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Ulaşım şebekesi tasarımı için çok amaçlı bir model

A Multiobjective approach to transportation network design

  1. Tez No: 21809
  2. Yazar: ALPASLAN FIĞLALI
  3. Danışmanlar: PROF. DR. ATAÇ SOYSAL
  4. Tez Türü: Doktora
  5. Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1992
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 176

Özet

ÖZET Leonard Euler'in 1736'da incelediği Königsberg Köprüleri probleminden bu yana ulaşım sistemlerinin planlanması ve tasarımı konusunda çalışılmaktadır. Son yıllara kadar, bu incelemelerin odak noktasını toplam uzaklığın veya toplam seyahat süresinin ya da yatırım maliyetlerinin minimizasyonu oluşturmuştur ve problemlerde bu sayılan amaçlardan yalnızca birisi temel alınmıştır. Ancak ulaşım problemlerinin doğasmda bir çok amaçlılık söz konusudur ve amacın birden fazla olması genellikle beraberinde bir takım çelişkileri getirmektedir. Tüm amaçlan aynı anda optimize eden bir çözüm bulunamadığında, amaçlar arasmda bir ödünleşmeye gidilerek en uzlaşık çözüm seçilmektedir. Bu çalışmada ulaşım şebekesi tasarım probleminin çok amaçlı çözümüne yönelik bir model sunulmaktadır. Amaçlar: (1) Belirli bir başlangıç düğümünden, belirli bir bitiş düğümüne olan ana yol uzunluğunun rninimizas- yonu, (2) ana yol üzerinde bulunmayan düğümlerdeki talebin anayola erişmek için katetmesi gereken, taleple ağırlıklandınlmış toplam yol uzunluğunun minimizasyonu ve (3) anayol ve buna bağlı tali yollardan oluşan şebekenin toplam yapım maliyetinin minimizasyonudur. Problem 0-1 tamsayılı programlama modeli olarak formüle edilmiş ve çözüm aşamasında, karar vericinin bulunabileceği üç değişik karar durumu için farklı çözüm yöntemteri- önerilmiştir. Karar vericiyle etkileşim sonucu- planlama: durumuna uygun ek kriterlerin de probleme eklenerek, en iyi uzlaşık çözümün belirlenmesi müm kündür. VUJL

Özet (Çeviri)

SUMMARY A MULTIOBJECnVE APPROACH TO TRANSPORTATION NETWORK DESIGN Transportation Network Design Problem has been investigated by many researchers. Formerly, this problem was studied under the single objective of the minimization of total path length, travelling time or investment cost. Recently, multiobjective models have been developed. The presence of more than one objective usually results in conflict among the objectives, for example the least cost path may not be convenient for the majority of the population to reach the primary path in a reasonable time period or may be inconvenient due to pollution of the environment. Usually a solution which optimizes all the objectives simultaneously can not be found, therefore a trade-off among the objectives is accepted and the most compromising solution is selected. The main objectives met in Transportation Network Design Problems are cost, path length, demand satisfaction, travelling time, accessibility, capacity, revenue and environmental concerns. In this thesis, modelling and solution of the transportation network design problem with three objectives is interested. These objectives are: a) to minimize the primary path length (or travelling time) from a predetermined starting node to a predetermined terminus node. b) to minimize the total distance traversed by the demand to reach the primary path. c) to minimize the total road construction cost. Such transportation network design problems are encountered in the applications of the construction of a new rail line between two major cities of a developing country; in the construction of networks of highways and unimproved roads; in the design of airline routes and in the design of energy distribution systems. The first ideas on the Multiobjective.Transportation Network Design Problem belong to Dantzig et al (1966). The first studies of multiobjective transportation planning, focus on evaluation of alternative plans, rather than on making alternative plans (Ferguson, 1966; Schimpeler and Grecco, 1968; IXGolden et al, 1981). In the 1980's, new models have been developed by enlarging the covering concept from location problems to network design problems. Secondary path travel distance is also a major subject in transportation network design problems with the shortest path objective. In this subject, four models can be mentioned. They are the Shortest Covering Path Problem (Current et al, 1984), the Maximum Covering/Shortest Path Problem (Current et al, 1985 a), the Median Shortest Path Problem (Current et al, 1987), and the Minimum Covering/Shortest Path Problem (Current et al, 1988). The Shortest Covering Path Problem stipulates that the primary path be within some predetermined distance of all the demand nodes. The Maximum Covering/Shortest Path Problem is a two objective problem. The objectives are to minimize total path length and to maximize the demand within some predetermined distance from the path. The Median Shortest Path Problem also has two objectives. Its objectives are to minimize the total distance traversed by the demand to reach the primary path, and to minimize the total path length. The Minimum Covering/Shortest Path Problem's goal is the minimization of the negative effects of path on population. Therefore, the objectives are to minimize the path length and to minimize the population covered by the path. Another multiobjective modelling approach is the Covering Salesman Problem. The objectives are to cover all the demand nodes and to find the path with minimum length which returns to the predetermined starting node. This approach differs from the Travelling Salesman Problem in that, covering all nodes is sufficient, instead of passing from all nodes. The following assumptions are made to build the integer programming model of the networks with predetermined starting and terminus nodes with the objectives of minimum path length, the minimization of total distance traversed by the demand to reach the primary path and the minimization of the total road construction cost 1. Demand exists at every node. 2. Demand at every node must be satisfied. 3. Demand at a node is satisfied if either the node is on the primary path or is connected to the primary path via a secondary path. 4. Flow along all arcs in uncapacitated. 5. All arc costs are non-negative. 6. There is no budget constraint 7. Demands and costs are deterministics. 8. Transshipment costs are neglected.The defence of these assumptions depends, of course on the particular design setting in which the model is applied. However, as Magnanti and Wong (1984) have shown, these assumptions are not uncommon in network models because of the combinatorial nature of many network design problems. The problem can be formulated as an integer linear model, as follows: Minimize Z=(ZVZ212^ (1) Subject to E *u = i w ieMn E * J * x>n ik) ieM, keN, E^- + E Ytj = i i vf, im,» (5) yew* yePi rtf - E *i, * ° ; w,/) (6) ieAf^ E E xij ' + * ! = < > 0, if otherwise 1 if a secondary arc connects node i to node j Yjj ? = { to reach the primary path } 0, if otherwise Pi = {j / a path from node i to node j is defined} Nj = { j / arc (i,j) exists} M- = { i / arc (i,j) exists} node s = the starting node, node t = the terminus node, V = the set of nodes, Q = a nonempty subset of V 1 Q I = the cardinality of subset Q The variables in the formulation are X,. and Y4... If arc (i,j) is on the 1J 1,] v 'J' primary path, Xj = = 1 ; otherwise Xj, = 0. If arc (i,j) is on a secondary path which is connected to the primary path, Yj = = 1 ; otherwise Yj, = 0. Constraints (2) and (3) respectively ensure that the starting and the terminus nodes are on the primary path. Constraint set (4) ensures that, if one of the arcs entering node j is on the primary path, one of the arcs existing this node will also be on the primary path (If-j is not the starting or terminus node). Constraint set (5) ensures that each node is either on the primary path or on a secondary path connected to the primary path. Constraint set (6) prohibits a node, i, not on the primary path from assigning to another node, j, unless node j is on the primary path. xiiPrimary and secondary arc subtours are prohibited by constraint set (9), hence only one primary path is formed connecting the starting and the terminus nodes. Constraints (8) and (9) ensure that the variables Xj. and Yy are either“0”and“1”. Objective Equation (10) indicates the rninimization of total primary path length. Objective Equation (11) represents the minimization of total road construction cost. Objective Equation (12) indicates the minimization of the total distance traversed by the demand to reach the primary path. Solving the model without using constraint set (7), probably results in the formation of subtours in the solution. The appearance of subtours means that two or more nodes are not connected to the primary path. In that case, the appropriate subtour breaking constraints from constraint set (7) must be included and this modified problem solved. There is no guarantee that other subtours will not occur in the solution to this modified problem. Another way to avoid subtours, is to solve the model as relaxed continuous linear prograjiiming model. If fractional values for the variables occur, then a branch and bound algorithm may be employed to obtain 0 or 1 variable values. The procedure must be applied for all selected objective weights then after eliminating the non-efficient solutions, the qualitative criteria are included: The decision maker is asked to scale the efficient solutions according to alternate transportation facilites (Z^, environmental concerns (Z5)and, socio-economical structure of the nodes which are covered by the path (ie. regional development) (Zg). These values of the objectives are located in table form. For each objective, the best values are chosen to find the ideal point proposed by Zeleny (1977). The weighted Euclidian distance between each solution and ideal point are calculated as follows: d = [(Z\ - zxf + (Z*2 - z/ +(Z\-Zn)2}1/2 The solution having the minimum total weighted Euclidian distance is selected. In the model, three different solution procedure is suggested which depends on the preference position of the decision maker: if it's possible for the decision maker to compare the objectives precisely then it's convient to use Saaty (1977)'s pairwise comparision technique to find the objective weights, and the problem is solved as a single objective integer linear prograrmning model with a combined objective function. XlllIf it is'not possible for the decision maker to assign weights but to say how the objectives are ranked, then the problem is solved as a lexicographic integer linear programming model. If the decision maker doesn't have any idea about the objectives then it's suggested to use Steuer (1976, 1977)'s contracting cones method to find the non-dominated solutions of the problem. XIV

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