A fuzzy inventory model with unit production cost, time depended holding cost, with-out shortages under a space constraint: a parametric geometric programming approach

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered here a single objective inventory model. In most real world situation, the objective and constraint function of the decision makers are imprecise in nature, hence the coefficients, indices, the objective function and constraint goals are imposed here in fuzzy environment. Geometric programming provides a powerful tool for solving a variety of imprecise optimization problem. Here we have used nearest interval approximation method to convert a triangular fuzzy number to an interval number then transform this interval number to a parametric interval-valued functional form and solve the parametric problem by geometric programming technique. Here two necessary theorems have been derived. Numerical example is given to illustrate the model through this Parametric Geometric-Programming method

Fuzzy E.O.Q model with constant demand and shortages: A fuzzy signomial geometric programming (FSGP) approach

In this paper, a fuzzy economic order quantity (E.O.Q) model with shortages under fully backlogging and constant demand is formulated and solved. Here the model is solved by fuzzy signomial geometric programming (FSGP) technique. Fuzzy signomial geometric programming (FSGP) technique provides a powerful technique for solving many non-linear problems. Here we have proposed a new idea that is fuzzy modified signomial geometric programming (FMSGP) and some necessary theorems have been derived. Finally, these are illustrated by some numerical examples and applications

A solution to bi/tri-level programming problems using particle swarm optimization

© 2016 Elsevier Inc. Multilevel (including bi-level and tri-level) programming aims to solve decentralized decision-making problems that feature interactive decision entities distributed throughout a hierarchical organization. Since the multilevel programming problem is strongly NP-hard and traditional exact algorithmic approaches lack efficiency, heuristics-based particle swarm optimization (PSO) algorithms have been used to generate an alternative for solving such problems. However, the existing PSO algorithms are limited to solving linear or small-scale bi-level programming problems. This paper first develops a novel bi-level PSO algorithm to solve general bi-level programs involving nonlinear and large-scale problems. It then proposes a tri-level PSO algorithm for handling tri-level programming problems that are more challenging than bi-level programs and have not been well solved by existing algorithms. For the sake of exploring the algorithms' performance, the proposed bi/tri-level PSO algorithms are applied to solve 62 benchmark problems and 810 large-scale problems which are randomly constructed. The computational results and comparison with other algorithms clearly illustrate the effectiveness of the proposed PSO algorithms in solving bi-level and tri-level programming problems

New Fuzzy Parametric Linear Programming Approaches For Optimising The Performance Of Crude Oil Companies In Iraq

Refineries and crude oil industries are amongst the most important revenue generators of oil-producing countries. Iraq is an oil-exporting country. Although it has many refineries to process and refine crude oil, it suffers from severe production crises that ravage it from time to time. This study aims to optimise the scheduling, production planning and inventory control of multisite refineries located in Iraq. The study sample was taken from the Iraqi Midland Refineries (IMR) of the Iraqi Petroleum Company (IPC) company, which includes four refineries in four different sites in Iraq. In this research, different approaches based on fuzzy set theory are considered as demand and cost are explained as fuzzy. The parametric fuzzy linear programming (PFLP) problem is suggested on the basis of symmetric triangular fuzzy numbers (STFNs). Technically, this model involves three methods. The first method utilises the concept of the Spread Function (SF). We utilise two different functions of SFs to find the parameter values of λ and maximise the PFLP model. The second method is based on fractal analysis, where the fractional power λ of the fractal is the parameter used in our study. Lastly, the third method is based on fractional Tsallis entropy of order λ. Results indicate that the established models can deliver valuable information to the maximal profit production approach to evaluate oil refineries in a parametric fuzzy setting

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics

Multilevel decision-making: A survey

© 2016 Elsevier Inc. All rights reserved. Multilevel decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a multiple level hierarchy. Significant efforts have been devoted to understanding the fundamental concepts and developing diverse solution algorithms associated with multilevel decision-making by researchers in areas of both mathematics/computer science and business areas. Researchers have emphasized the importance of developing a range of multilevel decision-making techniques to handle a wide variety of management and optimization problems in real-world applications, and have successfully gained experience in this area. It is thus vital that a high quality, instructive review of current trends should be conducted, not only of the theoretical research results but also the practical developments in multilevel decision-making in business. This paper systematically reviews up-to-date multilevel decision-making techniques and clusters related technique developments into four main categories: bi-level decision-making (including multi-objective and multi-follower situations), tri-level decision-making, fuzzy multilevel decision-making, and the applications of these techniques in different domains. By providing state-of-the-art knowledge, this survey will directly support researchers and practical professionals in their understanding of developments in theoretical research results and applications in relation to multilevel decision-making techniques

Decision Support System for Managing Reverse Supply Chain

Reverse logistics are becoming more and more important in the overall Industry area because of the environment and business factors. Planning and implementing a suitable reverse logistics network could bring more profit, customer satisfaction, and an excellent social picture for companies. But, most of the logistics networks are not equipped to handle the return products in reverse channels. Reverse logistics processes and plans rely heavily on reversing the supply chain so that companies can correctly identify and categorize returned products for disposition, an area that offers many opportunities for additional revenue. The science of reverse logistics includes return policy administration, product recall protocols, repairs processing, product repackaging, parts management, recycling, product disposition management, maximizing liquidation values and much more. The focus of this project is to develop a reverse logistics management system/ tools (RLMS). The proposed tools are demonstrated in the following order. First, we identify the risks involved in the reverse supply chain. Survey tool is used to collect data and information required for analysis. The methodologies that are used to identify key risks are the six sigma tools, namely Define, Measure, Analyse, Improve and Control (DMAIC), SWOT analysis, cause and effect, and Risk Mapping. An improved decision-making method using fuzzy set theory for converting linguistic data into numeric risk ratings has been attempted. In this study, the concept of ‘Left and Right dominance approach’(Chen and Liu, 2001) and Method of ‘In center of centroids’ (Thoran et al., 2012a,b) for generalized trapezoidal fuzzy numbers has been used to quantify the ‘degree of risk’ in terms of crisp ratings. After the analysis, the key risks are identified are categorized, and an action requirement plan suggested for providing guidelines for the managers to manage the risk successfully in the context of reverse logistics. Next, from risk assessment findings, information technology risk presents the highest risk impact on the performance of the reverse logistics, especially lack of use of a decision support system (DSS). We propose a novel multi-attribute decision (MADM) support tool that can categorizes return products and make the best alternative selection of recovery and disposal option using carefully considered criteria using MADM decision making methodologies such as fuzzy MOORA and VIKOR. The project can be applied to all types of industries. Once the returned products are collected and categorized at the retailers/ Points of return (PoR), an optimized network is required to determine the number of reprocessing centres to be opened and the optimized optimum material flow between retailers, reprocessing, recycling and disposal centers at minimum costs. The research develops a mixed integer linear programming model for two scenarios, namely considering direct shipping from retailer/ PoR to the respective reprocessing centers and considering the use of centralized return centers (CRC). The models are solved using LINGO 15 software and excel solver tools respectively. The advantage of the implementation of our solution is that it will help improve performance and reduce time. This benefits the company by having a reduction in their cost due to uncertainties and also contributes to better customer satisfaction. Implementation of these tools at ABZ computer distributing company demonstrates how the reverse logistics management tools can used in order to be beneficial to the organization. The tool is designed to be easily implemented at minimal cost and serves as a valuable tool for personnel faced with significant and costly decisions regarding risk assessment, decision making and network optimization in the reverse supply chain practices