Consensus Strategies for Signed Profiles on Graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.median;consensus function;median graph;majority rule;plurality strategy;Graph theory;Hamming graph;Johnson graph;halfcube;scarcity strategy;Discrete location and assignment;Distance in graphs

Service Center Location with Decision Dependent Utilities

We study a service center location problem with ambiguous utility gains upon receiving service. The model is motivated by the problem of deciding medical clinic/service centers, possibly in rural communities, where residents need to visit the clinics to receive health services. A resident gains his utility based on travel distance, waiting time, and service features of the facility that depend on the clinic location. The elicited location-dependent utilities are assumed to be ambiguously described by an expected value and variance constraint. We show that despite a non-convex nonlinearity, given by a constraint specified by a maximum of two second-order conic functions, the model admits a mixed 0-1 second-order cone (MISOCP) formulation. We study the non-convex substructure of the problem, and present methods for developing its strengthened formulations by using valid tangent inequalities. Computational study shows the effectiveness of solving the strengthened formulations. Examples are used to illustrate the importance of including decision dependent ambiguity.Comment: 29 page

INTEGRATED HUB LOCATION AND CAPACITATED VEHICLE ROUTING PROBLEM OVER INCOMPLETE HUB NETWORKS

Hub location problem is one of the most important topics encountered in transportation and logistics management. Along with the question of where to position hub facilities, how routes are determined is a further challenging problem. Although these two problems are often considered separately in the literature, here, in this study, the two are analyzed together. Firstly, we relax the restriction that a vehicle serves between each demand center and hub pair and propose a mixed-integer mathematical model for the single allocation p-hub median and capacitated vehicle routing problem with simultaneous pick-up and delivery. Moreover, while many studies in hub location problem literature assume that there is a complete hub network structure, we also relax this assumption and present the aforementioned model over incomplete hub networks. Computational analyses of the proposed models were conducted on various instances on the Turkish network. Results indicate that the different capacity levels of vehicles have an important impact on optimal hub locations, hub arc networks, and routing design

Consensus strategies for signed profiles on graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from (+,-). Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Consensus Strategies for Signed Profiles on Graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Lojistik merkezi yer seçimi ve yerleştirme problemi

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Lojistik Merkez Yerleşimi, literatürde tesis yerleşim problemlerinin özel bir durumu olarak sınıflandırılmaktadır. Bir lojistik merkezin, nereye konumlandırılacağı birçok faktörü dikkate alarak karar verilmesi gereken karmaşık bir problemdir. Konumu doğru seçilmiş ve yük akışına göre optimal yerleşimi yapılmış bir lojistik merkez verimli ve bulunduğu çevre için kazançlı bir yatırım aracıdır. Bu çalışmada; lojistik merkez yer seçimi ve yerleşim problemi üzerinde durulmuştur. Öncelikli olarak, Aksiyomatik Tasarım (AT) ve Ağırlıklı Bulanık Aksiyomatik Tasarım (ABAT) yöntemleri ile Kayseri iline özel yapılması planlanan lojistik merkez için en uygun yerin belirlenmesi üzerinde çalışılmıştır. Sonrasında ise, lojistik merkez içerisinde olması gereken tesis sayıları ve onların alan değerleri dikkate alınarak oluşturulmuş karma tam sayılı doğrusal programlama problemi (MILP) ile yerleşim yapılmıştır. Lojistik merkez yerleşim problemi, NP-hard sınıfına ait olduğu için, belirli tesis sayısı büyüklüğünden sonra MILP modelinin sağlıklı sonuç verememe durumu dikkate alınarak, Meta sezgisel bir yaklaşım tercih edilerek karınca kolonisi algoritması ile çözülmüştür. Lojistik merkez yerleşimi için geliştirilen algoritma, literatürde bulunan kıyaslama problemleri ile test edilerek üstünlüğü ortaya konulmuştur. Çalışmada geliştirilen metot, lojistik merkezlerin yerleşimlerinde kullanılması açısından ilk olmakla birlikte, farklı tesis yerleşim problemlerinin çözümünde de kullanılabileceği aşikardır.Logistics Center Location is classified as a special case of facility layout problems in the literature. The location of a logistics center is a complex problem that needs to be decided by considering many factors. A logistics center with the right location and an optimal location based on the load flow is efficient and a profitable investment tool for the environment. In this study, logistics center location selection and design problem were studied. Firstly, Axiomatic Design and Weighted Fuzzy Axiomatic Design methods were used to determine the most suitable location for the logistics center planned to be built in Kayseri province. After that, it was placed with the mixed integer linear programming problem (MILP) which formed with taking into consideration the number of facilities and their field values which should be in the logistics center. Since the logistics center location design problem belongs to the NP-hard class, the proposed MILP model was unable to produce acceptable results after a certain number of facilities, hereby a meta-heuristic approach was preferred and the problem was solved by the ant colony algorithm. The developed algorithm was tested on the well-known benchmarking problems in the literature and its advantage was demonstrated. In addition, it can be claimed that the proposed algorithm in this study is the first attempt in terms of the designing of a logistics center. I believe that and it can be used to solve different location problem

The design of cement distribution network in Myanmar : a case study of "X" cement industry

The network design problem is one of the most comprehensive strategic decision issues that need to be optimized for the long-term efficient operation of whole supply chain. The problem treated in this thesis is a capacitated location allocation planning of distribution centers for the distribution network design. The distribution network in this research is considered from plants to distribution centers and distribution centers to demand points. The research will explore the optimal number and locations of cement distribution center of “X” cement industry in Myanmar. The Mixed Integer Linear Programming (MILP) was developed as a tool to solve optimization problem which involves 3 manufacturing plants, 6 distribution centers and 6 market regions. The data collection was done by the company. The (MILP) model provides useful information for the Company about which distribution centers should be opened and what would be the best distribution network in order to maximize profit while still satisfies the customers’ demand. In this study, we proposed three scenarios which are scenario two, six and eight. In all scenarios, the solution was to have only two distribution centers from Mandalay and Meikhtila markets are recommended to open in the distribution network

The Two-Echelon Multi-products Location-Routing problem with Pickup and Delivery: Formulation and heuristic approaches

The two-echelon location routing problem (LRP-2E) considers the first-level routes that serve from one depot a set of processing centers, which must be located and the second-level routes that serve customers from the open processing centers. In this paper, we consider an extension of the LRP-2E, where the second level routes include three constraints, that have not been considered simultaneously in the location routing literature, namely, multi-product, pickup and delivery and the use of the processing center as intermediate facility in the second-level routes. This new variant is named two-Echelon Multi-products Location-Routing problem with Pickup and Delivery (LRP-MPPD-2E). The objective of LRP-MPPD-2E is to minimize both the location and the routing costs, considering the new constraints. The first echelon deals with the selection of processing centers from a set of potential sites simultaneously with the construction of the first-level routes, such that each route starting from the main depot, visits the selected processing centers and returns to the main depot. The second echelon aims at assigning customers to the selected processing centers and defining the second-level routes. Each second-level route, starts at a processing center, visits a set of customers, through one or several processing centers, and then returns to the first processing center. We present a mixed integer linear model for the problem and use a Cplex solver to solve small-scale instances. Furthermore, we propose non-trivial extensions of nearest neighbour and insertion approaches. We also develop clustering based approaches that seldom investigated on location routing. Computational experiments are conducted to evaluate and to compare the performances of proposed approaches. The results confirm the effectiveness of clustering approaches.