In a transportation problem, generally, a single criterion of minimizing the total cost is considered. But in certain practical situations two or more objectives are relevant. For example, the objectives may be minimizations of total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation, etc. Clearly, this problem can be solved using any of the multiobjective linear programming techniques; but the computational efforts needed would be prohibitive in many cases. The computational complexity in these techniques arises from the fact that each of the methods finds the set of nondominated extreme points in the solution space where such extreme points are, generally, many. Therefore, this paper develops a method of finding the nondominated extreme points in the criteria space. Such extreme points in the criteria space would be generally less and only these are needed while choosing a nondominated solution for implementation. The method involves a parametric search in the criteria space. Although the method is developed with respect to a bicriteria transportation problem, it is applicable to any bicriteria linear program in general. The bottleneck criterion included as a third objective is particularly significant in time bound transportation schedules. A numerical example is included.programming: multiple criteria, transportation
Certain properties of a shortest chain subject to several side constraints are established. Based on these an implicit enumeration algorithm, that is, a generalization of the one given by Dijkstra for the case without any side constraint, is presented. Validation of the algorithm and an illustrative example are included.
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Consider a connected undirected graph GIN; El with N = S U P, the set of nodes, where P is designated as the set of Steiner points. A weight is associated with each edge ei of the set E. The problem of obtaining a minimal weighted tree which spans the set S of nodes has been termed in literature as the Steiner problem in graphs. A specialized integer programming (set covering) formulation is presented for the problem. The number of constraints in this formulation grows exponentially with the size of the problem. A method called the row generation scheme is developed to solve the above problem. The method requires knowing the constraints only implicitly. Several other problems which can be put in a similar framework can also be handled by the above scheme. The generality of the scheme and its efficiency is discussed. Finally the computational result is demonstrated.
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