The present paper deals with a trade off between cost and pipeline at a given time in a transportation problem. The time lag between commissioning a project and the time when the last consignment of goods reaches the project site is an important factor. This motivates the study of a bi criteria transportation problem at a pivotal time T. | Yugoslav Journal on Operations Research 23(2013) Number 2, 197–211 DOI: A COST AND PIPELINE TRADE-OFF IN A TRANSPORTATION PROBLEM Vikas SHARMA Department of Mathematics, Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India mathvikas@ Rita MALHOTRA Kamla Nehru College, University of Delhi, Khel Gaon Marg, New Delhi-110049, India drritamalhotra@ Vanita VERMA Department of Mathematics, Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India vanita@ Received: January, 2013 / Accepted: March, 2013 Abstract: The present paper deals with a trade off between cost and pipeline at a given time in a transportation problem. The time lag between commissioning a project and the time when the last consignment of goods reaches the project site is an important factor. This motivates the study of a bi-criteria transportation problem at a pivotal time T . An exhaustive set E of all independent cost-pipeline pairs (called efficient pairs) at time T is constructed in such a way that each pair corresponds to a basic feasible solution and in turn, gives an optimal transportation schedule. A convergent algorithm has been proposed to determine non-dominated cost pipeline pairs in a criteria space instead of scanning the decision space, where the number of such pairs is large as compared to those found in the criteria space. 197 198 Vikas Sharma, Rita Malhotra, Vanita Verma / A Cost And Pipeline Keywords: Transportation problem, Combinatorial optimization, Bottleneck transportation problem, Bi-criteria transportation problem, Efficient points MSC: 90B06, 90C05, 90C08 1. INTRODUCTION The cost minimization transportation problem is defined as: XX min cij xij (P1 ) i∈I j∈J subject to the following constraints: X xij = ai , ai > 0, i ∈ I, j∈J X xij = bj , bj > 0, j ∈ J, i∈I xij ≥ 0, ∀ (i, j) ∈ I × J () where I is the index set of supply points, J is .
