Improved Lagrangian-relaxation based approaches for multi-period multi-stage fixed charge transportation problem

Abstract

This paper considers the Fixed-Charge Transportation Problem (FCTP), which spans multiple time periods and includes multiple stages, termed as Multi-Period, Multi-Stage Fixed-Charge Transportation Problem (MPMS-FCTP) in a supply chain. A generalised mathematical model which minimises the fixed and variable transportation, storage and backlog costs is proposed for the problem under study. Subsequently, two improved Lagrangian-Relaxation (LR)-based approaches are developed to efficiently solve the MPMS-FCTP. In addition, heuristics based on the improved LR approaches are proposed to obtain good upper bounds. The experimental results show that the proposed LR approaches perform better than the traditional LR approach with the sub-gradient optimisation. The lower bounds obtained using the proposed approaches are always non-decreasing in successive iterations of LR, providing tighter lower bounds. In addition, the proposed LR-based heuristics yield better solutions than the existing heuristics in the literature. Finally, the convergence to optimality of the proposed approaches is also discussed.

Keywords:

• Transportation problem
• multi-period
• fixed charge
• Lagrangian relaxation
• heuristics
• bounds

Acknowledgements

Authors are grateful to reviewers for their insightful comments and suggestions which helped us to improve this paper.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Notes on contributors

S. A. Ezhil

S. A. Ezhil received a Ph.D. degree in Logistics from the Department of Management Studies, IIT Madras, India. He is a Software Engineering Manager at Trimble and has been employed since 2008. He has worked on implementing software solutions for fleet management, safety and location tracking (involving people, places, things and assets), mobile and IoT technologies, highly scalable cloud services, Data Analytics, video intelligence for vehicles and software security. His research areas include transportation logistics and the convoy movement problem.

Chandrasekharan Rajendran

Chandrasekharan Rajendran has been serving at the Indian Institute of Technology Madras since 1987 and has B.E. (Honours) from the University of Madras, M.E. from Anna University, and Ph.D. from the Indian Institute of Technology (IIT) Madras. He is currently a Professor and the RAGS Family Foundation Institute Chair at IIT Madras. His research interests are in the areas of Production and Operations Management, Supply Chain and Logistics Management, and Quality Management. Professor C Rajendran is the recipient of the prestigious Alexander von Humboldt Fellowship of Germany and has been awarded Honorary Doctorate from the University of Passau. He is an elected Fellow of the Indian National Academy of Engineering (FNAE).

Sharan Srinivas

Sharan Srinivas is an assistant professor with a joint appointment in the Department of Industrial and Systems Engineering and the Department of Marketing at the University of Missouri (MU). His area of specialization is data analytics and operations research with research interests in healthcare operations management, transportation/logistics, smart service systems and supply chain. Dr. Srinivas' research and development activities has been funded by several federal and state agencies. He has also been an investigator for several industry-sponsored projects. He has published over 80 peer-reviewed articles in journals, conferences, books, and trade publications. He is a certified six sigma black belt and recipient of multiple awards such as the INFORMS Koopman prize, INFORMS Data Mining and Decision Analytics Best Paper Finalist Award, and Winemiller Excellence Award.