Application of interactive fuzzy goal programming for multi-objective integrated production and distribution planning

Fuzzy multi-objective decision model for calibration supplier selection problem

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

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.

Background: People want to be able to evaluate different kinds of information in a good way. There are various methods that they develop in such situations. Among the optimization methods, the goal programming method is often used when there are multiple objectives that decision makers want to accomplish. Because scheduling and planning problems have multiple objectives that are desired to be achieved, the goal programming method helps the researcher in contradictory situations between these goals. Methods: This study includes, examines, and analyzes recent research on service scheduling and planning. In the literature, service scheduling and planning studies have been examined using goal programming method from past to today. Results: The studies are detailed according to the type of goal programming, according to scheduling types, the purpose used in the studies, and the methods integrated with the goal programming. There are 142 studies in Emerald, Science Direct, Jstor, Springer, Taylor and Francis, Google Scholar, etc. databases that are examined in detail. For readers, diversification has been made to facilitate the identification of these studies and a detailed overview has been presented. Conclusion: As a result of the study, studies with the goal programming in the literature have been seen. The readers’ perspectives for planning and scheduling are discussed.

This study aims to design a multi-period credit portfolio optimization model with a nonlinear multi-objective fuzzy mathematical modeling approach. In terms of data collection, this study is a descriptive-survey research and in terms of the nature and purpose of the research, it is an applied one. The statistical population of the research includes all facility files of the last 10 years as well as the statements of financial position of Ansar Bank branches affiliated with Sepah Bank, selected by census method. The risk criteria used in the models include Average Value at Risk (AVaR), Conditional Value at Risk (CVAR) and Semi-Entropy. First, having reviewed the research literature, the objectives and indices of the portfolio optimization issue were investigated based on the practical character of this issue and the main indices were selected. Then, each of the objectives and constraints were specified in a state of uncertainty and ambiguity, based on the principles of fuzzy credibility theory, for a state in which the expected rate of stock return is a triangular fuzzy number. Finally, three multi-objective fuzzy models were designed based on the selected criteria. Research models were implemented using MOPSO algorithm. The software used in conducting the research was MATLAB software. The results indicated that the CVAR model performed better than the other two models, i.e. AVAR and Semi-Entropy, in evaluating optimal portfolios.

In real-life logistics, distribution plans might be affected by weather conditions (rain, snow, and fog), since they might have a significant effect on traveling times and, therefore, on total distribution costs. In this paper, the distribution problem is modeled as a multi-depot vehicle routing problem with stochastic traveling times. These traveling times are not only stochastic in nature but the specific probability distribution used to model them depends on the particular weather conditions on the delivery day. In order to solve the aforementioned problem, a simheuristic approach combining simulation within a biased-randomized heuristic framework is proposed. As the computational experiments will show, our simulation-optimization algorithm is able to provide high-quality solutions to this NP-hard problem in short computing times even for large-scale instances. From a managerial perspective, such a tool can be very useful in practical applications since it helps to increase the efficiency of the logistics and transportation operations.

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.

This paper first reviews the current research status of the Vehicle Routing Problem (VRP), and analyzes the achievements of domestic and foreign scholars in VRP variants and the application of intelligent algorithms. Then, it describes in detail the distribution problem of Company M and establishes a mathematical model, which is solved by AMPL software. The research results show that the optimized distribution plan significantly improves the vehicle loading rate, reduces the number of distribution vehicles and the total driving distance, thereby greatly reducing the distribution cost. Specifically, before optimization, three vehicles were needed to complete the distribution task, with a total driving distance of 73.17 kilometers and a total distribution cost of 621.31 yuan; after optimization, only two vehicles are needed, the total driving distance is reduced to 55.56 kilometers, and the total distribution cost is reduced to 419.16 yuan, a cost reduction of 32%. This study verifies the effectiveness of AMPL software in vehicle routing optimization, providing a practical and feasible distribution optimization plan for Company M, significantly improving the efficiency of logistics distribution and reducing operating costs. Future research can further expand the data scale and consider more complex factors in actual scenarios to enhance the applicability and optimization effect of the model.

The aim of every manufacturing organization is to fulfil the demand of their customers at minimum total cost or at maximum profit. To fulfil the demand of geographically dispersed customers, manufacturing organizations need to produce products at multiple manufacturing sites located close to the customer. Although planning function in such a scenario becomes very complex, this multi-site environment has been found to improve efficiency and provide better services to customers. It involves interlinked decisions involving procurement, production and distribution at different plants and distribution sites. Production and distribution planning are very important aspects of planning in multi-site manufacturing. To compete in this globalized market, enterprises should focus on optimizing and integrating production and distribution functions simultaneously. The authors in the research work present an integrated production and distribution planning problem for a two-level supply chain consisting of multiple manufacturing sites serving multiple selling locations. The problem is formulated as a multi-objective mixed-integer programming model considering three important aspects of production and distribution planning, viz. set-up, backorder and transportation capacity. Total cost, delivery time and backlog level are the three conflicting objectives that need to be minimized. The proposed multi-objective mathematical problem is solved using pre-emptive goal programming method. The performance of the proposed model is illustrated through an example problem instance. Further analysis is conducted to visualize the effect of changing priority level on objective function and deviation variable values.

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.

In the face of current business competition, existing companies are competing with each other to get optimal output in order to compete with other companies. One of the steps that can be taken to be able to obtain optimal output is to choose potential suppliers in obtaining profits. This research uses the fuzzy analytical hierachy process method with the aim of knowing the priority of suppliers who will cooperate and also the goal programming method with the aim of determining the allocation of rice orders in order to minimize purchase costs, minimize the percentage of defects, maximize supplier weight and meet supply targets. The results of supplier 1, supplier 2, and supplier 3 weights are 0.3145; 0.3489; 0.3365 respectively. The goal programming method provides a better solution than the current order allocation. The total purchase cost set by the company did not decrease or increase but the total defective orders decreased by 23.43% in one year.

Two factors for customers to consider when purchasing a vehicle are the vehicle acoustical comfort and the vibration in the vehicle cabin, both of which contribute to a comfortable driving environment. The amount of discomfort is included by frequency, magnitude, direction, and the period during which the noise is experienced and also where the vibration is experienced in the cabin. The main sources of vibration that have been identified previously are the vibration transmitted from engine and the vibration transmitted from the interaction of the tires with the road surface. In this study, we investigate the effect of the vibration caused by the tire interaction with the road surface by estimating the amount of noise produced due to this phenomenon. The methodology focuses on the trends which occur in the noise exposure and on the vibration exposure that has been generated throughout the engine operating rpm range in both stationary and non-stationary conditions. The vibration dose value (VDV)f was used to assess the amount of vibration exposure that is transmitted to the driver’s body in the cabin. Through the study, we have proved that the vibration caused by the tire-road surface contact is a major contributor to the cabin’s interior noise. Based on the results, a goal programming method was developed to optimise the noise levelin the cabin by considering the vibration as an input in the model. Finally, a multi-objective goal programming was developed successfully which could be used to optimize the noise level in the cabin by looking at the value of the VDV required at particular engine speeds (rpm).

This paper presents a Goal Programming (GP) method to solve a class of Fractional Programming (FP) problems which have the characteristics of Dynamic Programming (DP) problems. The method is designed to solve the problems when one or more objective goals appear at the same priority level and the method works in such a way that the problem is solved recursively without linearizing the fractional objectives. In the solution process, the feasible regions of the decision variables are determined by using GP rather than the traditional DP method. An example is provided to illustrate the method outlined Keywords: Fractional programmingNon-linear programmingGoal programmingMultiple objectiveDynamic programming

Production, transportation, and distribution planning in a multi-commodity tri-echelon system : Hasan Pirkul and Vaidyanathan Jayaraman Transportation Science Vol. 30, No. 4, 1996, p. 291 ff

This paper addresses an integrated production and distribution planning problem for a two-echelon supply chain network comprising of multiple manufacturers serving multiple selling locations. A novel fuzzy multi-objective mixed integer programming model is formulated considering multi-product, multi-period, and multi-site manufacturing environment. Minimization of total cost, delivery time, and backorder level are the three fuzzy objectives represented by piecewise linear membership function. Three important production and distribution aspects viz. capacity of the heterogeneous transportation, backordering for unfulfilled demand, and set-up cost/time for different products at manufacturing site are incorporated in an integrated manner to represent closeness to the real-life problem. An illustrative example inspired from a real-world case of an automobile industry is taken to demonstrate analytical results of the proposed approach. The outcome of the research indicates the practical applicability of the approach. Sensitivity analysis on objective function values is conducted for analyzing the effect of change in aspiration levels of objective function values on decision maker’s satisfaction level.