Dipankar Chakraborty

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 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 New Approach to Solve Intuitionistic Fuzzy Optimization Problem Using Possibility, Necessity, and Credibility Measures

Corresponding to chance constraints, real-life possibility, necessity, and credibility measures on intuitionistic fuzzy set are defined. For the first time the mathematical and graphical representations of different types of measures in trapezoidal intuitionistic fuzzy environment are defined in this paper. We have developed intuitionistic fuzzy chance constraints model (CCM) based on possibility and necessity measures. We have also proposed a new method for solving an intuitionistic fuzzy CCM using chance operators. To validate the proposed method, we have discussed three different approaches to solve the intuitionistic fuzzy linear programming (IFLPP) using possibility, necessity and credibility measures. Numerical and graphical representations of optimal solutions of the given example at different possibility and necessity, levels have been discussed.

Multi-objective multi-item solid transportation problem with fuzzy inequality constraints

Zimmermann (Int. J. Gen. Syst. 2:209-215, 1976) first introduced the concept of fuzzy inequality in the field of linear programming problem (LPP). But this concept is hardly used in any real life applications of LPP. So, in this paper, a multi-objective multi-item solid transportation problem (MMSTP) with fuzzy inequality constraints is modeled. Representing different preferences of the decision maker for transportation, three different types of models are formulated and analyzed. Fuzzy inequality solid transportation problem is converted to parameter solid transportation problem by an appropriate choice of flexible index, and then the crisp solid transportation problem is solved by the algorithm (Cao in Optimal Models and Methods with Fuzzy Quantities, 2010) for decision values. Fuzzy interactive satisfied method (FISM), global criterion method (GCM) and convex combination method (CCM) are applied to derive optimal compromise solutions for MMSTP by using MatLab and Lingo-11.0. The models are illustrated with numerical examples and some sensitivity analysis is also presented.

A new approach to solve fully fuzzy transportation problem using triangular fuzzy number

In the literature, there are several methods for finding a fuzzy optimal solution to fully fuzzy transportation problems (FFTP). In this paper, a new approach is proposed for solving a fully fuzzy transportation problem. Assuming that the transportation cost, total supply, total demands and also the transportation amount are imprecise in nature. The proposed approach is an extension of popular approach of solving transportation problem (i.e., North West corner method, least cost method, Vogels approximation method, modified distribution method). The proposed methods are easy to understand and to apply for finding a fuzzy optimal solution to fuzzy transportation problems happening in real-life situations. To illustrate the proposed methods, a fully fuzzy transportation problem is solved using the proposed methods and the obtained results are compared with the results of existing approaches like Kumars method (Kumar and Singh, 2012) and Ezzati method (Ezzati et al., 2013).

A random fuzzy production inventory problem with backorder rate based on controllable preparation time and safety factor via genetic algorithm

A random fuzzy (Ra-Fu) production inventory model with Ra-Fu backorder and lost sales in which the preparation time, cycle length and safety factor is formulated and solved. Instead of having stockout term in the objective function, a service level constraint is introduced to the model which implies that the stockout level per cycle is bounded. Also, a non-serviceable cost, unit production cost are included in the objective function due to the lost sale. We relax the assumption about the probability distribution of preparation time demand and apply the minimax distribution free procedure to solve the proposed problem. We have developed a computational algorithm to find the optimal values of preparation time, cycle length, safety factor and the decision reorder point. Finally, we have solved the proposed problem using three different soft computing techniques: 1) genetic algorithm (GA) technique; 2) generalised reduced gradient (GRG) technique; 3) Lagrange multiplier method via LIngo-11.0. In addition, the effects of the parameters are also incorporated. The above Ra-Fu model is illustrated graphically with a practical problem.

A three-layer supply chain inventory model for non-instantaneous deteriorating item with inflation and delay in payments in random fuzzy environment

Abstract This article focuses on different types of three-layer supply chain models under inflation for non-instantaneous deteriorating item and the retailer has a pre-specified time to settle the account with the supplier. The total cost of each those integrated models under inflation is minimized to get the value of total cycle time and the credit period of the three-layer supply chain model. A numerical example is extracted to solve the proposed three-layer supply chain models using generalized reduced gradient technique. To test the feasibility of the proposed models, sensitivity analyses are explained under different rates of deterioration and inflation and then optimal results are illustrated numerically and graphically.

A multi-item periodic review probabilistic fuzzy inventory model with possibility and necessity constraints

This paper investigates a multi-item periodic review probabilistic inventory model in fuzzy environment. Here, we have considered a single source of the inventory model with zero lead time and varying order cost under two limitations, such as holding cost and safety stock. By employing the fuzzy expectation and possibility/necessity measure, the fuzzy model is transformed into an equivalent deterministic non-linear programming problem. Finally, the model is illustrated with the help of numerical example and few sensitivity analyses are also presented for different parameter to show the validity of the proposed model.

Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments

Abstract Decay or deterioration of physical goods while in stock is a natural phenomenon in many inventory systems. The three-parameter Weibull distribution is an excellent generalization of exponential decay, which can be used for items with any initial value of the rate of deterioration and for items which starts deteriorating only after a certain period of time. To reduce the amount of deterioration and the limited storage facility in own warehouse (OW) the retailer’s is moving their excess items to store in a rented warehouse (RW). Generally it is seen that for any new brand of consumer goods coming to the market, the demand rate increases with time up to a certain period and then ultimately stabilize and becomes constant. This kind of stabilization has been termed as ’ramp-type’ demand rate. So, in this paper, we have developed two warehouse inventory models with ramp type demand rate and three-parameter Weibull distribution deterioration (ThPWD) under inflationary conditions, where permissible delay in payment is available for retailer if outstanding amount is compensated within the given credit period. Since, not all customers are willing to wait for backlogged during the shortage period, in this investigation shortages are also allowed and partially backlogged. The purpose of this study is not only to find retailer’s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solutions with respect to major parameters is carried out using the Mathematica-8.0 software.

Arithmetic operations of trapezoidal fuzzy variable using credibility theory

In this paper, we have developed an alternative method of finding the fuzzy membership function which leads the functions of trapezoidal fuzzy variables. Here we have used the concept of credibility theory to find out an alternative method of computing different type arithmetic operations of trapezoidal fuzzy variables. This method also lead us to find the membership function for the nth root of a trapezoidal fuzzy variable. The method has been illustrated with the help of some numerical examples.