Possibilistic Linear Programming Research Articles

Integrated design of a sustainable waste management system with co-modal transportation network: A robust bi-level decision support system

Efficient waste management practices play a critical role in addressing the acute challenges of environmental protection, public health and resource conservation. A well-designed system guarantees that waste is efficiently collected, treated and disposed while minimizing negative impacts on ecosystems and human well-being. This work presents a robust bi-level decision support system to establish a sustainable waste management system using a co-modal transportation network to treat municipal solid waste timely and efficiently. Consequently, two integrated multi-objective mathematical models are developed to formulate the problem. Configuring the municipal solid waste network in the first level of the suggested decision support system, the transportation network is designed in the second level taking into account non-identical modes. The objectives are to minimize total cost and total emission in both levels, while maximization of total job creation is also addressed in the first level. Robust optimization method and weighted goal programming method are then utilized to accommodate the developed decision support system against uncertainty and multi-objectiveness, respectively. To validate the efficiency of these methods, they are assessed against possibilistic linear programming technique and Lp-metric approach with the help of simple additive weighting (SAW) method, respectively. Eventually, several numerical examples are generated based on the benchmarks given in the literature, which are then tackled using CPLEX solve to appraise the applicability and complexity of the developed methodology. The findings reveal the efficacy of the decision support system in terms of finding solutions in less than 448 s on average. Finally, sensitivity analyses are performed to draw out useful practical implications and decision aids.

Artificial intelligence‐enabled smart city management using multi‐objective optimization strategies

AbstractThis article outlines an integrated strategy that combines fuzzy multi‐objective programming and a multi‐criteria decision‐making framework to achieve a number of transportation system management‐related objectives. To rank fleet cars using various criteria enhancement, the Fuzzy technique for order of preference by resemblance to optimum solution are initially integrated. We then offer a novel Multi‐Objective Possibilistic Linear Programming (MOPLP) model, based on the rankings of the vehicles, to determine the number of vehicles chosen for the work while taking into consideration the constraints placed on them. The search for optimal solutions to MOPs has benefited from the decades‐long development of classical optimisation techniques. As a result of its potential for use in the real world, multi‐objective optimisation (MOO) under uncertainty has gained traction in recent years. Recently, fuzzy set theory has been used to solve challenges in multi‐objective linear programming. In this paper, we present a method for solving MOPs that makes use of both linear and non‐linear membership functions to maximize user happiness. A hypothetical case study of transportation issue is taken here. This innovative approach improves management for the betterment of transportation networks in smart cities. The method is a more robust and versatile approach to the complex difficulties of contemporary urban transportation because it incorporates the TOPSIS method for vehicle ranking and then using Distance Operator and variable Membership Functions in fuzzy goal programming operation on the selected vehicles. The results provide valuable insights into the strengths and limitations of each technique, facilitating informed decision‐making in real‐world optimization scenarios.

Possibilistic Aggregate Production Planning Considering Dynamic Workforce with Fuzzy Demand

This Aggregate Production Planning (APP) is a combination of Possibilistic Linear Programming (PLP), Fuzzy Goal Programming (FGP), and the Perfume Accounting System (PAS) to maximize profit. APP involves strategic decisions on Production levels, Inventory management, and Resource allocation to meet client demand while maximizing profit. Traditional planning models face significant challenges due to the uncertainties and complexities inherent in real world production environments. In this paper, there is an integration of PLP, Fuzzy Goal Programing, and throughput accounting system to overcome these challenges. At the very end of the paper, based on the data received from the company, the derived findings were by using Lingo Version 18 software. The model includes possibility distributions of the input parameters. Decision-makers can take into account the uncertainty and imprecision in demand forecasts and dynamic workforce in maximizing profit while taking into account risk tolerance.

Integrated design of sustainable supply chain and transportation network using a fuzzy bi-level decision support system for perishable products

This study introduces a fuzzy bi-level Decision Support System (DSS) to optimize a sustainable multi-level multi-product Supply Chain (SC) and co-modal transportation network for perishable products distribution. To this end, two integrated multi-objective Mixed Integer Linear Programming (MILP) models are proposed to formulate the problem. On-time delivery is taken into account as the main factor that determines model performance due to perishability of products. Optimizing the design of SC network using the first level of the proposed DSS, the transportation network configuration is provided optimally in the second level considering different modes and options. In order to contribute to the literature, mainly by addressing uncertainty and perishability, a hybrid solution technique based on possibilistic linear programming and Fuzzy Weighted Goal Programming (FWGP) approach is developed to accommodate our suggested bi-level model. This technique can deal with problem uncertainty while also ensuring the sustainability of the overall system. Lp-metric method is implemented along with three well-known quality indicators to assess the performance of the proposed solution method and quality of obtained solutions. Finally, three illustrative numerical examples are provided using the CPLEX solver to showcase the applicability of the proposed methodology and discuss the complexity of the model. Results demonstrate the efficiency of the proposed methodology in finding optimal solutions compared to Lp-metric method, such that it is able to treat a problem with more than 2.2 million variables and 1.3 million constraints in 1093.08 s.

Integrated Possibilistic Linear Programming with Beta-Skewness Degree for a Fuzzy Multi-Objective Aggregate Production Planning Problem Under Uncertain Environments

This study proposes an improved Fuzzy Programming (FP) approach to optimise multi-objective Aggregate Production Planning (APP) problem under uncertain environments. The proposed approach integrates the concept of Possibilistic Linear Programming (PLP) with Beta-Skewness Degree that decision-makers can manipulate the best level of data fuzziness as well as maintain such fuzziness in the optimisation process (by not turning it to deterministic data too early). The effectiveness of the proposed approach is demonstrated through a case study by minimising the highest overall deviation from the ideal solution of total costs under imprecise operating costs, customer demand, labour level, and machine capacity. Our comparative result clearly shows that the obtained solution outperforms the solutions from traditional defuzzification methods. The proposed approach also helps decision-makers not only to know and optimise the most likely situation, but also realise the outcomes in the optimistic and the pessimistic business situations so that decision makers can prepare and take necessary actions for future uncertainty.

Integrating a Weighted Additive Multiple Objective Linear Model with Possibilistic Linear Programming for Fuzzy Aggregate Production Planning Problems

This study uses an integrated optimization method by applying a weighted additive multiple objective linear model with Possibilistic Linear Programming (PLP) to fuzzy Aggregate Production Planning (APP) problems under an uncertain environment. The uncertainty conditions include uncertainties of operating times and costs, customer demand, labor level, as well as machine capacity. The aim of this study is to minimize total costs of the plan that consist of the production cost and costs of changes in labor level. The proposed hybrid approach minimizes the most possible value of the imprecise total costs, maximizes the possibility of obtaining lower total costs, and minimizes the risk of obtaining higher total costs from PLP as multiple objectives for the fuzzy multiple objective linear model optimization. The outcome of the proposed approach shows that the solution is closer to the ideal solution obtained from Linear Programming than a typical solution obtained from PLP. There is also a higher overall satisfaction value.

A fuzzy multi-objective optimization model for recoverable manufacturing systems in uncertain environments

ABSTRACTThis study develops a fuzzy multi-objective linear programming (FMOLP) model with an interactive two-phase possibilistic linear programming (ITPPLP) approach for solving remanufacturing production system problems with multiple goals in a fuzzy environment. Because the related parameters are imprecise/fuzzy in nature, a triangular possibility distribution can be used. The proposed model aims to simultaneously minimize total production costs and total lead time, while integrating multiple suppliers, multiple components, multiple time periods, and multiple machines to realize a remanufacturing production system. An air-conditioning compressor case was used to test the proposed models. The analytical results presented in this work will allow decision-making managers to better understand the systematic analysis, potential for cost-effectiveness and lead time of recoverable remanufacturing planning.

Lean Policies in Route Planning and Scheduling of Waste Collection with Fuzzy Demand

This study addresses a household waste collection routing problem with a heterogeneous fleet. The collection fleet includes hand carts and vehicles to transport wastes from houses to disposal sites. The authors attempt to enhance the system efficiency considering lean policies, which leads to minimizing the fleet size and the collection time concurrently. In reality, uncertainty of some parameters stems from environmental and living conditions. Hence, a bi-objective fuzzy possibilistic mixed integer linear programming model is developed to design an optimal collection network. To solve the model, a hybrid solution approach is applied, which combines fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, several numerical examples are tested to illustrate validation of the proposed model and applicability of the applied solution approach.

Measuring Cost Efficiency with New Fuzzy DEA Models

In conventional cost efficiency models, input and output data and their corresponding input prices are fundamentally known for each decision-making unit. However, the observed values of the input and output data in real problems are sometimes imprecise. This study shows that the cost efficiency evaluation method can be improved to account for situations where input–output data and their corresponding input prices are fuzzy numbers. A new fuzzy cost-minimizing model known as a possibilistic linear programming problem is proposed to evaluate the cost efficiency. In this model data information is considered as triangular fuzzy numbers. Using the \(\alpha\)-level-based approach, the model is transformed into an interval programming problem which is solved as a crisp parametric linear programming model. In addition, new definitions of the fuzzy cost efficiency and cost efficient unit are suggested. Finally, a numerical example is presented to illustrate the proposed method.

Possibilistic Linear Programming Problems involving Normal Random Variables

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.

An enhanced possibilistic programming approach for reliable closed-loop supply chain network design

Most of current logistics network design models in the literature typically assume that facilities are always available and absolutely reliable while in practice, they are always subject to several operational and disruption risks. This paper proposes a reliable closed-loop supply chain network design model, which accounts for both partial and complete facility disruptions as well as the uncertainty in the critical input data. The proposed model is of mixed integer possibilistic linear programming type that aims to minimise simultaneously the total cost of opening new facilities and the expected cost of disruption scenarios. An enhanced possibilistic programming approach is proposed to deal with the epistemic uncertainty in input data. Furthermore, the p-robustness criterion is used to limit the cost of disruption scenarios and protect the designed network against random facility disruptions. Several numerical experiments along with sensitivity analyses on uncertain parameters are conducted to illustrate the significance and applicability of the developed model as well as the effectiveness of the proposed solution approach. Our results demonstrate that operational and disruption risks considerably affect the whole structure of the designed network and they must be taken into account when designing a reliable closed-loop logistics network.

Combining possibilistic linear programming and fuzzy AHP for solving the multi-objective capacitated multi-facility location problem

The capacitated multi-facility location problem is a complex and imprecise decision-making problem which contains both quantitative and qualitative factors. In the literature, many objectives for optimizing many types of logistics networks are described: (i) minimization objectives such as cost, inventory, transportation time, environmental impact, financial risk and (ii) maximization objectives such as profit, customer satisfaction, and flexibility and robustness. However, only a few papers have considered quantitative and qualitative factors together with imprecise methodologies. Unlike traditional cost-based optimization techniques, the approach proposed here evaluates these factors together while considering various viewpoints. Decision-makers must deal both factors together to model complex structure of real-world applications. In this paper, a two-phase possibilistic linear programming approach and a fuzzy analytical hierarchical process approach have been combined to optimize two objective functions (“minimum cost” and “maximum qualitative factors benefit”) in a four-stage (suppliers, plants, distribution centers, customers) supply chain network in the presence of vagueness. The results and findings of this method are illustrated with a numerical example, and the advantages of this methodology are discussed in the conclusion.

An Approach to Solve a Possibilistic Linear Programming Problem

The objective of the paper is to deal with a kind of possibilistic linear programming (PLP) problem involving multiple objectives of conflicting nature. In particular, we have considered a multi objective linear programming (MOLP) problem whose objective is to simultaneously minimize cost and maximize profit in a supply chain where cost and profit coefficients, and related parameters such as available supply, forecast demand and budget are fuzzy with trapezoidal fuzzy numbers. An example is given to illustrate the strategy used to solve the aforesaid PLP problem.

A possibilistic linear programming model for supply chain network design under uncertainty

In this paper, we develop a possibilistic linear programming model for supply chain network design with imprecise inputs: market demands, supplied quantities, transportation costs, opening costs, treatment and storage costs are modelled as fuzzy numbers. An efficient possibilistic linear programme is constructed with fuzzy objective function that minimizes the sum of investment costs and operating costs of the supply chain. A method for solving the programming problem with fuzzy parameters is proposed. Application to a supply chain problem at a European textile company illustrates our methodology. Numerical results show that the performance of the proposed model in handling data uncertainty is better when compared to a classical deterministic model.

A fuzzy optimization model to the aggregate production/distribution planning decision in a multi-item supply chain network*

This paper develops a supply chain fuzzy model considering aggregate production/distribution planning. It also presents a fuzzy Mixed-integer Linear Programming Model (FMILP) for supply chain network design problems in a multi-echelon, multiproduct, multi-stage with different methods of manufacturing at each stage, multi-distribution centers and multi-period supply chain planning. Aggregate production planning (APP) with a supply chain aims to maximize profit through optimal levels of production, subcontracting, inventory, backorder and work levels to meet demand over a time period. Fuzzy logic is applied to solve the uncertain production, demand, capital and warehouse spaces with all costs being triangular fuzzy numbers. The model is developed such that the system takes minimum subcontracted units in each period and no inventory at the end of the planning horizon. In this approach, supply uncertainty is considered by assigning the proper weight. This supply chain network which includes suppliers, manufacturers, subcontractors, retailers and customers, was developed to illustrate the performance of the proposed model. The goal is to maximize the profit of all items with the best use of available resources in integrated businesses. Here, a possibilistic linear programming approach is taken to solve the FMILP model. A numerical example is presented to clarify the features of the proposed approach. In applying the model, decision makers should find the potential to represent their human resources policies regarding overtime and subcontracted production under material requirements constraints.

Possibilistic linear-programming approach for supply chain networking decisions

Supply chain networking decisions are very important for the medium- and long-term planning success of manufacturing companies. The inputs to supply chain planning models are subject to environmental and system uncertainties. In this paper, a fuzzy set theory-based model is proposed to deal with those uncertainties. For this purpose, a possibilistic linear programming (PLP) model is used to make strategic resource-planning decisions using fuzzy demand forecasts and fuzzy yield rates as well as other inputs such as costs and capacities. The objective of the proposed PLP is to maximize the total profit of the enterprise. The model is applied to Mercedes–Benz Türk, one of the largest bus-manufacturing companies in the world, and conclusions and suggestions for further research are provided.

Application of Fuzzy mathematical programming approach to the aggregate production/distribution planning in a supply chain network problem

This paper presented an application of Fuzzy mathematical programming model to solve network design problems for supply chains via considering aggregate production planning (APP). APP goals to minimize all costs through optimal levels of production, subcontracting, inventory, backorder and work levels over a time period to meet the demand. Fuzzy logic was applied to solve the uncertain production/distribution/subcontracting costs and capacities. However, most of the existing models deal the APP problems without integrating supply chain networks. In our model, APP and supply chain design problem were considered within a single plan horizon to get better managerial results. A supply chain network which includes suppliers, manufacturers, subcontracts, retailers and customers, was developed to illustrate the performance of the proposed model. A numerical example was presented to clarify the features proposed approach. In applying the model, decision makers should find a potential to represent their human resources policies regarding the overtime and subcontract production under material requirements constraints. Key words: Supply chain network optimization, aggregate production planning, material requirements constraint, triangular Fuzzy numbers, possibilistic linear programming.

Integrated manufacturing/distribution planning decisions with multiple imprecise goals in an uncertain environment

This work presents a possibilistic linear programming (PLP) method for solving the integrated manufacturing/distribution planning decision (MDPD) problems with multiple imprecise goals in supply chains under an uncertain environment. The imprecise PLP model designed here aims to simultaneously minimize total net costs and total delivery time with reference to available supply, capacities, labor levels, quota flexibility and cost budget constraints at each source, as well as forecast demand and warehouse space at each destination. The proposed method achieves greater computational efficiency by employing the simplified triangular distribution to represent imprecise numbers. An industrial case is used to demonstrate the feasibility of applying the proposed method to a real MDPD problem. Overall, the proposed PLP method provides a practical means of solving the multi-objective MDPD problems in an uncertain environment, and can effectively improve manufacturer/ distributor relationships in a supply chain.

An improvement in possibilistic linear programming approach for imprecise production/transportation planning decisions

In many existing applications of possibilistic linear programming (PLP) model, the decision makers (DM) are asked to specify the positive ideal solution (PIS) and negative ideal solution (NIS) for defining the linear membership function proposed by Zimmermann. In practice, this is a real difficulty for an ordinary DM without possessing acute sense of arithmetic operation and adequate comprehension of PLP model. Furthermore, this task is obviously subjective and will influence the search route of the solution process via the linear membership functions. This study provides an objective method to specify appropriate PIS and NIS for defining efficient linear membership functions so as to rapidly approach a better compromise solution, and also presents a simple way for further improvement of the compromise solution to reach a satisfactory solution. The proposed approaches aim to facilitate the decision making process and promote computational efficiency as well as improve the compromise solution for the PLP method. Additionally, an integrated production/transportation planning decision (PTPD) problem is used to demonstrate the feasibility of applying the proposed methods to real industrial case. Not only the simplicity and objectivity in specifying PIS and NIS but also the computational efficiency, the results of this study show definite advantage of the proposed methods in solving PLP problem.

Application of fuzzy sets to multi-objective project management decisions

In real-world project management (PM) decision problems, input data and/or related parameters are frequently imprecise/fuzzy over the planning horizon owing to incomplete or unavailable information, and the decision maker (DM) generally faces a fuzzy multi-objective PM decision problem in uncertain environments. This work focuses on the application of fuzzy sets to solve fuzzy multi-objective PM decision problems. The proposed possibilistic linear programming (PLP) approach attempts to simultaneously minimise total project costs and completion time with reference to direct costs, indirect costs, relevant activities times and costs, and budget constraints. An industrial case illustrates the feasibility of applying the proposed PLP approach to practical PM decisions. The main advantage of the proposed approach is that the DM may adjust the search direction during the solution procedure, until the efficient solution satisfies the DM's preferences and is considered to be the preferred satisfactory solution. In particular, computational methodology developed in this work can easily be extended to any other situations and can handle the realistic PM decision problems with simplified triangular possibility distributions.