Uttam Kumar Bera

Inventory model with fuzzy lead-time and dynamic demand over finite time horizon using a multi-objective genetic algorithm

The real-world inventory control problems are normally imprecisely defined and human interventions are often required in solving these decision-making problems. In this paper, a realistic inventory problem with an infinite rate of replenishment over a prescribed finite but imprecise time horizon is formulated considering time dependent ramp type demand, which increases with time. Lead time is also assumed as fuzzy in nature. Shortages are allowed and backlogged partially. Two models are considered depending upon the ordering policies of the decision maker (DM). The imprecise parameters are first transformed to corresponding nearest interval numbers depending upon some distance metric on fuzzy numbers and then following the interval mathematics, the objective function for total profit from the planning horizon is obtained (which is an interval function). Then interval objective decision making problem is reduced to multi-objective problems using different approaches. Finally a fast and elitist multi-objective genetic algorithm (FEMOGA) is used for solving these multi-objective models to find pareto-optimal decisions for the DM. The models are illustrated numerically. As a particular case, the results due to linear trended and constant demands have been presented.

An imperfect fuzzy production-inventory model over a finite time horizon under the effect of learning

This article develops a production-inventory model for a deteriorating item under a defective production process over a finite time horizon. Here, demand varies with marketing cost and mark-up to the production cost. There is a learning effect on the set-up cost in each production cycle. The objective of this model is to maximise total profit (TPF) which includes sale proceed shortage cost, holding cost, deterioration cost, production cost, set-up cost and marketing cost. Considering the fuzzy nature in demand parameter, marketing cost and defective fraction of production rate, a fuzzy model is also developed. Here, fuzziness is introduced using triangular fuzzy numbers. Now using signed distance method and centroid method, respectively, the objective function is reduced to two different crisp models. For the crisp model, analytically it is shown that it possesses a global optimal solution. The models are solved using a gradient based non-linear optimisation technique – generalised reduced gradient method. Numerical illustrations have been made with the help of examples. Changes in TPF due to different deterioration rate, defective fraction of production rate and marketing costs are also presented graphically.

Defuzzification of trapezoidal type-2 fuzzy variables and its application to solid transportation problem

The main proposal of this paper is to derive two different reduction process for a trapezoidal type-2 fuzzy number. The first reduction method is based on critical values and the second method is based on α-cut of fuzzy number. As an application a multi-objective solid transportation problem, minimizing the cost and time has been developed using trapezoidal type-2 fuzzy number as system parameters and hereby solved. Finally after solving the proposed multi-objective problem by intuitionistic fuzzy programming technique a comparison between the two proposed reduction methods are discussed briefly. The proposed models and techniques are finally illustrated by providing numerical examples at the end. Also this paper present a comparative study between the proposed method to the KM algorithm and NT method for type reduction.

A Profit Maximizing Solid Transportation Model Under a Rough Interval Approach

This study attempts to establish an innovative solid transportation problem that intends to maximize profit under the rough interval approximation methodology. Two transportation problems were constructed in this regard with interval coefficients corresponding to the upper approximations and the lower approximations of the rough intervals under study. Furthermore, from the contingent solid transportation problems, four different classical solid transportation problems were derived, which were subsequently solved on the LINGO iteration platform. The concepts of completely satisfactory solution and rather satisfactory solution, surely optimal range, possibly optimal range, and rough optimal range have been discussed with a perspective to its relevance to real-world practical problems. The rough chance-constrained programming and the expected value operator for rough interval have been applied to solve the problem under study. The distinct advantages of the proposed method over those existing have been outlined. Numerical examples have also been provided to illustrate the solution procedure and the methodologies adopted.

Defuzzification and application of trapezoidal type-2 fuzzy variables to green solid transportation problem

The main objective of this investigation is to propose a defuzzification process of a trapezoidal type-2 fuzzy variable centred on critical value-based reduction method and nearest interval approximation, i.e.

A breakable multi-item multi stage solid transportation problem under budget with Gaussian type-2 fuzzy parameters

\alpha

A Bi-Objective Solid Transportation Model Under Uncertain Environment

α-cut of fuzzy number. In this context, this paper proposes some theorems with proof. Also as an application of the proposed defuzzification process, a new multi-objective green solid transportation model has been formulated with all of its parameters as trapezoidal type-2 fuzzy variables, where the objectives are profit maximization and minimization of carbon emission produced by the modes of transport depending upon their loads, fuel type used, type of engine, driving characteristics, etc. After defuzzification, to solve the equivalent crisp multi-objective solid transportation problem the intuitionistic fuzzy programming technique is used. Also we have proposed the MOGA and LINGO 13.0 iterative platform for the soft computation related to the problem. At the end, proposed methodologies are finally illustrated by providing numerical examples which incorporate some real-life data and demonstrate how a decision maker makes a balance between the maximum profit and minimum carbon emission. Also a comparative study with N–T method has been provided, and some managerial decisions are drawn.

Models for solid transportation problems in logistics using particle swarm optimisation algorithm and genetic algorithm

A Two warehouse EPQ model with continuous release, under trade credit is solvedNew method for retailers payment to supplier, which increases profit is presentedComparison between conventional and new approach is drawn through tables and graphsIntegrated two warehouse inventory model with two level trade credit is introducedIn particular, results of models with single level credit/single store are derived The present study deals with the development of an integrated production inventory model of supplier and retailer where a delay in payment is accessible by supplier towards the retailer and also by retailer en route for customer. Moreover, this paper relates to two warehouse inventory policy with continuous discharge along with two-level of credit period in a finite planning horizon. A retailer- the owner of two warehouses offers and accepts a credit period to the customer and from the wholesaler respectively. Depending upon the time of offering and accepting credit periods and with respect to the time of exhaust of inventory in two warehouses, different scenarios have been depicted in this approach of study. The objective of the current study is to minimize the total integrated cost of both supplier and retailer. Furthermore, an alternative approach of payment for the remaining inventory after the credit period has also been proposed in the present study. This new approach to analyze the interest earned by the retailer has been specified in this model, which has been explained with the help of numerical examples in conjunction with sensitivity analysis and the outcome is contrasted against the above cited traditional approach as well. The model has been developed as a cost minimization problem with respect to the retailer and supplier and has been optimized using the non-linear optimization technique - Generalized Reduced Gradient method (LINGO). The optimal solutions under different scenarios have been exemplified numerically and graphically in this study.