Volume 51, Number 2, April-June 2017
|Page(s)||447 - 467|
|Published online||30 March 2017|
Capacitated two-stage time minimization transportation problem with restricted flow
1 University Institute Of Engineering and Technology, Panjab University, 160014 Chandigarh, India
2 Department of Mathematics, Panjab University, 160014 Chandigarh, India
Received: 15 December 2015
Accepted: 29 April 2016
This paper discusses a capacitated time minimization transportation problem in which transportation operation takes place in two stages. In the first stage, due to some constraints, only a specified flow F1 is transported from available sources to various destinations and in the second stage, a flow F2 is transported depending upon the total demand of the destinations. The current problem is motivated by a production system of a steel industry where semi-finished jobs, initially located at various bins in its warehouse, are transported to various manufacturing facilities by transporters for the final processing and finishing. Due to some additional constraints, it is not possible to transport the number of semi-finished jobs equal to the exact number of final products to be manufactured, in one go. Therefore the transportation operation has to take place in two stages. Further, a capacity is associated with each bin-machine link which makes the current problem, a capacitated, two stage time minimization transportation problem with restricted flow. The objective is to minimize the sum of the transportation times for Stage-I and Stage-II. A polynomial time iterative algorithm is proposed that within each iteration, solves a restricted version of a related standard capacitated time minimization transportation problem and generates a pair of Stage-I and Stage-II times with Stage-II time strictly less than the Stage-II time of the previous iteration, whereas Stage-I time may increase. Out of these generated pairs, a pair with the minimum sum of transportation times of Stage-I and Stage-II is selected that gives the global optimal solution. Numerical illustration is included in the support of the theory.
Mathematics Subject Classification: 90C26 / 90C27
Key words: Non-convex programming / combinatorial optimization / time transportation problem / capacitated transportation problem / flow constraint
© EDP Sciences, ROADEF, SMAI 2017
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