A multi-objective multi-item solid transportation problem with vehicle cost, volume and weight capacity under fuzzy environment

TL;DR

This paper develops a fuzzy multi-objective model for multi-item transportation considering vehicle costs, capacity constraints, and time, addressing uncertainties with credibility theory and providing a numerical example.

Contribution

It introduces a novel fuzzy multi-objective transportation model incorporating volume, weight, and time constraints, with a chance-constraint approach for uncertainty.

Findings

Model effectively handles fuzzy transportation costs and times.

Numerical example demonstrates applicability and solution approach.

Addresses multi-item, multi-vehicle transportation complexities.

Abstract

Generally, in transportation problem, full vehicles (e.g., light commercial vehicles, medium duty and heavy duty trucks, etc.) are to be booked, and transportation cost of a vehicle has to be paid irrespective of the fulfilment of the capacity of the vehicle. Besides the transportation cost, total time that includes travel time of a vehicle, loading and unloading times of products is also an important issue. Also, instead of a single item, different types of items may need to be transported from some sources to destinations through different types of conveyances. The optimal transportation policy may be affected by many other issues like volume and weight of per unit of product, unavailability of sufficient number of certain types of vehicles, etc. In this paper, we formulate a multi-objective multi-item solid transportation problem by addressing all these issues. The problem is formulated with the transportation cost and time parameters as fuzzy variables. Using credibility theory of fuzzy variables, a chance-constraint programming model is formulated, and is then transformed into the corresponding deterministic form. Finally numerical example is provided to illustrate the problem.