Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
---|---|---|
Page(s) | 2733 - 2766 | |
DOI | https://doi.org/10.1051/ro/2024086 | |
Published online | 02 July 2024 |
An efficient algorithm for two-stage capacitated time minimization transportation problem with restricted flow
1
Department of Mathematics, Panjab University, Chandigarh 160014, India
2
Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh 160014, India
3
Department of Computer Science and Applications, Panjab University, Chandigarh 160014, India
4
University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India
* Corresponding author: kalpanas@pu.ac.in
Received:
10
June
2023
Accepted:
8
April
2024
This paper discusses a two-stage capacitated time minimization transportation problem with the restricted flow (TSCTMTP-F) in which the transportation takes place in two stages and only a specified amount of commodity is transported in both stages. The total amount F1 is transported during Stage-I and F2 during Stage-II, and the objective is to minimize the sum of the transportation times for Stage-I and Stage-II. In 2017, Kaur et al. [RAIRO-Oper. Res. 51 (2017) 1169–1184] studied this problem and developed a polynomially bounded iterative algorithm (Algorithm-A) to solve TSCTMTP-F. However, their proposed algorithm has some flaws and may not always yield an optimal solution to the problem TSCTMTP-F. An improved iterative algorithm (Algorithm-C) is proposed in this paper that guarantees an optimal solution to the problem. Various theoretical results prove the convergence and efficiency of Algorithm-C to obtain an optimal solution to the problem TSCTMTP-F. Numerical problems are included in the support of theory along with a counter-example for which Algorithm-A fails to obtain its optimal solution. Computational experiments on a variety of test problems have been carried out to validate the convergence and efficiency of Algorithm-C.
Mathematics Subject Classification: 90C26 / 90C27
Key words: Time transportation problem / capacitated problem / flow constraint / two-stage
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
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