Dipak Kumar Jana

Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments

Multi-item integrated supply chain models with deterioration has been developed.Supply chain models with budget and space constraints has been formulated.The objective and constraints under imprecise environments has been introduced.An example, with some sensitivity analysis has been provided to validate the model.Chance constraint techniques and CMGA have been used to solve the models. In this paper, we have investigated multi-item integrated production-inventory models of supplier and retailer with a constant rate of deterioration under stock dependent demand. Here we have considered suppliers production cost as nonlinear function depending on production rate, retailers procurement cost exponentially depends on the credit period and suppliers transportation cost as a non-linear function of the amount of quantity purchased by the retailer. The models are optimized to get the value of the credit periods and total time of the supply chain cycle under the space and budget constraints. The models are also formulated under fuzzy random and bifuzzy environments. The ordering cost, procurement cost, selling price of retailers and holding costs, production cost, transportation cost, setup cost of the suppliers and the total storage area and budget are taken in imprecise environments. To show the validity of the proposed models, few sensitivity analyses are also presented under the different rate of deterioration. The models are also discussed in non deteriorating items as a special case of the deteriorating items. The deterministic optimization models are formulated for minimizing the entire monetary value of the supply chain and solved using genetic algorithm (GA). A case study has been performed to illustrate those models numerically.

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.

Multi-item partial backlogging inventory models over random planninghorizon in random fuzzy environment

Abstract In this paper, some multi-item inventory models for deteriorating items are developed in a random planning horizon under inflation and time value money with space and budget constraints. The proposed models allow stock dependent consumption rate and partially backlogged shortages. Here the time horizon is a random variable with exponential distribution. The inventory parameters other than planning horizon are deterministic in one model and in the other, the deterioration and net value of the money are fuzzy, available budget and space are fuzzy and random fuzzy respectively. Fuzzy and random fuzzy constraints have been defuzzified using possibility and possibility–probability chance constraint techniques. The fuzzy objective function also has been defuzzified using possibility chance constraint against a goal. Both deterministic optimization problems are formulated for maximization of profit and solved using genetic algorithm (GA) and fuzzy simulation based genetic algorithm (FAGA). The models are illustrated with some numerical data. Results for different achievement levels are obtained and sensitivity analysis on expected profit function is also presented. Scope and purpose The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However for more sale, inventory should be maintained at a higher level. Of course, this would result in higher holding or procurement cost, etc. Also, in many real situations, during a shortage period, the longer the waiting time is, the smaller the backlogging rate would be. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging diminishes with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But at present, the economic situation of most of the countries has been much deteriorated due to large scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any further. The purpose of this article is to maximize the expected profit of two inventory control systems in the random planning horizon.

A three-layer supply chain integrated production-inventory model under permissible delay in payments in uncertain environments

In this paper, an integrated production-inventory model is presented for a supplier, manufacturer, and retailer supply chain under conditionally permissible delay in payments in uncertain environments. The supplier produces the item at a certain rate, which is a decision variable, and purchases the item to the manufacturer. The manufacturer has also purchased and produced the item in a finite rate. The manufacturer sells the product to the retailer and also gives the delay in payment to the retailer. The retailer purchases the item from the manufacture to sell it to the customers. Ideal costs of supplier, manufacturer, and retailer have been taken into account. An integrated model has been developed and solved analytically in crisp and uncertain environments, and finally, corresponding individual profits are calculated numerically and graphically.

A fuzzy simulation via contractive mapping genetic algorithm approach to an imprecise production inventory model under volume flexibility

In this paper, an economic production quantity model for multi-item with storage space and budget constraints in a volume flexible manufacturing system is developed. Here it is assumed that the demand rate is constant up to a certain level of stock and after that it depends on stock itself. The unit production cost is taken to be a function of the finite production rate involving labour cost and wear and tear expenditure. Here, the inventory costs, selling price, storage space and available budget are defined imprecisely. Using necessary measure theory, the imprecise problem is reduced to deterministic problem. Here, necessity measure approach has been used for triangle fuzzy number and parabolic fuzzy number. Finally the crisp nonlinear optimization problem is solved by Fuzzy simulation, Contractive Mapping Genetic Algorithm and Generalized Reduced Gradient technique. The model is illustrated numerically and the results are compared.

A new approach to solve multi-objective multi-choice multi-item Atanassov's intuitionistic fuzzy transportation problem using chance operator

In some practical situations the decision maker is interested in setting multi aspiration levels for objectives that may not be expressed in a specific manner. So in this paper, Atanassovs intuitionistic fuzzy transportation problem with multi-item, multi-objective function assuming multiple choices is considered. We have modeled multi-objective multi-choice multi-item Atanassovs intuitionistic fuzzy transportation problem (MMMIFTP), and its several special cases. Possibility, necessity and credibility measures for Atanassovs intuitionistic fuzzy numbers for the first time have been developed here. Solution methodology of those models using chance operator has been discussed. A real life example is presented to illustrate proposed models numerically and the results are compared. The optimal results are obtained by using three different soft computing techniques (i) Interactive satisfied method, (ii) Global criteria method and (iii) Goal programming method.

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.

Availability and cost-centered preventive maintenance scheduling of continuous operating series systems using multi-objective genetic algorithm: A case study

Abstract This article presents a multi-objective (maximization of availability and minimization of maintenance cost) preventive maintenance (PM) scheduling model for a continuous operating series system (COSS) which do not provide an off-working period for PM. The objective functions are optimized by using a Multi-Objective Genetic Algorithm (MOGA). The effectiveness of the model is demonstrated through a coal-fired boiler-tube. The case study shows that the model can improve the availability along with profound reduction of the maintenance cost, i.e., increases the profit of the plant.

A Partial Backlogging Inventory Model for Deteriorating Item under Fuzzy Inflation and Discounting over Random Planning Horizon: A Fuzzy Genetic Algorithm Approach

An inventory model for deteriorating item is considered in a random planning horizon under inflation and time value money. The model is described in two different environments: random and fuzzy random. The proposed model allows stock-dependent consumption rate and shortages with partial backlogging. In the fuzzy stochastic model, possibility chance constraints are used for defuzzification of imprecise expected total profit. Finally, genetic algorithm (GA) and fuzzy simulation-based genetic algorithm (FSGA) are used to make decisions for the above inventory models. The models are illustrated with some numerical data. Sensitivity analysis on expected profit function is also presented. Scope and Purpose. The traditional inventory model considers the ideal case in which depletion of inventory is caused by a constant demand rate. However, to keep sales higher, the inventory level would need to remain high. Of course, this would also result in higher holding or procurement cost. Also, in many real situations, during a longer-shortage period some of the customers may refuse the management. For instance, for fashionable commodities and high-tech products with short product life cycle, the willingness for a customer to wait for backlogging is diminishing with the length of the waiting time. Most of the classical inventory models did not take into account the effects of inflation and time value of money. But in the past, the economic situation of most of the countries has changed to such an extent due to large-scale inflation and consequent sharp decline in the purchasing power of money. So, it has not been possible to ignore the effects of inflation and time value of money any more. The purpose of this paper is to maximize the expected profit in the random planning horizon.