Shyamal Kumar Mondal

Multi-item fuzzy EOQ models using genetic algorithm

A soft computing approach is proposed to solve non-linear programming problems under fuzzy objective goal and resources with/without fuzzy parameters in the objective function. It uses genetic algorithms (GAs) with mutation and whole arithmetic crossover. Here, mutation is carried out along the weighted gradient direction using the random step lengths based on Erlang and Chi-square distributions. These methodologies have been applied to solve multi-item fuzzy EOQ models under fuzzy objective goal of cost minimization and imprecise constraints on warehouse space and number of production runs with crisp/imprecise inventory costs. The fuzzy inventory models have been formulated as fuzzy non-linear decision making problems and solved by both GAs and fuzzy non-linear programming (FNLP) method based on Zimmermanns approach. The models are illustrated numerically and the results from different methods are compared.

Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one is a own warehouse (OW) of finite dimension and other a rented warehouse (RW), is developed with interval-valued lead-time under inflation and time value of money. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item is increasing with time at a decreasing rate. Shortages are allowed in each cycle and backlogged them partially. Shortages may or may not be allowed in the last cycle and under this circumstance, there may be three different types of model. Here it is assumed that the replenishment cycle lengths are of equal length and the stocks of RW are transported to OW in continuous release pattern. For each model, different scenarios are depicted depending upon the re-order point for the next lot. Representing the lead-time by an interval number and using the interval arithmetic, the single objective function for profit is changed to corresponding multi-objective functions. These functions are maximized and solved by Fast and Elitist Multi-objective Genetic Algorithm (FEMGA). The models are illustrated numerically and the results are presented in tabular form.

A balanced solution of a fuzzy soft set based decision making problem in medical science

The purpose of this paper is two folded. Firstly, the concept of mean potentiality approach (MPA) has been developed and an algorithm based on this new approach has been proposed to get a balanced solution of a fuzzy soft set based decision making problem. Secondly, a parameter reduction procedure based on relational algebra with the help of the balanced algorithm of mean potentiality approach has been used to reduce the choice parameter set in the parlance of fuzzy soft set theory and it is justified to the problems of diagnosis of a disease from the myriad of symptoms from medical science. Moreover the feasibility of this proposed method is demonstrated by comparing with Analytical Hierarchy Process (AHP), Naive Bayes classification method and Fengs method.

Integrated supply chain model for a deteriorating item with procurement cost dependent credit period

This study develops an integrated production inventory model of supplier and retailer where a delay in payment is offered by supplier to retailer for a constant deteriorating item. Here shortages are not allowed. In this model retailers procurement cost linearly depends on the credit period and suppliers process cost also is a linear function of the amount of quantity purchased by retailer. In this model, the objective is to decide the position of the credit period and number of replenishment of retailer in finite time horizon in such a way that the integrated system gets the optimum cost. The model is explained with the help of numerical examples and the sensitivity analysis of some parameters are also carried out.

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 Chebyshev approximation for solving the optimal production inventory problem of deteriorating multi-item

In this paper, some realistic multi-period production-inventory models are formulated for deteriorating items with known dynamic demands for optimal productions. Here, the rates of production are time dependent (quadratic/linear) or constant expressed by a Chebyshev polynomial and considered as a control variable. The models are solved using Chebyshev spectral approximations, the El-Hawary technique and a genetic algorithm (GA). The models have been illustrated by numerical data. The optimum results for different production functions are presented in both tabular and graphical forms.

Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application

HighlightsA new method of similarity measure of the generalized trapezoidal fuzzy numbers.Properties regarding the proposed new method.Comparison of this method with the existing methods.Application in a production system. In this paper, we have proposed a new method of similarity measure associating the geometric distance, area and height of generalized trapezoidal fuzzy numbers. Some properties regarding the proposed new method of similarity measure have been derived. To illustrate the effectiveness of this method, it is compared with existing techniques taking thirty two different sets of generalized trapezoidal fuzzy numbers. Moreover, the proposed method has been used for calculating the fuzzy risk analysis in a production system in which different parameters are represented by linguistic trapezoidal fuzzy numbers.

An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets

Graphical abstractDisplay Omitted HighlightsIt is an integrated production inventory model of a manufacturer and multiple markets which have different selling seasons.Raw-materials supplier offers a credit period to the manufacturer which may be crisp and fuzzy.The fuzziness of the credit period is analyzed in two different ways such as - triangular and trapezoidal fuzzy numbers.Raw-materials for production and finished item are both considered as deteriorating and nondeteriorating cases.Manufacturer allows a conditional part-payment to the markets and his selling price is assumed as an increasing function of production run time. The presence of multiple markets create profitable opportunities to the supply chain system. In this regard, this paper consists of the joint relationship between a manufacturer and multiple markets in which manufacturer offers part-payment to the markets due to their collection of finished products during the production run time. Here it is also considered that manufacturer is facilitated with credit period by raw material supplier where credit period has been presented as an interactive fuzzy fashion. In this paper, two types of deterioration have been assumed such as one for finished products and the other for raw materials. A solution algorithm is presented to get fuzzy optimal profit for the proposed integrated production inventory system optimizing production run time. A numerical example is used to illustrate the proposed model. Finally, sensitivity analysis has been carried out with respect to the major parameters to demonstrate the feasibility of the proposed model.

Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand

Defective rate of items is production rate dependent in an imperfect production model.Production rate and screening rate are different.Demand of perfect items is advertisement dependent.Advertisement rate is increasing with time at a decreasing rate.Some demand of perfect items is lost due to depreciation and long run of the business. In this article, an economic production quantity (EPQ) model with imperfect production system and advertisement dependent demand has been presented. The advertisement rate has been assumed to be a function of time which has been increased with respect to time at a decreasing rate i.e., it has grown exponentially with respect to time but rate of growth gradually has decreased. Here, the rate of producing defective units has been followed to be a function of production rate. Also, the produced units have been inspected in order to screen the defective units but the screening rate is less than or equal to the production rate and greater than the demand rate. For the developed EPQ model, the total profit has been maximized to obtain the optimum production rate and production run time in the system. Here, algorithms have been developed for finding the optimal profit of the imperfect production inventory model. Finally, different numerical examples have been considered to illustrate the feasibility of the model taking different special cases in the system and then some sensitivity analyses have been carried out to get the impact of some parameters on the objective function of the model.

A multi-item transportation problem with fuzzy tolerance

Abstract This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated where unit transportation costs are imprecise. Also available spaces and budgets at destinations are limited but imprecise. The objective is to find a shipment schedule for the items that minimizes the total cost subjected to imprecise warehouse and budget constraints at destinations. The proposed model is reduced to a multi-objective optimization problem using tolerances, then to a crisp single-objective one using fuzzy non-linear programming (FNLP) technique and Zimmermanns method. The above fuzzy MIBTP is also reduced to another form of deterministic one using modified sub-gradient method (MSM). These two crisp optimization problems are solved by Genetic Algorithm (GA). As an extension, fuzzy multi-item balanced solid transportation problems (STPs) with and without restrictions on some routes and items are formulated and reduced to deterministic ones following FNLP and Zimmermanns methods. These models are also solved by GA. Models are illustrated numerically, optimum results of fuzzy MIBTP from two deductions are compared. Results are also presented for different GA parameters.