Title: Time paradox in transportation problems

Authors: Sonia; Subramanian Chidambaran

Addresses: Indian Institute of Management, Lucknow, India ' Indian Institute of Management, Lucknow, India

Abstract: The boom in e-commerce industry in recent years is reshaping delivery landscape and logistics needs to keep pace with this rapid e-commerce growth. One of the most important customer satisfaction KPIs in the e-commerce industry is to reduce the delivery time and is a key focus area for the market players. The present paper attempts to address this challenge by introducing the concept of a paradox in a time minimising transportation problem (TMTP) which is a concave minimisation problem. The paradoxical situations in cost minimising transportation problems, fixed charge transportation problems, minimum cost flow problems and in many other variants of transportation problem have been extensively researched and well applied except for TMTPs. After defining the time paradox in a TMTP, we develop the condition of its existence. Further, a comparative study of paradox for a cost minimising and time minimising transportation problems has also been carried out. We then discuss the immunity conditions for a time matrix. At the end, the method for finding the best paradoxical solution along with practical applications is also presented.

Keywords: time paradox; time minimising transportation problem; TMTP; bottleneck transportation problem; BTP.

DOI: 10.1504/IJOR.2022.128397

International Journal of Operational Research, 2022 Vol.45 No.4, pp.540 - 552

Received: 31 Oct 2019
Accepted: 01 Feb 2020
Published online: 20 Jan 2023 *

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