb-LS obtains better solutions than the upper bound found by the MILP solver for at least one instance.     

A sequence-pair representation and MIP-model-based heuristic for the facility layout problem with rectangular departments

In Facility Layout Problem (FLP) research, the continuous-representation-based FLP can consider all feasible all-rectangular-department solutions. Given this flexibility, this representation has become the representation of choice in FLP research. Much of this research is based on a methodology of Mixed-Integer Programming (MIP) models. However, these MIP-FLP models can only solve problems with a limited number of departments to optimality due to the large number of combinations of the binary variables used in the models to maintain feasibility with respect to departments overlapping. Our research centers around the sequence-pair representation, a concept that originated in the Very Large Scale Integration (VLSI) design literature. We show that an exhaustive search of the sequence-pair solution space will result in finding the optimal layout of the MIP-FLP and that every sequence-pair solution is position consistent (although possibly not layout feasible) in the MIP-FLP. We propose a genetic-algorithm-based heuristic that combines the sequence-pair representation with the MIP-FLP model. Numerical experiments based on different sized test problems from both the literature and industrial applications are provided and the solutions are compared with both the optimal solutions and the solutions from other heuristics to show the effectiveness and efficiency of our heuristic. For 11 data sets from the literature we provide solutions better than those previously found. For two large industrial application data sets we perform a sensitivity analysis with respect to the department aspect ratio constraint.     

A local genetic approach to multi-objective,facility layout problems with fixed aisles

We develop a new local genetic algorithm hybridized tabu search, to solve multi-criteria facility layout problems. Within these types of problems, we consider two objectives involving material handling costs and non-material relationship requirements according to the idea of systematic layout planning. Our focus is on a particular case which involves the explicit consideration of fixed aisles and transverse passageways between sections. Numerical experiments as well as comparative tests show the great effectiveness of the proposed method in dealing with multi-criteria facility layout problems up to some moderate scales.     

Lagrangean relaxation and hybrid simulated annealing tabu search procedure for a two-echelon capacitated facility location problem with plant size selection

In this paper, we study a two-echelon capacitated facility location problem with plant size selection (TECFLP-PSS). Given a set of potential sites for plants, each of which is associated with several possible sizes and corresponding unit production costs, a set of potential sites for capacitated depots and a set of customers with demands, the TECFLP-PSS aims to optimise the plant locations and sizes, the depot locations and the product flows from the opened plants to the opened depots and then to the end customers under single-source constraints. The objective is to satisfy all customers’ demands with a minimum total cost of facility opening, production and transportation. We develop a mixed integer programming model and propose a Lagrangean relaxation approach combined with new valid inequalities and core problem to achieve tight lower and upper bounds for this problem. We then improve the upper bound with a hybrid simulated annealing tabu search procedure. Computational experiments on benchmarks and randomly generated instances are conducted to validate the effectiveness and efficiency of the proposed method.     

On the impact of spatial pattern,aggregation, and model parameters in planar Huff-type competitive location and design problems

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximize the profit obtained for the chain. Several types of constraints and costs are considered. Applying an interval analysis based global optimization method on several spatial patterns in a quasi-real-world environment, the behaviour of optimal solutions is investigated when changes are made in the basic model parameters. The study yields valuable insight for modellers into the impact of spatial pattern and various model parameters of the model on the resulting location and design decision. Spatial patterns differ in distribution of demand, of own and/or competing facilities, and of facility qualities. Studied model parameters include push force effects, investment restrictions and aggregation of demand. An extended version of this paper including additional studies on model parameters and the exact data used in the computational experiments is available at Optimization Online (see Tóth et al. (2008)). This work has been supported by grants from the Ministry of Science and Innovation of Spain (TIN2008-01117, SEJ2005-06273/ECON and ECO2008-00667/ECON), Junta de Andalucía (P08-TIC-3518), and in part by the European Regional Development Fund (ERDF).     

Dynamic scheduling of oil tankers with splitting of cargo at pickup and delivery locations: a Multi-objective Ant Colony-based approach

Maritime crude oil transportation problem have been drawing the attention of researchers for quite a long time. The cost incurred in the supply chain for the oil products is one of the biggest driving factors for these researchers. In the present paper, we have addressed the problem faced by the logistics section of the petroleum downstream industry. This industry mainly deals with the transportation of finished oil products like fuel oil, high speed diesel, etc. from refineries to the demand points. For this purpose, we have developed a mathematical model to represent the problem appropriately, aiming at total cost minimisation as well as service-level maximisation. The problem in hand is then tackled with a modified Multi-objective Ant Colony optimisation algorithm which besides considering more than one pheromone structure also involves non-dominated sorting of the results to give us the best-performing solution fronts. For the purpose of dealing with the uncertainties causing docking problems at a port, we have incorporated a second stage of route allocation for the vessels. Towards the end, we have carried out a sensitivity analysis for the parameters of the ant colony algorithm to get the combination of parameters for which this new type of algorithm performs best. The comparison of obtained results with one of the other contemporary algorithms also establishes the superiority of our heuristic.     

A possibilistic programming approach for the location problem of multiple cross-docks and vehicle routing scheduling under uncertainty

This article considers the design of cross-docking systems under uncertainty in a model that consists of two phases: (1) a strategic-based decision-making process for selecting the location of cross-docks to operate, and (2) an operational-based decision-making process for vehicle routing scheduling with multiple cross-docks. This logistic system contains three echelons, namely suppliers, cross-docks and retailers, in an uncertain environment. In the first phase, a new multi-period cross-dock location model is introduced to determine the minimum number of cross-docks among a set of location sites so that each retailer demand should be met. Then, in the second phase, a new vehicle routing scheduling model with multiple cross-docks is formulated in which each vehicle is able to pickup from or deliver to more than one supplier or retailer, and the pickup and delivery routes start and end at the corresponding cross-dock. This article is the first attempt to introduce an integrated model for cross-docking systems design under a fuzzy environment. To solve the presented two-phase mixed-integer programming (MIP) model, a new fuzzy mathematical programming-based possibilistic approach is used. Furthermore, experimental tests are carried out to demonstrate the effectiveness of the presented model. The computational results reveal the applicability and suitability of the developed fuzzy possibilistic two-phase model in a variety of problems in the domain of cross-docking systems.     

A two-tiered model for simulating the ecological and evolutionary dynamics of rapidly evolving viruses, with an application to influenza

Understanding the epidemiological and evolutionary dynamics of rapidly evolving pathogens is one of the most challenging problems facing disease ecologists today. To date, many mathematical and individual-based models have provided key insights into the factors that may regulate these dynamics. However, in many of these models, abstractions have been made to the simulated sequences that limit an effective interface with empirical data. This is especially the case for rapidly evolving viruses in which de novo mutations result in antigenically novel variants. With this focus, we present a simple two-tiered ‘phylodynamic’ model whose purpose is to simulate, along with case data, sequence data that will allow for a more quantitative interface with observed sequence data. The model differs from previous approaches in that it separates the simulation of the epidemiological dynamics (tier 1) from the molecular evolution of the virus''s dominant antigenic protein (tier 2). This separation of phenotypic dynamics from genetic dynamics results in a modular model that is computationally simpler and allows sequences to be simulated with specifications such as sequence length, nucleotide composition and molecular constraints. To illustrate its use, we apply the model to influenza A (H3N2) dynamics in humans, influenza B dynamics in humans and influenza A (H3N8) dynamics in equine hosts. In all three of these illustrative examples, we show that the model can simulate sequences that are quantitatively similar in pattern to those empirically observed. Future work should focus on statistical estimation of model parameters for these examples as well as the possibility of applying this model, or variants thereof, to other host–virus systems.     

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.     

A note on the divergence problem arising in calculation of Green’s function for a 2D piezoelectric thin film strip with free boundaries and containing straight line defects: Fourier approach for bodies of cubic symmetry

Analytic formulas for the Green’s function and the coupled electro-elastic fields for a 2D piezoelectric strip with free boundaries and containing a distribution of straight line defects have already been found some years ago. These formulas exploit the well-known Stroh formalism and the Fourier approach, so the result is given as the Fourier integral and therefore its numerical implementation should pose no problem. However, in this note we show that for the case of cubic symmetry this form of the Green’s function contains strong divergences, excluding possibilities of direct application of well-known numerical schemes. It is also shown that these divergences translate to divergences of the corresponding electro-elastic fields of a single defect. By means of a rigorous analysis it is demonstrated that imposing physical conditions implied by the nature of the problem all of these divergences cancel and the final, physical result exhibits expected, regular behavior at infinity. Unfortunately, although the nature of this problem is purely mathematical, it leads to irremovable numerical ∞ − ∞ uncertainties which tend to spread over the whole Fourier domain and severely impede engineering applications of the Green’s function. This motivates us to compute the exact form of all divergent terms. These novel formulas will serve as a guide when establishing numerically stable algorithms for engineering computations involving the system in question.     

A novel nanostructured composite formed by interaction of copper octa(3-aminopropyl)octasilsesquioxane with azide ligands: Preparation, characterization and a voltammetric application

This study presents the preparation, characterization and application of copper octa(3-aminopropyl)octasilsesquioxane following its subsequent reaction with azide ions (ASCA). The precursor (AC) and the novel compound (ASCA) were characterized by Fourier transform infrared spectra (FTIR), nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), scanning electronic microscopy (SEM), X-ray diffraction (XRD), Thermogravimetric analyses and voltammetric technique. The cyclic voltammogram of the modified graphite paste electrode with ASCA (GPE-ASCA), showed one redox couple with formal potential () = 0.30 V and an irreversible process at 1.1 V (vs. Ag/AgCl; NaCl 1.0 M; v=20 mV s−1). The material is very sensitive to nitrite concentrations. The modified graphite paste electrode (GPE-ASCA) gives a linear range from 1.0 × 10⁻⁴ to 4.0 × 10⁻³ mol L⁻¹ for the determination of nitrite, with a detection limit of 2.1 × 10⁻⁴ mol L⁻¹ and the amperometric sensitivity of 8.04 mA/mol L⁻¹.