Goal Programming Problem Research Articles

Neutrosophic goal programming technique with bio inspired algorithms for crop land allocation problem

In agriculture, crop planning and land distribution have been important research subjects. The distribution of land involves several multi-functional tasks, such as maximizing output and profit and minimizing costs. These functions are influenced by a variety of uncertain elements, including yield, crop price, and indeterminate factors like seed growth and suitable fertilizer. In order to address this problem, other researchers have used fuzzy and intuitionistic fuzzy optimization approaches, which did not include the indeterminacy membership functions. However, the neutrosophic optimization technique addresses the problem by using individual truth, falsity, and indeterminacy membership functions. So, to improve the optimal solution, the Neutrosophic Goal Programming (NGP) problem with hexagonal intuitionistic parameters is employed in this study. The membership functions for truth, indeterminacy, and falsity are constructed using hyperbolic, exponential, and linear membership functions. Minimizing the under deviations of truth, over deviations of indeterminacy, and falsity yields the NGP achievement function, which is used to attain optimal expenditure, production, and profit under the constraints of labour, land, food requirements, and water. Bio-inspired computing has been a major research topic in recent years. Optimization is mostly accomplished through the use of bio-inspired algorithms, which draw inspiration from natural behaviour. Bio-inspired algorithms are highly efficient in exploring large solution spaces, and helps to manage trade-offs between various goals, and providing the global optimal solution. Consequently, bio-inspired algorithms such as Grey Wolf Optimization (GWO), Social Group Optimization (SGO), and Particle Swarm Optimization (PSO) are employed in the current work to determine the global optimal solutions for the NGP achievement function. The data for the study was collected from the medium-sized farmers in Ariyalur District, Tamil Nadu, India. To illustrate the uniqueness and application of the developed method, the optimal solutions of the suggested method are compared with Zimmermann, Angelov, and Torabi techniques. The proposed technique demonstrates that the bioinspired algorithms’ optimal solution to the neutrosophic goal is superior to the existing approaches.

Inverse Linear Goal Programming Problem

This paper considers the inverse linear goal programming problem of multi-objective function in case the change in coefficient of the objective function. 
 Let denote the set of feasible solutions points of linear goal programming problem of a multi-objective function, and let be the positive and negative deviation variables of the maximum and minimum goals respectively, be a specified cost vector, be given feasible solution vector, and be given tow vectors denoted the feasible positive deviation and the feasible negative deviation points of the max or min goals, respectively.
 The inverse linear goal programming problem of multi-objective function is as follows:
 Consider the change of the cost vectors as less as possible such that the vectors feasible solution becomes an optimal solution of LGP of multi-objective function under the new cost vectors and is minimal, where is some selected -norm. 
 In this paper, we consider the inverse version ILGP of LGMP. under the -norm where the objective is to minimize , with denoting the index set of variables . We show that the inverse version of the considered under -norm reduces to solving a problem for the same kind; that is, an inverse multi-objective assignment problem reduces to an assignment problem.
 

Application of cohort intelligence algorithm for goal programming problems with improved constraint handling method

Application of cohort intelligence algorithm for goal programming problems with improved constraint handling method

A goal programming approach for agile-based software development resource allocation

In the current proposal, three objectives have defined which need to be considered while solving the resource allocation problem in ASD. This multi objective has then been solved using Goal Programming approach. The three approaches to solving a Goal Programming Problem i.e. the Weighted Approach (or the Archimedean Goal Programming), the Preemptive Approach (or the Lexicographic Approach) and the Chebyshev Approach (or the Min–Max Goal Programming) have been discussed to cater to the problem thoroughly. Furthermore, the three objectives have been handled singularly as well, i.e. as a single objective problem. The proposed optimization models have been validated on an agile-based software development dataset. Sensitivity analysis has been performed to gauge the impact of the variables involved.

Unmanned Aerial Vehicle Base Station Assisted Licensed Shared Access

A major issue in deploying aerial base stations is the strain it places on the already scarce spectrum and the associated required re-design of the radio resource allocations. To solve this problem, we propose a Licensed Shared Access- (LSA-) based aerial-terrestrial system. The proposed scheme is an integration of unmanned aerial vehicle base station (UAV-BS), as a licensee system, utilising the radio spectrum allocated to other wireless systems- the incumbent system, with the ground base-station operating at the traditional frequency band for cellular systems. However, a major challenge in using LSA for D-BSs is the spectrum unavailability while the incumbent system is active. In conventional terrestrial networks, this leads to service unavailability in a wide geographical area. To tackle this, we define a dynamic UAV-BS positioning scheme that takes into account the presence or otherwise of the incumbent on the spectrum (incumbent Busy and, Idle mode) while taking into consideration the spatial capacity demand in the licensee network. In the busy incumbent mode, the problem of the UAV-BS positioning is tantamount to a goal programming problem with the first level priority goal of fulfilling the incumbent’s interference threshold constraint. Simulation result show that in addition to, the proposed (LSA-) based aerial-terrestrial scheme, solving the challenge posed by scarcity of spectrum in aerial base station deployment, a significant improvement in the system efficiency is obtained. It is seen that the proposed dynamic UAV-BS positioning scheme achieved the desired capacity requirement of the licensee network, while ensuring the interference threshold is not exceeded, at a relatively smaller distance of 1000 m to the boundary of the incumbent’s system transmission coverage as opposed to a larger distance of about 19 Km.

A Robust Fuzzy Decision Making on Global Warming

Background: In this article we develop a global warming indicator model under fuzzy system. It is the light of sun that environmental pollution is responsible for the cause and immediate effect of global warming. Limited amount of oxygen in the air, continuous decrease of fresh water volume, more especially the amount of drinking water and the rise of temperature in the globe are the major symptoms (variants) of global warming. Thus, to capture the facts we need to develop a mathematical model which has not yet been developed by the earlier researchers. Introduction: An efficient literature survey has been done over the three major parameters of the environment namely oxygen, fresh water and surface temperature exclusively. In fact we have accumulated 150 years-data structure for these major components and have analyzed them under fuzzy system so as to develop an efficient global warming indicator model. Method: First of all, we gave few definitions on fuzzy set. Utilizing the data set we have constructed appropriate membership functions of the three major components of the environment. Then applying goal programming problem, we have constructed a fuzzy global warming indicator (GWI) model subject to some goal constraints with respective priority vectors (Scenario 1 and Scenario 2). An extension has also been included for multi-valued goal programming problem and numerical illustrations have been done with the help of LINGO software. Result: Numerical study reveals that the GWI takes maximum and minimum values in a decreasing manner as time increases. It is seen that for scenario 1, the global environmental system will attain its stability after 30 years by degrading 31% of GWI with respect to present base line. For scenario 2, after the same time the global environmental system will attain its stability quite slowly by degrading 28% of GWI with respect to present base line. Conclusion: Here we have studied a mathematical model of global warming first time using fuzzy system. No other mathematical models have been existed in the literature. Thus, the basic novelty lies in a robust decision-making approach which shows the expected time of extinction of major species in this world. However, extensive study on data analytics over major environmental components can tell the stability of the global warming indicator and hence the future fate of the globe also.

Application of Cohort Intelligence Algorithm for Goal Programming Problems with Improved Constraint Handling Method

Application of Cohort Intelligence Algorithm for Goal Programming Problems with Improved Constraint Handling Method

A novel approach for solving decision-making problems with stochastic linear-fractional models

Stochastic chance-constrained optimization has a wide range of real-world applications. In some real-world applications, the decision-maker has to formulate the problem as a fractional model where some or all of the coefficients are random variables with joint probability distribution. Therefore, these types of problems can deal with bi-objective problems and reflect system efficiency. In this paper, we present a novel approach to formulate and solve stochastic chance-constrained linear fractional programming models. This approach is an extension of the deterministic fractional model. The proposed approach, for solving these types of stochastic decision-making problems with the fractional objective function, is constructed using the following two-step procedure. In the first stage, we transform the stochastic linear fractional model into two stochastic linear models using the goal programming approach, where the first goal represents the numerator and the second goal represents the denominator for the stochastic fractional model. The resulting stochastic goal programming problem is formulated. The second stage implies solving stochastic goal programming problem, by replacing the stochastic parameters of the model with their expectations. The resulting deterministic goal programming problem is built and solved using Win QSB solver. Then, using the optimal value for the first and second goals, the optimal solution for the fractional model is obtained. An example is presented to illustrate our approach, where we assume the stochastic parameters have a uniform distribution. Hence, the proposed approach for solving the stochastic linear fractional model is efficient and easy to implement. The advantage of the proposed approach is the ability to use it for formulating and solving any decision-making problems with the stochastic linear fractional model based on transforming the stochastic linear model to a deterministic linear model, by replacing the stochastic parameters with their corresponding expectations and transforming the deterministic linear fractional model to a deterministic linear model using the goal programming approach

Maritime Supply Chain Optimization by Using Fuzzy Goal Programming

Fuzzy goal programming has important applications in many areas of supply chain, logistics, transportation and shipping business. Business management has complications, and there exist many interactions between the factors of its components. The locomotive of world trade is maritime transport and approximately 90% of the products in the world are transported by sea. Optimization of maritime operations is a challenge in order to provide technical, operational and financial benefits. Fuzzy goal programming models attract interests of many scholars, therefore the objective of this paper is to investigate the problem of minimization of total cost and minimization of loss or damage of containers returned from destination port. There are various types of fuzzy goal programming problems based on models and solution methods. This paper employs fuzzy goal programming with triangular fuzzy numbers, membership functions, constraints, assumptions as well as the variables and parameters for optimizing the solution of the model problem. The proposed model presents the mathematical algorithm, and reveals the optimal solution according to satisfaction rank from 0 to 1. Providing a theoretical background, this study offers novel ideas to researchers, decision makers and authorities.

Pre-Emptive and Non-Pre-Emptive Goal Programming Problems for Optimal Menu Planning in Diet Management of Indian Diabetes Mellitus Patients.

Diet management or caloric restriction for diabetes mellitus patients is essential in order to reduce the disease’s burden. Mathematical programming problems can help in this regard; they have a central role in optimal diet management and in the nutritional balance of food recipes. The present study employed linear optimization models such as linear, pre-emptive, and non-pre-emptive goal programming problems (LPP, PGP and NPGP) to minimize the deviations of over and under achievements of specific nutrients for optimal selection of food menus with various energy (calories) levels. Sixty-two food recipes are considered, all selected because of being commonly available for the Indian population and developed dietary intake for meal planning through optimization models. The results suggest that a variety of Indian food recipes with low glycemic values can be chosen to assist the varying glucose levels (>200 mg/dL) of Indian diabetes patients.

Pareto efficient buy and hold investment strategies under order book linked constraints

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and “level II order book data”, i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of “golden strategies”, i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded.

A novel intuitionistic fuzzy preference relations for multiobjective goal programming problems

This paper investigates novel intuitionistic fuzzy preferences relations to determine the imprecise linguistic terms with fuzzy goals. The proposed intuitionistic fuzzy goal programming (IFGP) considers the degree of vagueness and hesitations simultaneously. Different sorts of membership functions such as linear, exponential, parabolic, and hyperbolic have been introduced to depict the linguistic importance term. The overall satisfaction level is achieved by maximizing the convex combination of each fuzzy goals and the preference relations simultaneously. To verify and validate the proposed IFGP model, a numerical example is presented with the comparative study. Further, it is also applied to a banking financial statement management system problem. The proposed IFGP approach outperforms over others. At last, the conclusion and future research direction are suggested based on the performed study.

Compromise allocation problem in multivariate stratified sampling with flexible fuzzy goals

In a multivariate stratified sample survey, we assumed p-characteristics which are to be measured on each unit of the population and the population is further subdivided into L subpopulations. For estimating the p-population means of all characteristics, which are not known in advance usually, a random sample is taken out from the population with the help of simple random sampling. In a multivariate stratified sample survey, the optimum allocation of one character is not considered as optimum for others. Then a solution is needed to work out an allocation that may be optimum for all characteristics in some sense, called as compromise allocation in sampling literature. The estimation of p-population means in the presence of non-response, for a fixed cost, is discussed. The formulated integer non-linear programming problem is converted into a binary goal programming problem. The problem's solution is obtained by using the concept of flexible fuzzy goal programming.

An Extended Multi-Objective Capacitated Transportation Problem with Mixed Constraints in Fuzzy Environment

In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearisation of fractional goal for solving the MOCTP. In this paper imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Relating Optimization Problems to Systems of Inequalities and Equalities

In quantitative decision analysis, an analyst applies mathematical models to make decisions. Frequently these models involve an optimization problem to determine the values of the decision variables, a system S of possibly non- linear inequalities and equalities to restrict these variables, or both. In this note, we relate a general nonlinear programming problem to such a system S in such a way as to provide a solution of either by solving the other—with certain limitations. We first start with S and generalize phase 1 of the two-phase simplex method to either solve S or establish that a solution does not exist. A conclusion is reached by trying to solve S by minimizing a sum of artificial variables subject to the system S as constraints. Using examples, we illustrate how this approach can give the core of a cooperative game and an equilibrium for a noncooperative game, as well as solve both linear and nonlinear goal programming problems. Similarly, we start with a general nonlinear programming problem and present an algorithm to solve it as a series of systems S by generalizing the “sliding objective function method” for two-dimensional linear programming. An example is presented to illustrate the geometrical nature of this approach.

Developing an Exact Method for Solving Non Linear Integer Goal Programming Problems

The nonlinear goal programming problem focused in this paper has a special structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, as used in linear goal program, combined with the reduced gradient method, has been developed. This strategy is used to force the appropriate non-integer basic variables within a priority level to move to their neighbourhood integer points.

A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems

This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all the linear fractional programming models on the given set of constraints were solved separately. Next, all the linear fractional objective functions were linearized, membership functions of objective functions and decision variables controlled by decision-makers at the highest level calculated, and a fuzzy multi-objective linear programming model formed and solved as linear goal programming problem by using simplex algorithm. The efficiency of the proposed algorithm was investigated using an economic example, and the obtained results compared with those obtained using an existing method.

Performance Optimization of Public Transport Using Integrated AHP\u2013GP Methodology

The State Road Transport Undertakings (SRTUs) are the economic providers of mass transport in India. The institutional constraints imposed on the SRTUs result in low productivity and inefficiency. In this fiercely competitive environment, the state-owned public transport industry cannot operate sustainably, showing mediocre performance. With relatively scarce financial resources, high political expectations, and competition between operators, the efficiency and performance of the industry must be improved by optimizing the available resources. In this study, an integrated analytical hierarchy process–goal programming technique considering both operators’ and users’ perceptions is used for performance optimization. The methodology starts with the selection of various performance indicators, considering both operators’ and users’ perceptions. The decision variables are then categorized into user-oriented and operator-oriented. The analytical hierarchy process (AHP), a multicriteria decision-making tool, is then used to evaluate the decision variables and calculate their weights to be used as penalties in goal programming (GP). Pairwise comparison of decision variables on the AHP rating scale was carried out by experts associated with bus transportation and academia. This was used to assign weights to the variables to denote their priority based on their importance. Then, these weights were assigned to the objective function of the GP problem to find a solution that minimizes the weighted sum of deviations from the goal values. As a case study, performance optimization of the Kerala State Road Transport Corporation was undertaken. Twelve decision variables were identified, by taking into account both user and operator perceptions, viz. controllable costs, noncontrollable costs, taxes, staff per bus ratio (fleet operated), safety, accessibility, regularity, load factor, fleet utilization, percentage of dead kilometers to effective kilometers, journey speed, and percentage of cancelled kilometers to scheduled kilometers. The perceived importance of each of these decisive factors from both the users’ and operators’ perspectives was obtained from the experts and prioritized using the AHP. The results indicated that operator cost and staff per schedule were the most important variables for the operators, while safety of travel had the highest weighting according to the users’ perceptions. The optimal solution indicated that increasing the accessibility, safety, and regularity would attract passengers to public transport, which would in turn improve the load factor and influence operators to maximize fleet utilization and reduce cancellation of schedules. Moreover, the solution also suggested that decreasing the staff per bus would further reduce the operating cost. Furthermore, sensitivity analysis was carried out to identify the impact of variations in the decision variables on the performance of the system. The presented method could be used for performance evaluation and optimization of urban rail, metro, and various other public transport systems.

Optimum allocation in multivariate stratified sampling design in the presence of nonresponse with Gamma cost function

ABSTRACTIn multivariate stratified sample survey with L strata, let p-characteristics are defined on each unit of the population. To estimate the unknown p-population means of each characteristic, a random sample is taken out from the population. In multivariate stratified sample survey, the optimum allocation of any characteristic may not be optimum for others. Thus the problem arises to find out an allocation which may be optimum for all characteristics in some sense. Therefore a compromise criterion is needed to workout such allocation. In this paper, the procedure of estimation of p-population means is discussed in the presence of nonresponse when the use of linear cost function is not advisable. A solution procedure is suggested by using lexicographic goal programming problem. The numerical illustrations are given for its practical utility.

Goal programming model for predicting the parameters involved in growth of cancer cells

Some nonlinear goal programming problems are formulated for predicting the decision parameters involved in the cancer and related cell growths such growth rate of normal and malignant cells, death rate of normal and malignant cells and mutation rate of normal cells. An application of preemptive and non-preemptive goal programming problem, some optimisation programming problems are constructed using the statistical moments derived from two state cancer cell growths model and solved using the optimisation LINGO software.