A Novel Method for Optimal Solution of Fuzzy Chance Constraint Single-Period Inventory Model

A method is proposed for solving single-period inventory fuzzy probabilistic model (SPIFPM) with fuzzy demand and fuzzy storage space under a chance constraint. Our objective is to maximize the total profit for both overstock and understock situations, where the demand D~j for each product j in the objective function is considered as a fuzzy random variable (FRV) and with the available storage space area W~, which is also a FRV under normal distribution and exponential distribution. Initially we used the weighted sum method to consider both overstock and understock situations. Then the fuzziness of the model is removed by ranking function method and the randomness of the model is removed by chance constrained programming problem, which is a deterministic nonlinear programming problem (NLPP) model. Finally this NLPP is solved by using LINGO software. To validate and to demonstrate the results of the proposed model, numerical examples are given

Solving bi-objective bi-item solid transportation problem with fuzzy stochastic constraints involving normal distribution

In today's competitive world, entrepreneurs cannot argue for transporting a single product. It does not provide much profit to the entrepreneur. Due to this reason, multiple products need to be transported from various origins to destinations through various types of conveyances. Real-world decision-making problems are typically phrased as multi-objective optimization problems because they may be effectively described with numerous competing objectives. Many real-life problems have uncertain objective functions and constraints due to incomplete or uncertain information. Such uncertainties are dealt with in fuzzy/interval/stochastic programming. This study explored a novel integrated model bi-objective bi-item solid transportation problem with fuzzy stochastic inequality constraints following a normal distribution. The entrepreneur's objectives are minimizing the transportation cost and duration of transit while maximizing the profit subject to constraints. The chance-constrained technique is applied to transform the uncertainty problem into its equivalent deterministic problem. The deterministic problem is then solved with the proposed method, namely, the global weighted sum method (GWSM), to find the optimal compromise solution. A numerical example is provided to test the efficacy of the method and then is solved using the Lingo 18.0 software. To highlight the proposed method, comparisons of the solution with the existing solution methods are performed. Finally, to understand the sensitivity of parameters in the proposed model, sensitivity analysis (SA) is conducted

A Redundancy Detection Algorithm for Fuzzy Stochastic Multi-Objective Linear Fractional Programming Problems

The computational complexity of linear and nonlinear programming problems depends on the number of objective functions and constraints involved and solving a large problem often becomes a difficult task. Redundancy detection and elimination provides a suitable tool for reducing this complexity and simplifying a linear or nonlinear programming problem while maintaining the essential properties of the original system. Although a large number of redundancy detection methods have been proposed to simplify linear and nonlinear stochastic programming problems, very little research has been developed for fuzzy stochastic (FS) fractional programming problems. We propose an algorithm that allows to simultaneously detect both redundant objective function(s) and redundant constraint(s) in FS multi-objective linear fractional programming problems. More precisely, our algorithm reduces the number of linear fuzzy fractional objective functions by transforming them in probabilistic-possibilistic constraints characterized by predetermined confidence levels. We present two numerical examples to demonstrate the applicability of the proposed algorithm and exhibit its efficacy

Satisficing solutions for multiobjective stochastic linear programming problems

Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out.Decision Science

Supply chain outsourcing risk using an integrated stochastic-fuzzy optimization approach.

a b s t r a c t A stochastic fuzzy multi-objective programming model is developed for supply chain outsourcing risk management in presence of both random uncertainty and fuzzy uncertainty. Utility theory is proposed to treat stochastic data and fuzzy set theory is used to handle fuzzy data. An algorithm is designed to solve the proposed integrated model. The new model is solved using the proposed algorithm for a three stage supply chain example. Computation suggests an analysis of risk averse and procurement behavior, which indicates that a more risk-averse customer prefers to order less under uncertainty and risk. Tradeoff game analysis yields supported points on the trade-off curve, which can help decision makers to identify proper weighting scheme where Pareto optimum is achieved to select preferred suppliers

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

Application of Multi-Objective Optimization Based on Genetic Algorithm for Sustainable Strategic Supplier Selection under Fuzzy Environment

Purpose: The incorporation of environmental objective into the conventional supplier selection practices is crucial for corporations seeking to promote green supply chain management (GSCM). Challenges and risks associated with green supplier selection have been broadly recognized by procurement and supplier management professionals. This paper aims to solve a Tetra “S” (SSSS) problem based on a fuzzy multi-objective optimization with genetic algorithm in a holistic supply chain environment. In this empirical study, a mathematical model with fuzzy coefficients is considered for sustainable strategic supplier selection (SSSS) problem and a corresponding model is developed to tackle this problem. Design/methodology/approach: Sustainable strategic supplier selection (SSSS) decisions are typically multi-objectives in nature and it is an important part of green production and supply chain management for many firms. The proposed uncertain model is transferred into deterministic model by applying the expected value measure (EVM) and genetic algorithm with weighted sum approach for solving the multi-objective problem. This research focus on a multiobjective optimization model for minimizing lean cost, maximizing sustainable service and greener product quality level. Finally, a mathematical case of textile sector is presented to exemplify the effectiveness of the proposed model with a sensitivity analysis. Findings: This study makes a certain contribution by introducing the Tetra ‘S’ concept in both the theoretical and practical research related to multi-objective optimization as well as in the study of sustainable strategic supplier selection (SSSS) under uncertain environment. Our results suggest that decision makers tend to select strategic supplier first then enhance the sustainability. Research limitations/implications: Although the fuzzy expected value model (EVM) with fuzzy coefficients constructed in present research should be helpful for solving real world problems. A detailed comparative analysis by using other algorithms is necessary for solving similar problems of agriculture, pharmaceutical, chemicals and services sectors in future. Practical implications: It can help the decision makers for ordering to different supplier for managing supply chain performance in efficient and effective manner. From the procurement and engineering perspectives, minimizing cost, sustaining the quality level and meeting production time line is the main consideration for selecting the supplier. Empirically, this can facilitate engineers to reduce production costs and at the same time improve the product quality. Originality/value: In this paper, we developed a novel multi-objective programming model based on genetic algorithm to select sustainable strategic supplier (SSSS) under fuzzy environment. The algorithm was tested and applied to solve a real case of textile sector in Pakistan. The experimental results and comparative sensitivity analysis illustrate the effectiveness of our proposed model.Peer Reviewe