Risk Management in Uncapacitated Facility Location Models with Random Demands

In this paper we consider a location-optimization problem where the classical uncapacitated facility location model is recast in a stochastic environment with several risk factors that make demand at each customer site probabilistic and correlated with demands at the other customer sites. Our primary contribution is to introduce a new solution methodology that adopts the mean–variance approach, borrowed from the finance literature, to optimize the “Value-at-Risk” (VaR) measure in a location problem. Specifically, the objective of locating the facilities is to maximize the lower limit of future earnings based on a stated confidence level. We derive a nonlinear integer program whose solution gives the optimal locations for the p facilities under the new objective. We design a branch-and-bound algorithm that utilizes a second-order cone program (SOCP) solver as a subroutine. We also provide computational results that show excellent solution times on small to medium sized problems

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Distribution planning in a weather-dependent scenario with stochastic travel times: a simheuristics approach

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.Peer ReviewedPostprint (published version

Distribution planning in a weather-dependent scenario with stochastic travel times: a simheuristics approach

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.Peer ReviewedPostprint (published version

Facility Location Planning Under Disruption

Facility Location Problems (FLPs) such as the Uncapacitated Facility Location (UFL) and the Capacitated Facility Location (CFL) along with the k-Shortest Path Problem (k-SPP) are important research problems in managing supply chain networks (SCNs) and related operations. In UFL, there is no limit on the facility serving capacity while in CFL such limit is imposed. FLPs aim to find the best facility locations to meet the customer demands within the available capacity with minimized facility establishment and transportation costs. The objective of the (k-SPP) is to find the k minimal length and partial overlapping paths between two nodes in a transport network graph. In the literature, many approaches are proposed to solve these problems. However, most of these approaches assume totally reliable facilities and do not consider the failure probability of the facilities, which can lead to notably higher cost. In this thesis, we investigate the reliable uncapacitated facility location (RUFL)and the reliable capacitated facility location (RCFL) problems, and the k-SPP where potential facilities are exposed to disruption then propose corresponding solution approaches to efficiently handle these problems. An evolutionary learning technique is elaborated to solve RUFL. Then, a non-linear integer programming model is introduced for the RCFL along with a solution approach involving the linearization of the model and its use as part of an iterative procedure leveraging CPLEX for facility establishment and customer assignment along with a knapsack implementation aiming at deriving the best facility fortification. In RUFL and RCFL, we assume heterogeneous disruption with respect to the facilities, each customer is assigned to primary and backup facilities and a fixed fortification budget allows to make a subset of the facilities totally reliable. Finally, we propose a hybrid approach based on graph partitioning and modified Dijkstra algorithm to find k partial overlapping shortest paths between two nodes on a transport network that is exposed to heterogeneous connected node failures. The approaches are illustrated via individual case studies along with corresponding key insights. The performance of each approach is assessed using benchmark results. For the k-SPP, the effect of preferred establishment locations is analyzed with respect to disruption scenarios, failure probability, computation time, transport costs, network size and partitioning parameters

A taxonomy for emergency service station location problem

The emergency service station (ESS) location problem has been widely studied in the literature since 1970s. There has been a growing interest in the subject especially after 1990s. Various models with different objective functions and constraints have been proposed in the academic literature and efficient solution techniques have been developed to provide good solutions in reasonable times. However, there is not any study that systematically classifies different problem types and methodologies to address them. This paper presents a taxonomic framework for the ESS location problem using an operations research perspective. In this framework, we basically consider the type of the emergency, the objective function, constraints, model assumptions, modeling, and solution techniques. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions