Enhancement of Capacitated Transportation Problem in Fuzzy Environment

This research work aims to study a capacitated transportation problem (CTP) with penalty cost, supplies, and demands represented by hexagonal fuzzy numbers. Based on ranking function, the supplies and demands are converted to the crisp form. Through the use of the α‐level, the problem is converted into interval linear programming. To optimize the interval objective function, we define the order relations represented by policy maker’s choice between intervals. The maximization (minimization) problem considering the interval objective function is transformed to multiobjective optimization problem based on order relations introduced by the preference of policy makers between interval profits (costs). A numerical example is given for illustration and to check the validity of the suggested approach.

An Iterative Solution Technique to Minimize the Average Transportation Cost of Capacitated Transportation Problem with Bounds on Rim Conditions

The average transportation cost minimization of capacitated transportation problem with bounds on rim conditions (CTPBRC) is an important optimization problem due to the requirement of low unit cost consumption in production system. In the literature, there is only one approach to solving a special case of this problem, but it is not applicable to the general case. In this paper, this problem is reduced to a series of finding the minimum cost maximum flow in a network with lower and upper arc capacities, and two iterative algorithms are proposed as more generalized solution method for this problem as compared to the existing approach. Computational experiments on randomly generated instances validate that the two iterative algorithms are generally able to find the minimum average transportation cost solution to CTPBRC efficiently for the general case, in which one iterative algorithm has higher efficiency than the other for large size instances.

Multi-Objective Multi Time Span Fractional Capacitated Transportation Problem in the Two Echelon Supply Chain with Multiform Items and Mixed Constraints

One of the most useful techniques for the transport companies is multi-level distribution to minimize the cost. This paper presents multi-objective multi time span fractional capacitated transportation problem (MOMTMIFCTP) in the two echelon supply chain with multiform items and mixed constraints. Moreover the fractional objective functions in the supply chain are important because many real life problems are based on the ratio of physical or economical values. The goal of this investigation is to minimize damage cost, labor cost, the cost related to transportation, inventory carrying cost, quality cost and packing cost, also determine an optimal inventory level for the warehouse and distribution centers using fuzzy programming approach through LINGO software.

Environmentally Liable Multi-Objective Multi Time Span Fuzzy Fractional Capacitated Transportation Problem in the Two Echelon Supply Chain with Heterogeneous Items and Mixed Constraints

In today’s world supply chain is an integral part of business. This paper proposed a model of environmentally liable multi-objective multi time span fuzzy fractional capacitated transportation problem (ELMOMTHIFFCTP) in the two echelon supply chain with heterogeneous items and mixed constraints. In this model, few objectives are considered as a linear function and few are fractional functions. Especially the objective function related to emission cost is considered as linear fractional objective function. The damage cost, labor cost, packing cost and quality cost are considered as triangular intuitionistic fuzzy numbers. This paper focuses on minimization of damage cost, labor cost, quality cost, packing cost and the ratio related to transportation cost , inventory carrying cost and emission cost of the entire supply chain. An industrial case demonstrates the feasibility of applying the proposed model to real world problem in a two – echelon supply chain under uncertain environment also determine an optimal inventory level for the warehouse and distribution centers using fuzzy programming approach through LINGO software.