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We consider a continuous location problem forpconcentric circles serving a given set of demand points. Each demand point is serviced by the closest circle. The objective is to minimize the sum of weighted distances between demand points and their closest circle. We analyze and solve the problem when demand is uniformly and continuously distributed in a disk and when a finite number of demand points are located in the plane. Heuristic and exact algorithms are proposed for the solution of the discrete demand problem. A much faster heuristic version of the exact algorithm is also proposed and tested. The exact algorithm solves the largest tested problem with 1000 demand points in about 3.5 hours. The faster heuristic version solves it in about 2 minutes. [ABSTRACT FROM AUTHOR]

This article introduces a risk-averse stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities. The sizes and locations of the response facilities and the inventory levels of relief supplies at each facility are determined while guaranteeing a certain level of network reliability. A probabilistic constraint on the existence of a feasible flow is introduced to ensure that the demand for relief supplies across the network is satisfied with a specified high probability. Responsiveness is also accounted for by defining multiple regions in the network and introducing local probabilistic constraints on satisfying demand within each region. These local constraints ensure that each region is self-sufficient in terms of providing for its own needs with a large probability. In particular, the Gale–Hoffman inequalities are used to represent the conditions on the existence of a feasible network flow. The solution method rests on two pillars. A preprocessing algorithm is used to eliminate redundant Gale–Hoffman inequalities and then proposed models are formulated as computationally efficient mixed-integer linear programs by utilizing a method based on combinatorial patterns. Computational results for a case study and randomly generated problem instances demonstrate the effectiveness of the models and the solution method. [ABSTRACT FROM PUBLISHER]

Most of the literature on facility location assumes a fixed setup and a linear variable cost. It is known, however, that as volume increases cost savings are achieved through economies of scale, but when the volume exceeds a certain level, diseconomies of scale occur and marginal costs start to increase. This is best captured by an inverse S-shaped cost function that is initially concave and then turns convex. This article studies such a class of location problems and solution methods are proposed that are based on Lagrangian relaxation, column generation, and branch-and-bound methods. A nonlinear mixed-integer programming formulation is introduced that is decomposable by environment type; i.e., economies or diseconomies of scale. The resulting concave and convex subproblems are then solved efficiently as piecewise convex and concave bounded knapsack problems, respectively. A heuristic solution is found based on dual information from the column generation master problems and the solution of the subproblems. Armed with the Lagrangian lower bound and the heuristic solution, the procedure is embedded in a branch-and-price-type algorithm. Unfortunately, due to the nonlinearity of the problem, global optimality is not guaranteed, but high-quality solutions are achieved depending on the amount of branching performed. The methodology is tested on three function types and four cost settings. Solutions with an average gap of 1.1% are found within an average of 20 minutes. [ABSTRACT FROM AUTHOR]

This article considers a class of dynamic single-article facility location problems in which the facility must determine order and inventory levels to meet the dynamic demands of the customers over a finite horizon. The motivating application of this class of problems is in military logistics and the decision makers in this area are not only concerned with the logistical costs of the facility but also with centering the facility among the customers in each time period in order to be able to provide other services. Both the location plan and inventory plan of the facility in the problem must be determined while considering these different metrics associated with the performance of these plans. Effective dynamic programming algorithms for this class of problem are provided for both of these metrics. These dynamic programming algorithms are utilized in order to construct the efficient frontier associated with these two metrics in polynomial time. Computational testing indicates that these algorithms can be used in planning activities for military logistics. [Supplemental materials are available for this article. Go to the publisher’s online edition ofIIE Transactionsfor a worst-case example of constructing the efficient frontier.] [ABSTRACT FROM AUTHOR]

This article addresses a stochastic facility location and vehicle assignment problem in which customers are served by full return trips. The problem consists of simultaneously locating a set of facilities, determining the vehicle fleet size at each facility, and allocating customers to facilities and vehicles in the presence of random travel times. Such travel times can arise, for example, due to daily traffic patterns or weather-related disturbances. These various travel time conditions are considered as different scenarios with known probabilities. A stochastic programming with bounded penalties model is presented for the problem. In order to solve the problem, integer programming and two-level and three-level logic-based Benders’ decomposition models are proposed. Computational experiments demonstrate that the Benders’ models were able to substantially outperform the integer programming model in terms of both finding and verifying the optimal solution. [ABSTRACT FROM AUTHOR]

Both public and private facilities often have to provide adequate service under a variety of conditions. In particular travel times, that determine customer access, change due to changing traffic patterns throughout the day, as well as a result of special events ranging from traffic accidents to natural disasters. This article studies the maximum covering location problem on a network with travel time uncertainty represented by different travel time scenarios. Three model types—expected covering, robust covering, and expected p-robust covering—are studied; each one is appropriate for different types of facilities operating under different conditions. Exact and approximate algorithms are developed. The models are applied to the analysis of the location of fire stations in the city of Toronto. Using real traffic data it is shown that the current system design is quite far from optimality. The best locations for the four new fire stations that the city of Toronto is planning to add to the system are determined and alternative improvement plans are discussed. [ABSTRACT FROM AUTHOR]

Recent research has pointed out that the optimal strategies to mitigate supply disruptions and demand uncertainty are often mirror images of each other. In particular, risk diversification is favorable under the threat of disruptions and risk pooling is favorable under demand uncertainty. This article studies how dynamic sourcing in supply chain design provides partial benefits of both strategies. Optimization models are formulated for supply chain network design with dynamic sourcing under the risk of temporally dependent and temporally independent disruptions of facilities. Using computational experiments, it is shown that supply chain networks that allow small to moderate degrees of dynamic sourcing can be very robust against both disruptions and demand uncertainty. Insights are attained on the optimal degree of dynamic sourcing under different conditions. [ABSTRACT FROM PUBLISHER]