Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority's point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution; but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the flow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the importance of the number and locations of shelter sites and the trade-off between efficiency and fairness. © 2014 Elsevier Ltd

Shelters are safe facilities that protect a population from possible damaging effects of a disaster. For that reason, shelter location and traffic assignment decisions should be considered simultaneously for an efficient evacuation plan. In addition, as it is very difficult to anticipate the exact place, time, and scale of a disaster, one needs to take into account the uncertainty in evacuation demand, the disruption/degradation of evacuation road network structure, and the disruption in shelters. In this study, we propose an exact algorithm based on Benders decomposition to solve a scenario-based two-stage stochastic evacuation planning model that optimally locates shelters and that assigns evacuees to shelters and routes in an efficient and fair way to minimize the expected total evacuation time. The second stage of the model is a second-order cone programming problem, and we use duality results for second-order cone programming in a Benders decomposition setting. We solve practical-size problems with up to 1,000 scenarios in moderate CPU times. We investigate methods such as employing a multicut strategy, deriving Pareto-optimal cuts, and using a preemptive priority multiobjective program to enhance the proposed algorithm. We also use a cutting plane algorithm to solve the dual subproblem since it contains a constraint for each possible path. Computational results confirm the efficiency of our algorithms.

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Shelter location and traffic allocation decisions are critical for an efficient evacuation plan. In this study, we propose a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to nearest shelters and to shortest paths within a tolerance degree to minimize the expected total evacuation time. Our model considers the uncertainty in the evacuation demand and the disruption in the road network and shelter sites. We present a case study for a potential earthquake in Istanbul. We compare the performance of the stochastic programming solutions to solutions based on single scenarios and mean values.

Depolama alanları tedarik zinciri yönetiminde kritik öneme sahiptir. Ürün dağıtımı yapmak ve ürünleri depolamak maksadıyla kullanılırlar. Bu çalışmada, bir imalat firması tarafından yönetilen bir depolama alanının depolama yeri ataması kararları optimize edilmiştir. Depo yönetim sistemi tarafından kaydedilen tarihsel verileri kullanarak doğrusal olmayan karışık tam sayılı bir problem, yani depolama alanı atama problemini çözmek için bir matematiksel model sunulmuştur. İki ürünün beraber toplanma sıklığı ve her ürünün toplanma sıklığını baz alarak sırasıyla kümeleme ve ABC analizi yapılmıştır ve sonuçlar matematiksel modele yerleştirilmiştir. Aynı zamanda, firmanın depolama yeri problemini çözmek için açgözlü algoritma geliştirilmiştir. Elde edilen bulgular ışığında, mevcut sistem ve önerilen sistemin G/Ç noktasına olan mesafelerinin karşılaştırılması yapılmış, %49.99'a varan iyileşme görülmüştür.Warehouses are crucial in supply chain management. They are used to distribute and store products. In this study, we optimize storage location assignment decisions in a warehouse managed by a manufacturing firm. A mathematical model is introduced to solve the nonlinear mixed integer optimization problem (NLMIP), i.e., the Storage Location Assignment Problem (SLAP) by using historical data from warehouse management system (WMS). Clustering and ABC analysis are conducted based on the number of times two items are picked together and the picking frequency of items, respectively and results are embedded into our optimization model. Also, a greedy heuristic is developed to solve SLAP of the firm. Analysis results show that there is an improvement of up to 49.99% in total distances between filled slots and the I/O point due to proposed solution compared to that of the current system.Anahtar kelimeler: Depolama yeri ataması, Ürün toplama, K-Ortalamalar kümelemesi, ABC analizi, Karışık tam sayılı karesel optimizasyon, Aç gözlü sezgisel.