A MULTIOBJECTIVE APPROACH TO

TRANSPORTATION NETWORK DESIGN

PRESENTED BY: SUBMITTED TO:Umang Ugra Prof. S. KannanBhawana GoelHitesh MehtaPrateek Singh BapnaSakshi Garg

Transportation Network Design Problem Transportation problem is a special kind of

LP problem in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the source and the destination respectively, such that the total cost of transportation is minimized.

Formerly, this problem was studied under the single objective of the minimization of : total path length travelling time investment cost

Applications

Location 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

Article Chosen:

A Multiobjective Approach to Transportation Network DesignAuthors:Alpaslan FiglaliAtaq ScysalIstanbul Technical University, Faculty of Management, Industrial Engineering Department, Macka, Istanbul, TurkeySource: IEEE

Objectives

In this article, a two-layer transportation network design model with three objectives is introduced.

The objectives are: The minimization of the primary path length (or

traveling time) from a predetermined starting node to a predetermined terminus node.

The minimization of the total distance traversed by the demand to reach a node on the primary path.

The minimization of the total network construction cost

Integer Programming Formulation of the Problem

Assumptions: Demand exists at every node. Demand at every node must be satisfied. 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.

Flow along all arcs is incapacitated.

All arc costs are non-negative. There is no budget constraint. Demands and costs are deterministic. Primary and secondary arc costs are not

proportional to the arc length. Transshipment costs are neglected

Formulations and Constraints

Xi,j = (0,1) (8)

Yi,j = (0,1) (9)

Z1 = ∑i ∑j Li,j Xi,j (10)Z2 = ∑i ∑j Ci,j Xi,j + ∑i ∑j C’i,j Xi,j (11)Z3 = ∑i ∑j Di Ti,j Yi,j (12)

WhereDi = demand at node i

Li,j = length of arc (i,j)

Ti,j = distance (or travel time) via the shortest path from node i to node jCi,j = the primary road construction cost of arc (i, j)

C’i,j = the secondary road construction cost of arc (i, j)Xi,j = 1 if a primary path connects node i to node j

0 if otherwise

Yi,j = 1 if a secondary path connects node i and node j to reach the primary path

0 if otherwise Pi = (j/a path from node i to node j is defined) Ni = (j/arc (i, j) exists) Mj = (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 |Q| = the cardinality of subset Q

Proposed Method

Incorporates a K-shortest path algorithm.STEPS:

1. By using this algorithm, all primary paths, from a predetermined starting node to a predetermined terminus node are determined.

2. After finding all shortest paths, all secondary path combinations are determined for each primary path.

3. The objective values are calculated for all combinations.

4. After eliminating the non-efficient solutions, the qualitative criteria are included.

5. The decision maker is asked to scale the efficient solutions according to:alternate transportation facilities (Z4)environmental concerns (Z5)socio-economic structure of the nodes which are covered by the path ( i e . regional development) (Z6).

For each objective, the best values are chosen to find the ideal point proposed by Zeleny. The weighted Euclidian distance between each solution and ideal point are calculated as follows:

d = [(Z1* - Z1)2 + (Z2* - Z2)2 + … + (Zn* - Zn)2]1/2

The solution having the minimum total weighted Euclidian distance is selected.

Conclusion

The major drawbacks to solving the model as a relaxed linear program are the necessity for an interactive solution technique to eliminate sub tours and the computational burden imposed by the branch and bound algorithm.

And also the need to combine all objective functions in one function in a weighted form. Because of these drawbacks the authors proposed an interactive combinatorial solution method especially preferable for small networks.

In general, the integer programming solution approach yields only one feasible solution, the optimal one.

Proposed method, however, yields the whole set of feasible solutions. Since many network design problems are multi objective in nature these additional feasible solutions may be of interest to the network planner.

But of course the proposed method can be used efficiently only for small networks.

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