tailieunhanh - Limitation and modification: On a cost pipeline trade-off in a transportation problem
We have observed one limitation of the proposed algorithm which directly affects the global minimum character of the pipeline. In the present paper, we suggest a modification of the limitation found in the procedural formulation developed by Sharma et al. | Yugoslav Journal of Operations Research 27 (2017), Number 4, 439–450 DOI: LIMITATION AND MODIFICATION: ON A COST PIPELINE TRADE-OFF IN A TRANSPORTATION PROBLEM Sanchita SHARMA Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Kashmere Gate, Delhi, INDIA sanchitasharma88@ Shalini ARORA Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Kashmere Gate, Delhi, INDIA shaliniarora@ Received: May 2016 / Accepted: November 2016 Abstract: The present paper attempts to foreground a modified approach to the algorithm as conceived by Sharma et al. [1] in the paper entitled ’A cost and pipeline trade-off in a transportation problem’. In 2013, Sharma et al. [1] came up with an idea of pivotal time and consequentially evolved a convergent algorithm to determine cost pipeline trade off pairs corresponding to the chosen pivotal time. We have observed one limitation of the proposed algorithm which directly affects the global minimum character of the pipeline. In the present paper, we suggest a modification of the limitation found in the procedural formulation developed by Sharma et al. [1]. Keywords: Transportation Problem, Combinatorial Optimization, Bottleneck Transportation Problem, Bi-criteria Transportation Problem, Efficient Points. MSC: 90B06, 90C05, 90C08. 1. INTRODUCTION Note:Definitions, notations and symbols as per the paper [1] given in Appendix. The authors [1] proposed an algorithm to find the cost pipeline trade off pairs corresponding to the chosen pivotal time. S. Sharma, S. Arora / Limitation and Modification 440 The mathematical models of the problems considered by authors [1] are as follows: Note: For the detail description of the models and definitions one can refer the paper [1] (P1 ) min XX i∈I ci j xi j j∈J subject to the constraints: X xi j = ai , ai > 0, i ∈ I, j∈J X xi j = b j , b j >
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