Sutapa Pramanik

A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments

This paper presents two mathematical models representing imprecise capacitated fixed-charge transportation problems for a two-stage supply chain network in Gaussian fuzzy type-2 environment. It is a two-stage transportation process from a manufacturing center to m potential distribution centers (DCs) and then from DCs to business centers of n retailers with particular demands. Retailers are situated at some distances apart. Here unit transportation costs, fixed charges, availabilities, and demands are imprecise and represented by Gaussian type-2 fuzzy numbers. The proposed models are formulated as profit maximization problems in such a way that some DCs are selected in order to satisfy the demands at all retailers. The type-2 fuzziness has been removed by using generalized credibility measure developed with the help of CV-based reduction method and hence the models are reduced to chance constrained programming problems with different credibility labels. The deterministic models are then solved using both genetic algorithm (GA) based on Roulette wheel selection, arithmetic crossover with uniform mutation and modified particle swarm optimization (PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. Finally models are illustrated with some numerical data. Some sensitivity analyses on the proposed models are presented.

A multi objective solid transportation problem in fuzzy, bi-fuzzy environment via genetic algorithm

In this paper, we concentrate on developing a bi-fuzzy multi objective transportation problem (MOSTP) according to bi-fuzzy expected value method (EVM). In a transportation model, the available discount is normally offered on items/criteria, etc., in the form of all unit discount (AUD) or incremental quantity discount (IQD) or combination of these two. Here, transportation model is considered with fixed charges and vehicle costs where AUD, IQD or combination of AUD and IQD on the price depending upon the amount is offered and varies on the choice of origin, destination and conveyance. To solve the problem, multi objective genetic algorithm (MOGA) based on Roulette wheel selection, arithmetic crossover and uniform mutation has been suitably developed and applied. To illustrate the models, numerical examples have been presented. Here, two types of problems are introduced and the corresponding results are obtained. To provide better customer service, the entropy function is considered.

Mean and CV reduction methods on Gaussian type-2 fuzzy set and its application to a multilevel profit transportation problem in a two-stage supply chain network

Abstract The transportation problem (TP) is an important supply chain optimization problem in the traffic engineering. This paper maximizes the total profit over a three-tiered distribution system consisting of plants, distribution centers (DCs) and customers. Plants produce multiple products that are shipped to DCs. If a DC is used, then a fixed cost (FC) is charged. The customers are supplied by a single DC. To characterize the uncertainty in the practical decision environment, this paper considers the unit cost of TP, FC, the supply capacities and demands as Gaussian type-2 fuzzy variables. To give a modeling framework for optimization problems with multifold uncertainty, different reduction methods were proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method and CV reduction method. Then, the TP was reformulated as a chance-constrained programming model enlightened by the credibility optimization methods. The deterministic models are then solved using two different soft computing techniques—generalized reduced gradient and modified particle swarm optimization, where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrated the application and effectiveness of the proposed approaches.

A Parametric Programming Method on Gaussian Type-2 Fuzzy Set and Its Application to a Multilevel Supply Chain

The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, distribution centers, and customers. Plants manufacture several products that are delivered to distribution centers. If a distribution center is used then fixed cost is charged. Customers are replenished by an only one distribution center. To characterize the uncertainty that typically occurs in many practical decision environments, this paper considers the supply capacities, demands as Gaussian type-2 fuzzy variables. To provide a modelling framework for optimization problems with multi-fold uncertainty, different reduction methods are proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method. Then the transportation problem is reformulated as a chance-constrained expected value model enlightened by the credibility optimization method. The deterministic models are then solved using two different soft computing techniques (i) Generalized Reduced Gradient (Lingo-14.0), and (ii) modified Particle Swarm Optimization(PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrate the application and effectiveness of the proposed solution approaches.

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

In this paper, a multi-objective solid transportation problem (MOSTP) for damageable item is formulated and solved. First, we minimised the total cost of transportation and transportation time and maximise the reliability of transportation system. Here, transportation costs, resources, demands and capacities of conveyances are random fuzzy in natures. The transported item is likely to be damaged during transportation and damageability are different for different conveyances along different roots. The solid transportation problem (STP) is formulated as a decision making model optimising possibilistic value at risk (pVaR) by incorporating the concept of value at risk (VaR) into possibility and necessity measure theory. The reduced deterministic constrained problem is solved using generalised reduced gradient (GRG) method (LINGO-14.0). Some particular models has been presented. The model is illustrated with numerical examples and some sensitivity analysis is made on damageability.