P-median Location Model Research Articles

Hybrid manufacturing—Locating AM hubs using a two-stage facility location approach

Hybrid Manufacturing is defined as the integration of Additive Manufacturing (AM), specifically metal AM, with traditional manufacturing post-processing such as heat treatment and machining. Hybrid AM enables Small and Medium Enterprises (SME) who can offer post-processing services to integrate into the growing AM supply chain. Most near-net metal AM parts require heat treatment processes (e.g. residual stress relieving/annealing) before machining to achieve final engineering specification. This research investigates a two-stage facility model to optimize the locations and capacities for new metal AM hubs which require two sequential post-processing services: heat treatment and machining. Using North American Industry Classification System (NAICS) data for machine shops and heat treatment facilities in the U.S., a p-median location model is used to determine the optimal locations for AM hub centers based on: (1) geographical data, (2) demand and (3) fixed and operational costs of hybrid-AM processing. Results from this study have identified: (a) candidate US counties to locate metal AM hubs, (b) total cost (fixed, operational and transportation), (c) capacity utilization of the AM hubs and (d) demand assignments across machine shops – heat treatment facilities – AM hubs. It was found that 2-stage p-Median model identified 22 A M hub locations as the initial sites for AM hubs which grows to 35 A M hubs as demand increases. It was also found that relatively fewer number of heat treatment facilities than machine shops resulted in a more concentrated locations of AM hubs. In addition, transportation costs were not adversely affected by the inclusion of as-build plates and showed that including heat treatment facilities as part of the hybrid AM supply chain will be mutually beneficial to all stakeholders of metal hybrid AM supply chain, i.e. AM → Heat treatment → Machining.

Optimal Algorithms for Integer Inverse Undesirable p-Median Location Problems on Weighted Extended Star Networks

This paper is concerned with the problem of modifying the edge lengths of a weighted extended star network with n vertices by integer amounts at the minimum total cost subject to be given modification bounds so that a set of p prespecified vertices becomes an undesirable p-median location on the perturbed network. We call this problem as the integer inverse undesirable p-median location model. Exact combinatorial algorithms with $$ {\mathcal {O}}\left( p^2 n \log n\right) $$ and $${{\mathcal {O}}}\left( p^{2}(n \log n+ n \log \eta _{\max })\right) $$ running times are proposed for solving the problem under the weighted rectilinear and weighted Chebyshev norms, respectively. Furthermore, it is shown that the problem under the weighted sum-type Hamming distance with uniform modification bounds can be solved in $$ {\mathcal {O}}(p^2n \log n)$$ time.

English

In this study an economic analysis was conducted to evaluate problem associated with a geographical information system (GIS) using facility location models for the p-median in order to optimize the location of aerodromes for the aerial fertilization (coverage fertilization) of eucalyptus plantations. The location model was tested on a 9,095.65 ha farm located in the Tres Lagoas municipality in the Mato Grosso do Sul State, in Brazil. The non-capacitated p-median location model, available in ArcGIS, was evaluated in the location-allocation module. Simulations were performed based on one to five aerodromes. The fertilization and setup costs were calculated for each scenario. The results showed that the p-median location model was efficient in determining the optimal location of aerodromes. The economic analysis of the location model found that the lowest costs are incurred when using three aerodromes. Key words: Combinatorial optimization, operational research, aerial fertilization.

A stochastic mathematical model to locate field hospitals under disruption uncertainty for large-scale disaster preparedness

In this study, we consider field hospital location decisions for emergency treatment points in response to large scale disasters. Specifically, we developed a two-stage stochastic model that determines the number and locations of field hospitals and the allocation of injured victims to these field hospitals. Our model considers the locations as well as the failings of the existing public hospitals while deciding on the location of field hospitals that are anticipated to be opened. The model that we developed is a variant of the P-median location model and it integrates capacity restrictions both on field hospitals that are planned to be opened and the disruptions that occur in existing public hospitals. We conducted experiments to demonstrate how the proposed model can be utilized in practice in a real life problem case scenario. Results show the effects of the failings of existing hospitals, the level of failure probability and the capacity of projected field hospitals to deal with the assessment of any given emergency treatment system’s performance. Crucially, it also specifically provides an assessment on the average distance within which a victim needs to be transferred in order to be treated properly and then from this assessment, the proportion of total satisfied demand is then calculated.

Improving Accessibility and Efficiency of Service Facility through Location-Based Approach: A Case Study at Narvik University College

Location problem of service facility has never lost its appeal to both academics and practitioners due to the complexity in balancing availability, responsiveness and efficiency. In this paper, a location-based study is performed in order to improve the accessibility of service facility in terms of availability and responsiveness for customers as well as the efficiency for service providers. This study employs two well-known location models for service facility: Maximal covering location model which aims to maximize the coverage of customer demands with limited number of facilities (efficiency) and p-median location model which aims to minimize the overall distance travelled from customs to service facilities (accessibility), and location-based comparison of the two solutions in a case study at the 3rd floor of the main building of Narvik University College (NUC) for improving the overall performance of printing service is conducted so as to illustrates a deep insight of real-world application. The optimal solutions for maximizing the overall performance are obtained under different scenarios, and Lingo software is applied for resolving the computational optimization problems.

Optimizing the Electric Charge Station Network of EŞARJ

In this study, we adopt the classic capacitated p-median location model for the solution of a network design problem,in the domain of electric charge station network design, for a leading company in Turkey. Our model encompasses the location preferences of the company managers as preference scores incorporated into the objective function. Our model also incorporates the capacity concerns of the managers through constraints on maximum number of districts and maximum population that can be served from a location. The model optimally selects the new station locations and the visualization of model results provides additional insights.

Network Voronoi Diagram Heuristic-based Particle Swarm Continuous Spatial Optimization Modeling

Spatial optimization modeling for multi facilities in urbanized area is a practical and key technique,and it can provide balance configuration optimization and spatial decision support for urban public resource. A method of particle swarm spatial optimization modeling for multi facilities location based on network Voronoi diagram heuristic is proposed in this paper, in which we presented respectively some p-median location models and maximal covering location models by using ordinary Voronoi diagram heuristic and network Voronoi diagram heuristic. Those models can quantitatively extract the demands coved by the function and service of facilities through the Voronoi diagrams, and inspire spatial optimization to maximize the coverage for distributed demands by minimizing overlapped coverage. The proposed p-median location model considers the factor of demand attenuation with path distance, and the proposed maximal covering model takes it into account that facility's service provides full coverage for the demands within maximal coverage radius and partial attenuation coverage for the demands without maximal coverage radius. The genetic evolution mechanism and the dynamic neighborhood structure of particles simulated by ordinary Voronoi diagram are integrated in the particle swarm spatial optimization to improve global search and optimization performance of the algorithm. Through the research of spatial optimization configuration experiments for multi facilities in experimental city, the proposed method has been verified to be the effective and practical, it can be applied for the spatial location optimization decision in urbanized area.

A bilevel mixed-integer program for critical infrastructure protection planning

Vulnerability to sudden service disruptions due to deliberate sabotage and terrorist attacks is one of the major threats of today. In this paper, we present a bilevel formulation of the r-interdiction median problem with fortification (RIMF). RIMF identifies the most cost-effective way of allocating protective resources among the facilities of an existing but vulnerable system so that the impact of the most disruptive attack to r unprotected facilities is minimized. The model is based upon the classical p-median location model and assumes that the efficiency of the system is measured in terms of accessibility or service provision costs. In the bilevel formulation, the top level problem involves the decisions about which facilities to fortify in order to minimize the worst-case efficiency reduction due to the loss of unprotected facilities. Worst-case scenario losses are modeled in the lower-level interdiction problem. We solve the bilevel problem through an implicit enumeration (IE) algorithm, which relies on the efficient solution of the lower-level interdiction problem. Extensive computational results are reported, including comparisons with earlier results obtained by a single-level approach to the problem.

The influence of data aggregation on the stability of p-median location model solutions : Alan T. Murray and Jonathan M. Gottsegen Geographical Analysis Vol. 29, No. 3, 1997, pp. 200–213

The influence of data aggregation on the stability of p-median location model solutions : Alan T. Murray and Jonathan M. Gottsegen Geographical Analysis Vol. 29, No. 3, 1997, pp. 200–213

A general construct for the zonally constrained p-median problem

The well-known p-median location model is designed to site p facilities with respect to population centers such that the average travel distance of facility users is minimized. Many locational applications would benefit from a median problem that distributes, according to the discretion of the model user, some or all of the p facilities among defined zones. The notion of this ‘zonally constrained’ p-median can be defined as: locate p facilities to achieve the minimum average user distance while ensuring that (in those zones with such requirements) each zone receives at least its allotted minimum number of facilities and no more than its allotted maximum number of facilities. Authors of three recent articles have defined subsets of this problem but have not developed a completely general form. Previous work falls short in one or more of the following respects: (1) defining a minimum facility limit for zones other than one, (2) including any kind of maximum facility limit for zones, (3) allowing demand to b...