Multiple Objective Linear Programming Research Articles

An approach to duality via image space analysis and applications to linear vector optimization problems

In Yao et al. [Yao CL, Wang SQ, Tammer C. Construction of vector-valued weak separation functions with applications to conjugate duality in vector optimization; 2024. Submitted.], based on the idea of image space analysis and abstract convexity, we proposed a uniform framework of conjugate duality for the constrained vector optimization problems. This paper aims to apply this framework to linear vector optimizations. With the aid of a special collection of separation functions, a set-valued dual problem, which was also derived by Heyde, Löhne, Tammer in [Heyde F, Löhne A, Tammer C. The attainment of the solution of the dual program in vertices for vectorial linear programs. In: Barichard V, Ehrgott M, Gandibleux X, T'Kindt V, editors. Multiobjective programming and goal programming. 2009. p. 13–24. (Lecture Notes in Economics and Mathematical Systems; 618).; Heyde F, Löhne A, Tammer C. Set-valued duality theory for multiple objective linear programs and application to mathematical finance. Math Meth Oper Res. 2009;69:159–179.], is obtained by this approach. Within the uniform framework, we provide a new way to construct this dual model, and to investigate the duality theory of it. In this method, the strong duality is established by the separation of sets in the image space and the generalized saddle points.

On application of linear fractional programming problem using e-education system

This article focuses on an area of nonlinear programming problems known as linear fractional programming problems with multiple objectives. When tackling real-world linear fractional optimization problems, ambiguity and uncertainty in decision-making are inherent. This research aims to present a simple and computationally quick approach to solving multiple objective linear fractional programming problems with all decision variables and parameters described in terms of crisp. The proposed solution algorithm is based primarily on the fuzzy-based technique, and a membership function strategy. To resolve the multi-objective linear fractional programming problem, first consider the problem as a single objective function and along with the fuzzy programming model obtain the optimal solution using LINGO software. LINGO is a software application primarily used for solving linear, nonlinear, and integer optimization problems Moreover, an e-education setup problem demonstrates the steps of the proposed method.

Optimizing Chance Constraint Multiple-Objective Fractional Mathematical Programming Problem Involving Dependent Random Variable

This manuscript suggests a methodology to solve chance constraint multiple-objective linear fractional mathematical programming problem in which the parameters are dependent random variables to each other. The proposed problem is formulated by taking few of the parameters as continuous dependent random variables. The proposed model cannot be solved directly by using existing methodology. Thus in order to solve the proposed model, an equivalent deterministic model is derived. The procedure to solve the proposed model is accomplished in two main steps. Initially, the proposed multiple-objective chance constraint linear fractional mathematical problem is transformed to deterministic equivalent multiple-objective linear fractional mathematical programming by the help of chance constrained method. In the second step, multiple-objective functions, which consist of fractional functions is solved by using lexicographic programming approach. Finally, an example is mentioned to illustrate the methodology.

Existence of solutions for polyhedral convex set optimization problems

Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear programs and multiple objective linear programs provide proper subclasses. In this article, we choose a solution concept for arbitrary polyhedral convex set optimization problems out of several alternatives, show existence of solutions and characterize the existence of solutions in different ways. Two known results are obtained as particular cases, both with proofs being easier than the original ones: The existence of solutions of bounded polyhedral convex set optimization problems and a characterization of the existence of solutions of vector linear programs.

Neuro-Fuzzy Programming to Finding Fuzzy Multiple Objective Linear Programming Problems

Neuro-Fuzzy Programming to Finding Fuzzy Multiple Objective Linear Programming Problems

Simulating multiple scenarios of land use/cover change using a coupled model to capture ecological and economic effects

AbstractThe conflict between the demands of ecological protection and economic development is increasingly prominent. Land use change is sensitive to whether economic or ecological profits dominate, and prediction of future land use changes has become an important scientific issue. This article constructs a coupled model that comprises the grey model (GM), the fuzzy multiple objective linear programming model (FMOLP) and the future land use simulation model (FLUS). We used this model to calculate a macro‐scale quantitative forecast using the top‐down GM‐FMOLP model, and calculated micro‐scale spatial simulations of land use/cover change (LUCC) using the bottom‐up FLUS model under three dissimilar future scenarios, with different emphases on ecological and economic benefits. The scenarios were designed to meet different planning requirements in Chongqing: ecological benefits maximization, economic benefits maximization, and combined ecological and economic benefits maximization. The proposed model, FLUS, was applied to a LUCC simulation for Chongqing in 2015, beginning from verified historical land use data from 2010. The results show that the simulation agrees well with the actual land use in 2015. The overall accuracy and kappa coefficient are 85.92% and 0.76, respectively, which indicates the model performs well. The three land use types with the highest producer and user accuracies are forest, cropland and water areas. The GM‐FMOLP model was used to forecast future LUCC quantity demand, and the FLUS model was then used to calculate spatial predictions for the three scenarios for 2040. The prediction results for the six land use types were significantly different under the three different scenarios. The total areas of forest, urban land and water increased by different degrees under the three scenarios, and the unused land area dwindled. Cropland areas were largely converted into forest, urban land and water areas. The increases in forest and urban land areas generally represents internal gap‐filling between disparate areas and peripheral expansion of areas of the same land use type. The increase in water area results from increased surface runoff in mountainous valleys with severe terrain. Areas of unused land are fully transformed into other land use types. The outcomes from the designed scenarios demonstrate that the proposed models are reliable and effective for future LUCC simulation, and highlight key areas where land use changes differently according to the scenario. In summary, in the predictions for the scenario that combined ecological and economic benefits maximization, each land use type tried to maximize ecological and economic benefits under the constraints, taking into account ecological safety and economic growth, which is in line with the coordination, comprehensiveness and binding requirements in Chongqing's development plan. Therefore, this scenario becomes the optimal scenario for land use optimization in Chongqing in the future. This study provides an example of the application of simulation and forecast models in land use management, remediation and urban planning, and addresses the growing requirement for low‐cost and effective tools for prediction of dynamic land use succession patterns.

Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming

Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA), and returns best nondominated points which are of higher quality than those returned by NSGA-II. However, the nondominated points approximated by NSGA-II are evenly distributed across the nondominated front. The methods compare well with the four exact methods especially on the large instances which the exact methods failed to solve even when given generous amounts of computation times.

A fuzzy based solution to multiple objective LPP

<abstract><p>This study presents a Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) method to solve the Linear Programming Problem (LPP). Initially Multiple Objective Linear Programming Problem (MOLPP) is solved using Chandra Sen's approach along with various types of mean approaches. Furthermore, FMOLPP is solved using Chandra Sen's approach and various categories of fuzzy mean techniques. The simplex form is used to solve the LPP, where the three-tuple symmetric triangular fuzzy number with the constraints of the fuzzy objective function is considered. We have presented a comparative study of optimum values of MOLPP with optimum values of FMOLPP, to show the significance of our proposed method.</p></abstract>

A new interactive fuzzy programming with priority control for multi-objective decision-making problems

Fuzzy multiple objective linear programming (FMOLP) approaches have been used to be solved many applications of multi-objective decision-making (MODM) problems. Several methods have been proposed including max-min approaches, preemptive approaches, and weighted approaches. However, they have some limitations in use; some may not be able to obtain efficient solutions or can give only a few solutions. Some methods need to be solved in two steps or specify the target level, which may be difficult for decision-makers (DMs). In this research, a new single-phase interactive fuzzy programming approach with priority control that can find several efficient solutions is proposed. It is not necessary to specify the target value for each objective and it can solve with only one step for each solution. The DM can easily select the appropriate solutions from a set of efficient solutions. This method is different from existing single-phase approaches by controlling the satisfaction level of the last priority instead of using weight additive. Simple examples and a practical example of a perishable product supply chain network were tested to show the effectiveness of the proposed model. The performance of the proposed method was also compared with existing methods to verify and validate the model.

An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

Consistent and Sustainable Supplier Evaluation and Order Allocation: Evaluation Score based Model and Multiple Objective Linear Programming Model

Consistent and Sustainable Supplier Evaluation and Order Allocation: Evaluation Score based Model and Multiple Objective Linear Programming Model

Solving Patient Allocation Problem during an Epidemic Dengue Fever Outbreak by Mathematical Modelling.

Dengue fever is a mosquito-borne disease that has rapidly spread throughout the last few decades. Most preventive mechanisms to deal with the disease focus on the eradication of the vector mosquito and vaccination campaigns. However, appropriate mechanisms of response are indispensable to face the consequent events when an outbreak takes place. This study applied single and multiple objective linear programming models to optimize the allocation of patients and additional resources during an epidemic dengue fever outbreak, minimizing the summation of the distance travelled by all patients. An empirical study was set in Ciudad del Este, Paraguay. Data provided by a privately run health insurance cooperative was used to verify the applicability of the models in this study. The results can be used by analysts and decision makers to solve patient allocation problems for providing essential medical care during an epidemic dengue fever outbreak.

A Data Envelopment Analysis or Goal Programming Model with Fuzzy Preferences of Decision Makers

Due to the complexity and uncertainty involved in real world decision problems, the determination and interpretation of Decision Makers' preference relations remain a challenging task for them. This paper develops a novel procedure for incorporating preference information in the efficiency analysis of Decision Making Units. The efficiency of Decision Making Units is defined in the spirit of Data Envelopment Analysis, complemented with Decision Maker's preference information. Our procedure begins by aiding the different decision making group members to express their incomplete fuzzy preferences by using a multiple objective linear programming approach for generating a common set of weights in the DEA framework.

A novel inverse DEA-R model for inputs/output estimation

In this paper, we propose inverse data envelopment analysis (DEA) models in the presence of ratio data. We present the inputs/output estimation process based on ratio based DEA (DEA-R) models. We first present a multiple objective linear programming (MOLP) model to determine the level of inputs based on the perturbed outputs, assuming that the relative efficiency of the under evaluation decision making unit (DMU) preserve. We also present the relationship between the Pareto solutions of the proposed MOLP model and the optimal level of inputs and outputs of the new DMU. We presented criterion models to determine the efficiency of the new DMU in the inputs/output estimation process based on inverse DEA-R models in the presence of ratio data. We showed that in the presence of ratio data the selection of criterion model can be important, in order to we provide a new criterion model in the inputs/output estimation process in the presence of ratio data, and so on the amount of calculations is reduced. We have shown that the results for the new criterion model are the same as the existing criterion model presented in the paper. In order to show the validity of the proposed approach in the inputs/output estimation process based on the inverse DEA-R models, we provide an application of our models in a real life for a set of data regarding to medical centers in Taiwan and finally we present the research results.

A Comparison of Benson’s Outer Approximation Algorithm with an Extended Version of Multiobjective Simplex Algorithm

The multiple objective simplex algorithm and its variants work in the decision variable space to find the set of all efficient extreme points of multiple objective linear programming (MOLP). Other approaches to the problem find either the entire set of all efficient solutions or a subset of them and also return the corresponding objective values (nondominated points). This paper presents an extension of the multiobjective simplex algorithm (MSA) to generate the set of all nondominated points and no redundant ones. This extended version is compared to Benson’s outer approximation (BOA) algorithm that also computes the set of all nondominated points of the problem. Numerical results on nontrivial MOLP problems show that the total number of nondominated points returned by the extended MSA is the same as that returned by BOA for most of the problems considered.

Minimal Representations of a Face of a Convex Polyhedron and Some Applications

In this paper, we propose a method for determining all minimal representations of a face of a polyhedron defined by a system of linear inequalities. Main difficulties for determining prime and minimal representations of a face are that the deletion of one redundant constraint can change the redundancy of other constraints and the number of descriptor index pairs for the face can be huge. To reduce computational efforts in finding all minimal representations of a face, we prove and use properties that deleting strongly redundant constraints does not change the redundancy of other constraints and all minimal representations of a face can be found only in the set of all prime representations of the face corresponding to the maximal descriptor index set for it. The proposed method is based on a top-down search strategy, is easy to implement, and has many computational advantages. Based on minimal representations of a face, a reduction of degeneracy degrees of the face and ideas to improve some known methods for finding all maximal efficient faces in multiple objective linear programming are presented. Numerical examples are given to illustrate the method.

MULTIPLE OBJECTIVE LINEAR PROGRAMMING MODEL APPLIED TO SUSTAINABILITY

ABSTRACT This research studies sustainability which is viewed from triple bottom line (TBL) perspective. Multiple objective linear programming (MOLP) model is applied to sustainability. We further narrow down to triple objective of minimization of production cost, carbon emission generated and life-threatening accidents associated with work for a business case and discuss the tradeoffs of TBL. The example of the business case and its solution shed light for other businesses to achieve and balance goals in sustainability. Keywords Sustainability, triple bottom line, multiple objective linear programming, goal programming, carbon emission, weight.

On Multiple Objective Linear Programming Problems with Fuzzy Rough Coefficient. (Dept. P)

On Multiple Objective Linear Programming Problems with Fuzzy Rough Coefficient. (Dept. P)

On the simplex, interior-point and objective space approaches to multiobjective linear programming

Most Multiple Objective Linear Programming (MOLP) algorithms working in the decision variable space, are based on the simplex algorithm or interior-point method of Linear Programming. However, objective space based methods are becoming more and more prominent. This paper investigates three algorithms namely the Extended Multiobjective Simplex Algorithm (EMSA), Arbel’s Affine Scaling Interior-point (ASIMOLP) algorithm and Benson’s objective space Outer Approximation (BOA) algorithm. An extensive review of these algorithms is also included. Numerical results on non-trivial MOLP problems show that EMSA and BOA are at par and superior in terms of the quality of a most preferred nondominated point to ASIMOLP. However, ASIMOLP more than holds its own in terms of computing efficiency.

Global Criterion Approach for the Solution of Multiple Criteria Data Envelopment Analysis Model: An Application at Packaging Waste Collection and Separation Facilities

Adverse effects of packaging waste on the environment and economic losses resulting from the use of untouched resources have made the recycling process compulsory. The success of the collection and separation of packaging waste, which are the most important phases in the recycling process, depends on the effective management of these processes. In this paper, we analyzed the efficiency of 14 collection and separation facilities. A Global- Multiple Criteria Data Envelopment Analysis model (G-MCDEA) based on a global criterion method was proposed for the solution of the multiple criteria data envelopment analysis model, which is organized as a three-objective multiple objective linear programming model. With the proposed model, the three objective functions were transformed into a single objective function, and the normalized grades of the distance from the ideal solution was calculated for each decision making unit. In this was it was determined which objective was closer to the global activity achieved.