Proposing a Supply Chain Model for the Production-Distribution of Fuelwood in Greece using Multiobjective Programming

Multiobjective linear programming model on injection oilfield recovery system

In real-world decision-making, uncertainty plays a crucial role, especially when dealing with complex, multi-objective optimization problems. Traditional linear programming (LP) models often have the assumption that the data is precise and deterministic. However, this ‎assumption is often not realistic for many applications, as imprecision will always be present. This paper presents a fuzzy solution to ‎Z-Z-number-based multi-objective linear programming (ZMOLP) models. Z-numbers can combine fuzzy logic and Z-numbers to manage ‎uncertainty in (multi-objective) decision dilemmas. A Z-number consists of two parts: a fuzzy number for the uncertainty in the ‎data and a reliability score that indicates the degree of confidence in the data. The two aspects of Z-numbers make them ef‎fective for modeling imprecise data in multi-objective positioning. The effectiveness and overall computational efficiency of different ‎fuzzy membership functions (triangular, trapezoidal, Gaussian, etc.) were also explored to understand their impact on optimal solu‎tions. Z-numbers, through fuzzy numbers, provide a flexible and adaptable decision-making solution far superior to traditional methods ‎for managing imprecision that leads to a better representation of uncertainty related to objectives and constraints. To demonstrate the viability of Z-number-based approaches, practical applications were employed to illustrate their usage in healthcare decision-making and ‎engineering optimization‎.

In this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the $$\varepsilon$$-constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank.

Multiobjective linear programming (MOLP) models are developed to evaluate total phosphorus (TP) load reduction strategies for an off-stream reservoir. Cost, water quality, and equity are the three major objectives considered. Watershed-based, subwatershed-based, and equal-transport-path-length-based strategies are the three zone control strategies analyzed and compared. The agricultural nonpoint-source pollution (AGNSP) model is used to simulate the non–point-source pollution loads on the reservoir. A twostep modeling procedure is applied to verify sediment mass balance and water quality of storm runoff. MOLP models are established based on the simulation results for the three control strategies and are solved using the ADBASE package to generate the noninferior solution sets of the models. The subwatershed-based control strategy is observed to be the most cost-effective one based on results obtained for TP concentration between 13 and 20 ppb. With respect to equity, however, the watershed-based control strategy is superior to the others. The proposed multiobjective analyses are intended to improve the comparison and evaluation of nonpoint source pollution control strategies.

With the increasing pressure from global competition, manufacturers have realized that sustainable production is significant in supply chain management. Sustainable supplier selection and order allocation (SSS&OA) play a distinct and critical role for organizations to achieve sustainable development and build competitive advantage. In this paper, we aim to develop a novel SSS&OA model for selecting the most suitable sustainable suppliers and determining the optimal order sizes among them. First, double hierarchy hesitant linguistic term sets (DHHLTSs) are adopted to deal with uncertainty in evaluating the sustainable performance of alternative suppliers. Then, an extended decision field theory is proposed to choose efficient sustainable suppliers dynamically. Considering quantity discount, a multi-objective linear programming (MOLP) model is established to allocate reasonable order quantities among the selected suppliers. Finally, the applicability and effectiveness of the developed model are illustrated through its application in the electronic industry and through a comparative analysis with other methods.

Sustainable supply chain networks have attracted considerable attention in recent years as a means of dealing with a broad range of environmental and social issues. This paper reports a multi-objective mixed-integer linear programming (MILP) model for use in the design of a sustainable closed loop supply chain network under uncertain conditions. The proposed model aims to minimize total cost, optimize environmental impacts of establishment of facilities, processing and transportation between each level as well as social impacts including customer satisfaction. Due to changes in business environment the uncertainty existed in the research problem, in this paper the chance constrained fuzzy programming approach applied to cope with uncertainties in parameter of the proposed model. Then the proposed multi-objective model solves as single-objective model using LP-metric method.

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.

On computational methods for solutions of multiobjective linear production programming games

WITHDRAWN: Application of a fuzzy multi-objective defuzzification method to solve a transportation problem

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.

This study presents a novel multi-objective linear fractional interval programming model for sustainable waste management under uncertainty, with a focus on the Melbourne metropolitan region. The model integrates three conflicting objectives: minimizing the cost per recycled ton, minimizing emissions per processed ton, and minimizing the energy-related carbon footprint. In the existing literature, most traditional models rely on fixed decision variables, which often fail to capture the inherent uncertainty present in real-world, data-driven problems. Thus, in this study, all key parameters, including transport costs, recycling efficiencies, emissions, and facility capacities, are represented as interval values to account for parameter variability. The optimal solution allocates waste primarily to residential and green streams, yielding a cost per recycled ton in the range [21.01, 37.44] AUD, emissions per processed ton of [8.88, 20.75] kg CO $$_2$$ , and an energy-related carbon footprint of [4.44, 9.00] kg CO $$_2$$ . All solutions satisfy the prescribed budget and emission caps, demonstrating operational feasibility. The results further indicate that environmental objectives exhibit greater robustness to parameter uncertainty than economic costs, highlighting the effectiveness of the proposed interval-based framework for supporting sustainable municipal waste management decisions.

The purpose of this paper is to develop a new two-stage method for fuzzy multi-objective linear program and apply to engineering project portfolio selection. In the fuzzy multi-objective linear program, all the objective coefficients, technological coefficients and resources are trapezoidal fuzzy numbers (TrFNs). An order relationship for TrFNs is introduced by using the interval expectation of TrFNs. In the first stage, the fuzzy multi-objective linear program with TrFNs is transformed into an interval multi-objective linear program according to the order relationship of TrFNs. Combining the ranking order relation between intervals with the satisfactory crisp equivalent forms of interval inequality relations, the interval multi-objective linear program is further transformed into a crisp multi-objective linear program. In the second stage, the positive and negative ideal solutions are calculated as well as the closeness degrees from the positive ideal solution to all objectives on the basis of the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). Then, using the closeness degrees, we convert the crisp multi-objective linear program into mono-objective program to solve. The proposed method is not only mathematically rigorous, but also can adequately consider the acceptance degree of decision maker that the fuzzy constraints may be violated. The other possible cases of the fuzzy multi-objective linear program are also discussed. The proposed method is illustrated by means of a project portfolio selection problem.

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

This paper deals with a fuzzy goal programming methodology for solving multiobjective linear fractional chance constrained programming problems containing fuzzy numbers and exponentially distributed fuzzy random variables associated with the system constraints. In model formulation process, the problem is converted into an equivalent fuzzy programming model by applying chance constrained programming technique in a fuzzily defined probabilistic decision making situation. Then using the concept of α-cut for fuzzy numbers and by considering the tolerance level of fuzzy numbers the problem reduces to an equivalent sub problem with interval coefficients. In this method the convex combination of each interval is used and the problem is reduced to a nonlinear programming problem. Finally the model is solved by converting nonlinear model into its equivalent multiobjective linear programming model by using Taylor series; and a priority based fuzzy goal programming method is used for achievement of the highest membership degree. To demonstrate the efficiency of the proposed technique an illustrative example, studied previously, is solved and the solution is compared with the existing methodology.

In this paper, a multi-objective linear programming model was developed which sought to simultaneously optimize total costs and total GHG emissions for the Thai Rubber supply chain. The model was s...