Lexicographic Goal Programming Model Research Articles

LEXICOGRAPHIC GOAL PROGRAMMING APPROACH FOR THE OPTIMIZATION OF CROPPING PATTERN IN YASIN REGION GILGIT, PAKISTAN

The prosperity of the agricultural sector is crucial not only for the national economy but also for regional development. For the purpose of agricultural planning and decision making, mathematical programming models are widely used. This paper aims to formulate, apply and evaluate a Lexicographic Goal Programming (LGP) model for the best allocation of land under cultivation for the major crops of central Yasin. It is an extension of the research work [1] which was conducted in this area to maximize the profit of the three crops using Linear Programming (LP). Using the LP model the target was achieved but all the land was allocated for alfalfa being the most beneficial crop among the three. But wheat is a basic need which must be cultivated to a specific amount. Considering this problem we extended the previous work by implementing the LGP approach to satisfy multiple goals such as the allocation of land for wheat, maximization of profit and minimization of capital in the agricultural activity. The LGP model is solved using the Simplex method. The LGP model provided the most satisfactory set of allocations possible and satisfied all three goals. It gave optimum profit of Rs.170003 and capital is minimized to Rs. 73687.678. Compared with the farmer’s plan, the profit of the LGP model increased by 49.39% but compared with the LP model, the profit decreased by 13.11%. Likewise, the total crop production expenditure increased by 4.97% and 1.39% respectively in comparison with the farmer’s plan and LP model.

Lexicographic Goal Programming Model for Bank’s Performance Management

Any bank’s financial management is essential to preparing the assets and liabilities for multiple goals. In this paper, we develop an optimal bank model for the financial management department in the Kingdom of Saudi Arabia. The lexicographic goal programming model was used to formulate the banks’ performance management. In this study, the six goals of one of the leading banks in Saudi Arabia, namely, maximize asset, minimize liability, maximize equity, maximize operating income, maximize net income, and maximizing total goal achievements in the financial statement, were studied. To illustrate the model, we have focused on Al Rajhi Bank’s financial statements as a case study. The data was obtained from the banks’ financial statements. The outcomes of the study exhibited that all goals were accomplished. This proposed model is dynamic because it will help examine the banks’ financial strengths located in the kingdom. As a result, the proposed model can guide banking firms in making decisions and developing strategies to deal with numerous monetary circumstances.

Supported Evacuation for Disaster Relief through Lexicographic Goal Programming

Disasters have been striking human-beings from the beginning of history and their management is a global concern of the international community. Minimizing the impact and consequences of these disasters, both natural and human-made, involves many decision and logistic processes that should be optimized. A crucial logistic problem is the evacuation of the affected population, and the focus of this paper is the planning of supported evacuation of vulnerable people to safe places when necessary. A lexicographic goal programming model for supported evacuation is proposed, whose main novelties are the classification of potential evacuees according to their health condition, so that they can be treated accordingly; the introduction of dynamism regarding the arrival of potential evacuees to the pickup points, according to their own susceptibility about the disaster and the joint consideration of objectives such us number of evacuated people, operation time and cost, among which no trade-off is possible. The performance of the proposed model is evaluated through a realistic case study regarding the earthquake and tsunami that hit Palu (Indonesia) in September 2018.

An I-optimal experimental design-embedded nonlinear lexicographic goal programming model for optimization of controllable design factors

Optimal experimental designs are effective offline quality improvement techniques used to enhance existing products and develop new products for a constrained design region. For some practical situations, I-optimal experimental designs may be the most suitable way to construct optimal experimental design points, by addressing prediction variance to generate a measure of prediction performance over the non-standard experimental design region. The purpose of this article is three-fold: (1) the I-optimality criterion is selected for minimizing the average prediction variance; (2) fitted mean and variance response models are found; and (3) a nonlinear lexicographic goal programming model incorporating an I-optimal experimental design is proposed to find the optimum settings of controllable design factors. Comparison studies and a numerical example are provided to illustrate the effectiveness of the proposed methodology for improvement of the quality of products.

Sustainability in Forest Management Revisited Using Multi-Criteria Decision-Making Techniques

Since its origins, the idea of sustainability has always been linked to forest management. However, nowadays, sustainable forest management has usually been approached by defining a set of criteria and indicators. This paper aims to address sustainability in forest management including a set of criteria encompassing the most common decisions: whether the stands are even or uneven-aged, and the optimal silviculture that should be applied in each stand. For this purpose, a lexicographic goal programming model with two priority levels has been defined, into which six different criteria are integrated. Each criterion corresponds to a particular pillar (economic, technical, or environmental). Furthermore, also incorporated into the model are the preferences of diverse stakeholders, both for the criteria considered in the analysis and for the most suitable silvicultural alternatives to be applied in each stand. This methodology has been applied to a case study in Spain, and the results show much more attractive solutions than the current forest management planning, allowing the obtainment of multi-aged systems that could be favourable for other ecosystem services.

A Mixed-Integer Lexicographic Goal Programming Model for Achieving Estimated Targets in Multi-Product Systems

A Mixed-Integer Lexicographic Goal Programming Model for Achieving Estimated Targets in Multi-Product Systems

An integrated approach for resource allocation in manufacturing plants

Resource allocation in manufacturing plants can be characterized as an attempt to optimize a number of potentially conflicting objectives involving related activities, which often compete for the same limited resources. This paper proposes an integrated approach for resource allocation problem. The proposed approach combines the voting method and the Lexicographic Goal Programming (LGP) model and takes into account both qualitative and quantitative factors involved in the resource allocation decision process. The voting method is used to determine ratings of the evaluating goals. LGP models are then applied to determine the optimal allocation based on the ratings. The proposed approach is applied to a real-world resource allocation problem. The case company is the world’s largest manufacturer of switch power supplies. Results of the case study indicate that the proposed approach is a practical and useful tool for solving the resource allocation problem.

An Economic Impact Of Marylands Coastal Bays: A Goal Programming Approach

The purpose of this paper is to present a lexicographic goal programming (LGP) model to assess fishery management and related activities and their economic impact on Marylands Coastal Bays. The LGP model is designed to illustrate how LGP can be used as an aid to solving fishery management and related activities with multiple objectives. The technique allows us to find the optimal solution, based on the priorities of the goals in a decision-making environment. In this study, we have used LGP to examine a set of goals and objectives as they relate to the socioeconomic significance of fishery management in Marylands Coastal Bays.

A Multi-Objective Decision Making Approach For Mutual Fund Portfolio

<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt;"><span style="font-family: Times New Roman;"><span style="color: black; font-size: 10pt; mso-bidi-font-style: italic;">Investment decision-making problems ar</span><span style="font-size: 10pt;">e<span style="color: black; mso-bidi-font-style: italic;"> generally multi-objective in nature such as minimization of the risk and maximization of the return. <span style="mso-spacerun: yes;"> </span>These problems can be solved efficiently and effectively using multi-objective decision making (MODM) tools such as a lexicographic goal programming (LGP). <span style="mso-spacerun: yes;"> </span>This paper applies the LGP model for selecting an optimum mutual fund portfolio for an investor, while taking into account specific parameters including risk, return, expense ratio and others. <span style="mso-spacerun: yes;"> </span>Using sensitivity analysis on the weights in a priority structure of the goals identifies all possible solutions in the decision-making process. <span style="mso-spacerun: yes;"> </span>The Euclidean distance method is then used, to measure distances of all possible solutions from the identified ideal solution. <span style="mso-spacerun: yes;"> </span>The optimum possible solution is determined by the minimum distance between the ideal solution and other possible solutions of the problem. <span style="mso-spacerun: yes;"> </span>The associated weights will be the most appropriate weights in a given priority structure. <span style="mso-spacerun: yes;"> </span>The effectiveness and applicability of the LGP model is demonstrated via a case example from broad categories of mutual funds.</span></span></span></p>

A Multi-Objective Decision-Making Approach For Mutual Fund Portfolio

<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt;"><span style="font-family: Times New Roman;"><span style="font-size: 10pt; mso-bidi-font-style: italic;">Investment decision-making problems ar</span><span style="font-size: 10pt;">e<span style="mso-bidi-font-style: italic;"> generally multi-objective in nature such as minimization of the risk and maximization of the expected return.<span style="mso-spacerun: yes;">  </span>These problems can be solved efficiently and effectively using multi-objective decision making (MODM) tools such as a lexicographic goal programming (LGP).<span style="mso-spacerun: yes;">  </span>This paper applies the LGP model for selecting an optimum mutual fund portfolio for an investor, while taking into account specific parameters including risk, return, expense ratio and others.<span style="mso-spacerun: yes;">  </span>Sensitivity analysis on the assigned weights in a priority structure of the goals identifies all possible solutions for decision-making.<span style="mso-spacerun: yes;">  </span>The Euclidean distance method is then used, to measure distances of all possible solutions from the identified ideal solution.<span style="mso-spacerun: yes;">  </span>The optimal solution is determined by the minimum distance between the ideal solution and other possible solutions of the problem. The associated weights with the optimal solution will be the most appropriate weights in a given priority structure.<span style="mso-spacerun: yes;">  </span>The effectiveness and applicability of the LGP model is demonstrated via a case example from broad categories of mutual funds.</span></span></span></p>

Adaptive record-to-record travel method to solve lexicographic goal programming models

In this paper, a record-to-record travel (RRT) algorithm with an adaptive memory named taboo central memory (TCM) is adapted to solve the lexicographic goal programming problem. The proposed method can be applied to non-linear, linear, integer and combinatorial goal programmes. Because that the RRT has no memory, the adaptive memory TCM is inserted to diversify research. Computational experiments in several types of problems with different variable types (integer, continuous, zero-one and discrete) collected from the literature demonstrate that the proposed metaheuristic reaches high-quality solutions in short computational times. Furthermore, it requires very few user-defined parameters.

Sawing planning using a multicriteria approach

The lack of integration among the factors involved in the wood sawing planning process creates a gap in the production system and, thus, technical-economic inefficiency in these industries. In this paper we propose a Lexicographic Goal Programming model that enables the consideration of several criteria sequentially; first, production, as traditionally carried out, then performance, and finally appropriate use of the levels of warehoused logs. This multi-objective model is applied to a Cuban sawmill and a metaheuristic method is developed and implemented in order to solve it.

Goal Programming Model for Agricultural Land Allocation Problems

Most of the real-world problems in the agricultural sector are multi-objective. Multi-objective programming techniques such as lexicographic goal programming (LGP) can be used to solve agricultural land allocation problems. The purpose of this paper is to present an LGP model for optimal allocation of land under cultivation and to propose an annual agricultural plan for the various crops.. Sensitivity analysis on the priority structure of the goals as defined in the LGP model was performed to obtain different solutions in the decision-making environment. The study uses Euclidean distance function to measure distances of all possible solutions from the ideal solution. The minimum distance from different solutions to the ideal solution identifies the best compromise solution, and the associated priority structure is the appropriate structure according to the decision-making situation. The effectiveness of the LGP model is demonstrated via a case example.

An alternative agricultural plan for the food-deficient, environmentally fragile hills of Nepal

AbstractDemand-driven agricultural production is unsustainable in Nepal since it is destroying the land base through soil erosion. The forests are also degrading from excessive fodder lopping (excising branches with leaf material) to feed farm animals. This study suggests an alternative for agricultural production, which minimizes environmental problems without impairing the present economic interests of the farmers. The study was conducted in the low-income, food-deficient, environmentally fragile hill district of Dhading in Nepal. A lexicographic goal-programming model was employed to generate an alternative plan that minimizes the environmental impacts relating to soil erosion, cattle grazing, forest fodder lopping, and use of inorganic fertilizers, and pesticides. Food-grain production, milk production, and returns to fixed farm resources are maintained at least at existing levels in the alternative plan. For delineating relationships between farm production and environmental problems, production of these commodities is hypothetically targeted at successively higher levels. The results indicate that the levels of environmental problems, except those from use of inorganic nitrogen fertilizers, are considerably reduced in the alternative farm production system. The alternative crop plan proposes the total exclusion of corn and oilseed crops and a marked decrease in the area under main season paddy rice. Instead, the areas under early paddy, upland paddy, wheat, pulses, and fodder crops would increase. The livestock plan suggests a decrease in the number of bullocks required, due to modification of the crop plan and sharing of bullocks among neighboring farmers. Replacement of cows by buffaloes for milk production is also proposed. Increasing food-grain production is more damaging to the fragile hill ecosystem than an equivalent increase in milk production.

On goal programming formulations of the reference point method

This paper discusses connections between the multi-criteria techniques of goal programming (GP) and the reference point method (RPM). Both approaches use a certain target point in the criterion (outcome) space as a key element to model decision maker preferences. Therefore, RPM can be expressed, similarly to GP, in the modelling framework of deviational variables. The paper gives a systematic survey and analysis of the lexicographic GP models of RPM. The corresponding preference models are formalised and analysed with respect to target values interpretations as well as the Pareto efficiency of their solutions. The properties of equity among the individual achievements of solutions are also analysed with respect to the Rawlsian principle of justice.

Redundancy in lexicographic goal programming: An empirical approach

The purpose of this paper is to draw attention to modellers on the problems on the problems associated to redundant goals in lexicographic goal programming models. The meaning of a redundant goal and the possible causes for redundancy are studied. The analysis of 20 cases taken from the literature showed that almost 26% of the priority levels considered were redundant, i.e., more than one fourth of the goals considered did not play any actual role in the optimisation process. Some practical recommendations to avoid such an undesirable situation are given.

Nonlinear integer goal programming models for acceptance sampling

Two lexicographic goal programming models are developed for determining the optimal sample size and acceptance number for acceptance sampling plans in quality control. Both models address the conflicting criteria inherent in such sampling problems, namely the average lot inspection cost and the average outgoing quality. The first model assumes a known constant lot fraction defective, while the second relaxes this assumption and instead assumes knowledge of a prior distribution on the fraction of defectives. A three-phase algorithm is developed which exploits the problem structure in order to find optimal solutions after examining a small percentage of the feasible sampling plans. On a set of 64 test problems the algorithm always found the optimal solution, typically after evaluating only 3–5% (and never more than 9%) of the feasible points.