A fuzzy stochastic programming approach to solve the capacitated lot size problem under uncertainty

This work presents a novel fuzzy multi-objective linear programming (f-MOLP) model for solving integrated production-transportation planning decision (PTPD) problems in supply chains in a fuzzy environment. The proposed model attempts to simultaneously minimise total production and transportation costs, total number of rejected items, and total delivery time with reference to available capacities, labor level, quota flexibility, and budget constraints at each source, as well as forecast demand and warehouse space at each destination. An industrial case demonstrates that the proposed f-MOLP model achieves an efficient compromise solution and overall decision maker satisfaction with determined goal values. Additionally, the proposed model provides a systematic framework that facilitates decision makers to interactively modify the fuzzy data and parameters until a satisfactory solution is obtained. Overall, the f-MOLP model offers a practical method for solving PTPD problems with fuzzy multiple goals, and can effectively improve producer–distributor relationships within a supply chain.

This paper investigates a multi-objective supplier selection and order allocation problem under quantity discounts in a fuzzy environment. Prior research on supplier selection and order allocation with quantity discounts mainly considered partial fuzziness of the decision problem; a situation where both the objectives of the decision maker and the constraints are fuzzy has not been studied up to now. This paper closes this gap by integrating both aspects into a single model. First, a combination of fuzzy preference programming and interval-based TOPSIS is proposed for evaluating suppliers. Secondly, based on the scores obtained in the first step, a fuzzy multi-objective linear programming model is developed. Subsequently, a new solution procedure for solving the fuzzy multi-objective linear programming model is presented. The procedure first transforms fuzzy constraints and coefficients into deterministic coefficients, and then three different fuzzy programming approaches, namely interactive fuzzy multi-objective linear programming, and the weighted additive as well as the weighted max-min method are implemented. Finally, the performance of each method is evaluated by computing the distance between each solution and the preferred solution.

A multi-objective fuzzy linear programming model for optimization of natural gas supply chain through a greenhouse gas reduction approach

In this paper, three criteria scheduling problem of n jobs on a single machine is considered. Each of these n jobs is to be processed without interruption and becomes available for processing at time zero. The problem is to minimize three objectives simultaneously, which are the completion time, maximum tardiness, and maximum earliness. Here, we develop a fuzzy multi-objective linear programming (FMOLP) model for solving multi-objective scheduling problem in a fuzzy environment by using piecewise linear membership function (PLMF). A numerical example demonstrates the feasibility of applying the proposed model to scheduling problem, and yields a compromised solution to help the decision maker’s overall levels of satisfaction. The algorithm is tested to show the ability of applying this model to three criteria.

There are significant amount of literature on the capacitated lot sizing problem(CLSP) with different levels and approaches. In this article, immune complement algorithm (ICA) was discussed in scheduling optimization of CLSP under the condition of single level, single machine. The affinity function was the total cost which including order, inventory carrying and labor costs. Complement individual was represented by binary to determine order sequence and lot sizing. Experimentation performed with 5 production 6 period indicated that ICA had the characteristics of high speed of convergence, less generations besides approaching best solution, and it could be used in CLSP on medium scale.

In this paper, the optimal load curtailment (OLC) problem is formulated as a multi‐objective optimization framework, which objectives include maximizing the security margin and minimizing the cost incurred for load curtailment. A new and comprehensive multi‐objective fuzzy linear programming (MFLP) method is developed to solve this presented OLC model. Using the MFLP method, objectives and constrains of the OLC model are fuzzied and their enforcements are maximized. The MFLP model can deal with the uncertainties that exist in certain variables and overcome the limitations of minor constraint violations in normal LP model. The effectiveness of the developed method is tested on the modified IEEE 30 bus system and the IEEE 118 bus system. Copyright © 2009 John Wiley & Sons, Ltd.

Application of fuzzy optimization to a supply chain network design: A case study of an edible vegetable oils manufacturer

This paper aims to design a sustainable stochastic electricity production network where fossil fuels-based, biomass-based, and co-firing-based production strategies are simultaneously considered in order to take advantage of all the three production strategies. A multi-objective stochastic mixed integer linear programming model is proposed to achieve economic feasibility, as well as environmental and social benefits under multiple uncertainties. The model is solved by using the improved augmented epsilon constraint method. A case study is used to illustrate the effectiveness of the proposed model. Pareto optimal analysis is conducted to understand the trade-off between economic, environmental, and social aspects of sustainability.

This study focuses on solving multiobjective stochastic linear programming (MSLP) problems with partial information on probability distribution. The method presented in this paper utilises the concept of ranking function and linguistic hedges in the fuzzy transformation stage to take into account the internal values of the probability distribution. An adaptive arithmetic average approach is then used to convert the multiobjective problems into a single objective problem. Comparison of results with existing methods in the literature is presented which shows that the method presented performs as good as the existing methods in terms of solution quality but better in terms of computational effort.

The difficulty in solving either multi-objective linear programming (MOLP) problems or fuzzy multi-objective linear programming (FMOLP) problems is the trade-off among objectives. To deal with this difficulty, we proposed a new algorithm for solving FMOLP problems by using zero-sum game. First, FMOLP problem given is converted to a crisp MOLP problem by using ranking function, and then a payoff matrix is constructed to find the weights of each objective function of the MOLP problem. After that, each weight is multiplied with the corresponding objective function, a single-objective LP problem is obtained and thus, FMOLP problem is solved. The proposed algorithm is illustrated by numerical examples for the FMLOP problems having fuzzy constraints or not.

Integrating two interconnected processes and controlling conflicting goals of a production and distribution problem is necessary for better planning. The aim of this integration is to allocate the limited available resources to produce the products over the time periods and ensure economical dispatching to distribution centres. In a responsive and competitive market, production and distribution planning modules is considered here within the framework of satisfaction level of decision maker. Triangular fuzzy numbers and the concept of minimum accepted level are employed to formulate the problem. Minimum operator and weighted average operator method is used to aggregate all fuzzy set and solved by three algorithms and goal programming method. The proposed approach aims to formulate a fuzzy multi-objective linear programming model to simultaneously minimise the total production cost, distribution cost and delivery time for multi-product and multi-time period under multiple uncertainty. AHP is used to rank multiple objectives and solved with MATLAB.

Fuzzy multi-objective decision model for calibration supplier selection problem

Modeling Pooled Purchasing Strategy in Purchasing Consortium to Optimize Total Purchasing Cost

Joint production and maintenance optimization in flexible hybrid Manufacturing–Remanufacturing systems under age-dependent deterioration

This work applies fuzzy sets to the integration of purchasing, manufacturing and assembling of production planning decisions with multiple suppliers, multiple components and multiple machines in remanufacturing systems. The developed fuzzy multi-objective linear programming model (FMOLP) simultaneously minimizes total costs, total $text{CO}_2$ emissions and total lead time with reference to customer demand, due date, supplier/manufacturer capacity, lot-size release and machine yield. The proposed FMOLP model provides a recoverable remanufacturing framework that facilitates fuzzy decision-making, enabling the decision maker (DM) to adjust interactively the membership function or parameters during the solution procedure to obtain a preferred and satisfactory solution. To test the model, it was implemented in various scenarios with a remanufacturing production system. The analytical results in this work can help planner by enabling systematic analysis of the cost-effectiveness of remanufacturing systems and their potential for improving $text{CO}_2$ emissions and lead time in terms of remanufacturing planning. Future investigations may apply the related patterns of non-linear membership functions to develop an actual remanufacturing planning decision.