Short Communication: A compelling argument for the gravity p-median model

The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population always travels to the nearest facility. Drezner and Drezner (2006, 2007) provide three arguments on why this assumption might be incorrect, and they introduce the extended the gravity p-median model to relax the assumption. We favour the gravity p-median model, but we note that in an applied setting, Drezner and Drezner’s arguments are incomplete. In this communication, we point at the existence of a fourth compelling argument for the gravity p-median model.

An empirical test of the gravity p-median model

A customer is presumed to gravitate to a facility by the distance to it and the attractiveness of it. However regarding the location of the facility, the presumption is that the customer opts for the shortest route to the nearest facility.This paradox was recently solved by the introduction of the gravity p-median model. The model is yet to be implemented and tested empirically. We implemented the model in an empirical problem of locating locksmiths, vehicle inspections, and retail stores ofv ehicle spare-parts, and we compared the solutions with those of the p-median model. We found the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Testing the gravity p-median model empirically

Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Heuristic optimization of the p-median problem and population re-distribution

This thesis contributes to the heuristic optimization of the p-median problem and Swedish population redistribution.   The p-median model is the most representative model in the location analysis. When facilities are located to a population geographically distributed in Q demand points, the p-median model systematically considers all the demand points such that each demand point will have an effect on the decision of the location. However, a series of questions arise. How do we measure the distances? Does the number of facilities to be located have a strong impact on the result? What scale of the network is suitable? How good is our solution? We have scrutinized a lot of issues like those. The reason why we are interested in those questions is that there are a lot of uncertainties in the solutions. We cannot guarantee our solution is good enough for making decisions. The technique of heuristic optimization is formulated in the thesis.   Swedish population redistribution is examined by a spatio-temporal covariance model. A descriptive analysis is not always enough to describe the moving effects from the neighbouring population. A correlation or a covariance analysis is more explicit to show the tendencies. Similarly, the optimization technique of the parameter estimation is required and is executed in the frame of statistical modeling. 

Distance measure and the p-median problem in rural areas

The p-median model is used to locate P facilities to serve a geographically distributed population. Conventionally, it is assumed that the population patronize the nearest facility and that the distance between the resident and the facility may be measured by the Euclidean distance. Carling, Han, and Håkansson (2012) compared two network distances with the Euclidean in a rural region witha sparse, heterogeneous network and a non-symmetric distribution of thepopulation. For a coarse network and P small, they found, in contrast to the literature, the Euclidean distance to be problematic. In this paper we extend their work by use of a refined network and study systematically the case when P is of varying size (2-100 facilities). We find that the network distance give as gooda solution as the travel-time network. The Euclidean distance gives solutions some 2-7 per cent worse than the network distances, and the solutions deteriorate with increasing P. Our conclusions extend to intra-urban location problems.

Network density and the p-median solution

The p-medianmodel is commonly used to find optimal locations of facilities for geographically distributed demands. So far, there are few studies that have considered the importance of the road network in the model. However, Han, Håkansson, and Rebreyend (2013) examined the solutions of the p-median model with densities of the road network varying from 500 to 70,000 nodes. They found as the density went beyond some 10,000 nodes, solutions have no further improvements but gradually worsen. The aim of this study is to check their findings by using an alternative heuristic being vertex substitution, as a complement to their using simulated annealing. We reject the findings in Han et al (2013). The solutions do not further improve as the nodes exceed 10,000, but neither do the solutions deteriorate.

THE ISOLATION, CHARACTERIZATION AND OXIDATION REACTION OF ACTIVE INTERMEDIATES OF CYTOCHROME-P-450 MODEL SYSTEM OXOCHROMIUM(V) TETRAPHENYLPORPHYRIN COMPLEXES

Oxochromium (V) tetraphenylporphyrin complexes, O = Cr (V) TPP (Cl) PhI. O = Cr-(V) TPP (N3) PhI and O = Cr (V)TPP (p-CH3OC6H4O)1/2PhI were isolated from the reaction of Cr (III) TPP (Cl). Cr (III) TPP (N3) Py or Cr (III) TPP (p-CH3OC6H4O) THF with iodosy

The p-hub Model with Hub-catchment Areas, Existing Hubs, and Simulation: A Case Study of Serbian Intermodal Terminals

This paper addresses the problem of optimally locating intermodal freight terminals in Serbia. To solve this problem and determine the effects of the resulting scenarios, two modeling approaches were combined. The first approach is based on multiple-assignment hub-network design, and the second is based on simulation. The multiple-assignment p-hub network location model was used to determine the optimal location of intermodal terminals. Simulation was used as a tool to estimate intermodal transport flow volumes, due to the unreliability and unavailability of specific statistical data, and as a method for quantitatively analyzing the economic, time, and environmental effects of different scenarios of intermodal terminal development. The results presented here represent a summary, with some extension, of the research realized in the IMOD-X project (Intermodal Solutions for Competitive Transport in Serbia).

Fragile-glass behavior of a short-range p-spin model

We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.

Forest fire plumes over the North Atlantic: p-TOMCAT model simulations with aircraft and satellite measurements from the ITOP/ICARTT campaign

Intercontinental Transport of Ozone and Precursors (ITOP) (part of International Consortium for Atmospheric Research on Transport and Transformation (ICARTT)) was an intense research effort to measure long-range transport of pollution across the North Atlantic and its impact on O3 production. During the aircraft campaign plumes were encountered containing large concentrations of CO plus other tracers and aerosols from forest fires in Alaska and Canada. A chemical transport model, p-TOMCAT, and new biomass burning emissions inventories are used to study the emissions long-range transport and their impact on the troposphere O3 budget. The fire plume structure is modeled well over long distances until it encounters convection over Europe. The CO values within the simulated plumes closely match aircraft measurements near North America and over the Atlantic and have good agreement with MOPITT CO data. O3 and NOx values were initially too great in the model plumes. However, by including additional vertical mixing of O3 above the fires, and using a lower NO2/CO emission ratio (0.008) for boreal fires, O3 concentrations are reduced closer to aircraft measurements, with NO2 closer to SCIAMACHY data. Too little PAN is produced within the simulated plumes, and our VOC scheme's simplicity may be another reason for O3 and NOx model-data discrepancies. In the p-TOMCAT simulations the fire emissions lead to increased tropospheric O3 over North America, the north Atlantic and western Europe from photochemical production and transport. The increased O3 over the Northern Hemisphere in the simulations reaches a peak in July 2004 in the range 2.0 to 6.2 Tg over a baseline of about 150 Tg.

A computational comparison of different algorithms for very large p-median problems

In this paper, we propose a new method for solving large scale p-median problem instances based on real data. We compare different approaches in terms of runtime, memory footprint and quality of solutions obtained. In order to test the different methods on real data, we introduce a new benchmark for the p-median problem based on real Swedish data. Because of the size of the problem addressed, up to 1938 candidate nodes, a number of algorithms, both exact and heuristic, are considered. We also propose an improved hybrid version of a genetic algorithm called impGA. Experiments show that impGA behaves as well as other methods for the standard set of medium-size problems taken from Beasley’s benchmark, but produces comparatively good results in terms of quality, runtime and memory footprint on our specific benchmark based on real Swedish data.

A branch-and-price approach to p-median location problems

This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modifies; the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially difficult instances to the traditional column generation and also with some large-scale instances. (C) 2004 Elsevier Ltd. All rights reserved.