A Profit Maximisation Solid Transportation Problem Using Genetic Algorithm in Fuzzy Environment

Abstract

In this paper, a solid transportation problem has been considered in which the transportation is accomplished in two stages – firstly, from the origin(s) to the near by station(s) of the destination(s) and secondly, from the near by station(s) to the exact destination(s). Here, a fuzzy AUD (all unit discount) policy has been introduced based upon the amount of transportation along with a fuzzy fixed charge. In addition, a budget constraint has been incorporated taking fuzzy unit transportation cost. Then the proposed model has been converted into a single objective optimisation problem using interval arithmetic method. To solve the model, Genetic Algorithm (GA) has been used depending on roulette wheel selection, crossover and mutation. Finally, a numerical example has been illustrated to study the feasibility of the model.

KEYWORDS:

• All unit discount
• genetic algorithm
• profit maximisation solid transportation problem
• fuzzy resource and demand

Disclosure statement

Here for the first time different type of vehicle costs are consider in a STP. The fixed charge, the unit transportation cost (under AUD) all are treated as fuzzy parameters. The problem is formulated as a profit maximization problem. The budget constraint has been incorporated taking fuzzy unit transportation cost as constraint.

Additional information

Notes on contributors

S. Samanta

Mr. S. Samanta is an Assistant Teacher of Mathematics at Majurhati Junior High School. He completed his graduation , PG and Ph.D. with under Vidyasagar University.

A. Ojha

Dr. A. Ojha is an Assistant Teacher of Mathematics at Siromoni Birsa Munda High School. He completed his graduation, PG and Ph.D. from Vidyasagar University. His research fields are Transportations and Soft Computing. He has some publications in different reputed international journals like Tamsui Oxford Journal of Management Science, Fuzzy Systems and Soft Computing, Mathematical and Computer Modelling, Applied Mathematical Modelling, Applied Soft Computing, etc.

B. Das

Dr. B. Das is an Associate Professor in the department of Mathematics at Sidhu Kanhu Birsha University. He completed his graduation with gold medal under Vidyasagar University. He completed his PG and Ph.D. from Vidyasagar University. His research fields are Biomathematics, Inventory, Soft Computing and Supply Chain. He has been doctoral dissertation adviser to 4 students as of now and 6 students are working currently under his supervision. He is working in this department from 2013 and previously he was working at Jhargram Raj College. He has more than 70 publications in different reputed international journals like Journal of Computational and Applied Mathematics, Asian Journal of Mathematics and Physics, Applied Mathematical and Computation, Mathematical and Computer Modelling, Applied Mathematical Modelling, Applied Soft Computing, Journal of Computational Science, Journal of Simulation, Computers & Industrial Engineering, Transportation Research Part E: Logistics and Transportation Review, Annals of Operations Research, etc. He was died last year due to covid 19.

S. K. Mondal

Prof. S. K. Mondal is Professor and HOD in the department of Applied Mathematics with Oceanology and Computer Programming at Vidyasagar University. He was gold medalist of Vidyasagar University at UG and PG level. He completed his M.Tech. degree from ISM dhanbad. He completed his Ph.D. degree from Vidysagar University. His research interest areas are Biomathematics, Inventory, Supply Chain, Soft computing and Risk analysis. He has been doctoral dissertation adviser to 14 students as of now and 6 students are working currently under his supervision and 4 has been faced their pre submission seminar. He is working in this department from 2004 and working as a professor till 2015. He visited Vietnam, Thailand and Bangladesh to deliver speech in different international conferences. He has more than 150 international publications in different reputed international journals like Journal of Cleaner Production, Transportation Research Part E: Logistics and Transportation Review, Applied Soft Computing, Journal of Industrial and Production Engineering, Computers & Industrial Engineering, Annals of Operations Research, Chaos, Solutions & Fractals, Information Sciences, Nonlinear Dynamics etc.