Lexicographic Goal Programming Research Articles

An optimisation model for sustainable multi-commodity transportation planning

This paper aims to establish a supply chain model that significantly reduces economic and environmental costs. It comprises all activities related to procurement, production, and distribution planning. The proposed multi-objective multi-commodity optimisation model deals with the four conflicting objectives of reducing costs and emissions and choosing top-priority suppliers and the most efficient vehicles. We apply an integrated AHP (analytic hierarchy process) and TOPSIS (technique for order preference by similarity to an ideal solution) technique to determine the weights of suppliers, depending on three indices of criteria, alternatives, and raw material. This paper proposes a cross-efficiency evaluation method using data envelopment analysis (DEA) to ensure that the cross-evaluation of different types of vehicles for evaluating peers is as consistent as possible. The mutually contradictory objectives give rise to several Pareto-optimal solutions. The optimal compromise solutions are found using a lexicographic goal programming technique. We present a real-world case to demonstrate the effectiveness of the proposed methodology, followed by numerical comparisons and additional insights.

An integrated Lexicographic goal programming and dynamic satisfaction function model for effective nurse scheduling

The nurse-scheduling is a common problem in hospitals. The problem requires a timetable considering hospital regulations and nurses’ demands and preferences. This study proposes an integrated Lexicographic goal programming and dynamic satisfaction function model for solving nurse-scheduling problems. The proposed model provides the head nurses with a balanced and fair automated schedule. The model considers two aspects related to hospital regulation constraints. First, the dynamic aspect allows the decision-makers to integrate their judgment to the changing circumstances caused by nurse absenteeism. Second, the satisfaction aspect considers the decision maker’s preferences in assigning nurses’ surplus or shortages to the shifts. The model’s primary goal is to give nurses a fair and balanced schedule with an evenly distributed workload. A fair and balanced schedule helps maintain nurses’ welfare and provide quality patient service. We present a case study in an intensive care unit to demonstrate the effectiveness of our approach compared to the conventional goal programming method.

Can Lexicographic Goal Programming, Artificial Neural Networks, and Value-at-risk Methods be Effective in Analysis of 50 Highest Trade Frequency Issuers Optimum Portfolio

This study aims to describe the optimal stock portfolio as a series of processes for selecting a stock portfolio that suits the needs and desires of investors. The variable used is the daily closing price of the stock exchanges listed on the Indonesia Stock Exchange for the period September 1, 2016 to September 1, 2022 for 50 stocks with the highest trading frequency in the first quarter of 2022 using the value at risk, lexicographic goal method, programming, neural networks, and artificial neural networks. It is known that the value-at-risk method in generating shortfalls is carried out using a valuable approach that exceeds the threshold where the assumption of a 5% tail minimum return is generalized with the Pareto distribution. The input of the neural network in producing the output obtained through the PACF and ACF plots is t1. Issuer price forecasts are obtained using the neural network method and the backpropagation algorithm for each issuer, an SSMS of Rp. 1808.3, ICBP of Rp. 12,717, ASII Rp. 6832.1, BBNI of Rp. 6234.6, INCO of Rp. 2781.8, CPIN of Rp. 12,763, TLKM worth 2630.1, SCMA Rp. 2885.5, and WSKT worth Rp. 1575.7. The issuers obtained have a small MAPE value, which is below 10%. Programming the lexicographical objectives resulted in the nine selected issuers having a minimum standard of risk with maximum returns. Of the nine stocks selected, CPIN, SSMS, BBNI, ICBP, TLKM, ASII, INCO, SCMA and WSKT.
 Keywords: return, value at risk, lexicographic goal programming, backpropagation

Application of Lexicographic Goal Programming Method on Stock Portfolio Optimization With Expected Shortfall Approach

The purpose of this study is to form several optimal portfolios based on the proportion of funds invested in stocks, then the most optimal portfolio will be selected among the optimal portfolios that have been formed. The method used in this study is the lexicographic goal programming method, which is to determine the optimal portfolio based on the proportion of invested funds, then the selection of the most optimal portfolio is determined using the expected shortfall method. This study used data from 5 companies contained in Indonesia Stock Exchange (IDX). The results showed that from the proportion of invested funds, 11 optimal portfolios were obtained. Using the expected shortfall method, the most optimal portfolio of 11 portfolios was obtained, namely type 5 portfolio.

Optimizing Farm Plan in Saline and Normal Areas of West Bengal - A Lexicographic Goal Programming Approach

Salinity has deleterious effects on both crops and livestock. An optimum farm plan is essential to adapt to this hazard. The present study made an effort to develop an optimum farm plan for the livestock-based farming systems in saline and normal areas of West Bengal. In the case of both saline and normal areas, farmers put the highest priority on maximizing gross margin, followed by achieving self-financial support and minimizing the income risk of the farm. Optimal solutions under a few farming systems were over-achieved in the second goal (achieving self-financial support). Since it is maximizing type of goal constraint, over-achievement is not a problem. However, the third goal (minimizing income risk of the farm) was also over-achieved in most of the farming systems. The optimal solution does not always satisfy all the goals, but it will provide a solution that satisfies the goal with the highest priority and comes as close as possible to satisfy the least prioritized goal i.e., minimizing the income risk of the farm. The result of the optimum farm plan shows that if a farmer wants to maximize his income, he has to bear some risks. Since the major share of total income is received from livestock, the optimum plan would suggest increasing the number of livestock in the systems and hence the farmers should divert available resources to this enterprise.

Modelling and prediction of worker task performance using a knowledge-based system application

It is a difficult task for an assembly line manager to select an appropriate worker from the available workers' list to assign to an assembly line workstation. Since each available worker has a unique set of skills and abilities, this research considers the worker differences in their work performance. The worker's work performance is considered based on their working speed or productivity. Task execution time (TET) is the measure used to distinguish the worker's work performance. The TET prediction is made by the application of a knowledge-based system framework. Workers' historical work-time data is used to model the knowledge objects. Workers are classified as skilled and semi-skilled respective methodologies are given for both categories of workers. Statistical-based learning algorithms are proposed for skilled workers based on the worker's age, gender, and work skill. Similarly, worker's learning patterns are used for semi-skilled workers. The predicted TET is used in solving the assembly line worker assignment problem. The second part of this work is to prioritise the aged worker during the worker selection without increment of worker count. The illustrative example helps understand the scope of the proposed methodology in an assembly line worker assignment problem. • A novel method is proposed to model and predict an assembly line worker’ work performance. • Statistical-based learning techniques are used for performance modelling, and Knowledge-based system (KBS) methodology is used for the performance prediction. • The predicted performance can be integrated with the assembly line worker assignment problem. • Lexicographic goal programming is added at the end of the worker assignment problem to prioritise the aged worker during the worker allocation. • The developed framework is helpful for an assembly line manager during worker allocation.

Goal Programming Approach For Frozen Food Production Planning

This paper examines the Goal Programming (GP) approach in food production planning in order to further enhance and find better solutions. The objective of this paper is to determine the optimum level of frozen food production for small and medium enterprise (SME). Azali Frozen Food, a small and medium enterprise located in Penang was selected as it can produce a range of frozen foods throughout the country. The problem is handled through Lexicographic Goal Programming. The results are compared to the available data that was given and other findings were reviewed. The findings of this paper are expected to assist community small and medium enterprise and other decision makers involved in production planning. The developed method will also be of use for those who are interested in the model of goal programming to solve complex planning issues involving uncertain parameters.

Centralised resource allocation using Lexicographic Goal Programming. Application to the Spanish public university system

This paper deals with Data Envelopment Analysis (DEA) in centralised settings in which the operating units belong to the same organisation. In such a scenario, a global system-wide perspective may be adopted as regards resource allocation and target setting. In this paper, a new Lexicographic Goal Programming (lexGP) approach is proposed using three priority levels: the aggregated input consumption and output production goals; the input and output goals of the individual operating units; and the technical efficiency of the computed targets. It is assumed that the goals for the overall organisation are established by the Central Decision-Maker (CDM) and that they are consistent with those of the individual operating units. The proposed approach has been applied to the Spanish public university system, comprising 47 institutions. Given the CDM preferences in terms of input and output aggregate goals and relative importance weights, specific technical efficient targets have been computed for each university. The results show that the proposed approach is more suitable than the non-centralised DEA approach and produces targets that are more effective than other centralised resource allocation approaches in the sense that they are much closer to both the aggregate goals of the CDM and the specific goals of each university.

Social equity-based distribution networks design for the COVID-19 vaccine

This study aims to investigate the role of social equity in vaccine distribution network design problems. Inspired by the current COVID-19 vaccine allocation in-country context, we capture social equity-based distribution by modeling three theories: Rawls’ theory, Sadr’s theory, and utilitarianism. We consider various social groups based on degree of urbanization, including inhabitants of cities, towns and suburbs, and rural areas. The distribution problem is subject to, on the one hand, demand-side uncertainty characterized by the daily contamination rate and its space–time propagation that anticipate the in-need population. On the other hand, supply-side uncertainty characterized by the stochastic arrival of vaccine doses for the supply period. To tackle this problem, we propose a novel bi-objective two-stage stochastic programming model using the sample average approximation (SAA) method. We also develop a lexicographic goal programming approach where the social equity objective is prioritized, thereafter reaching an efficiency level. Using publicly available data on COVID-19 in-country propagation and the case of two major provinces in Iran as example of middle-income country, we provide evidence of the benefits of considering social equity in a model-based decision-making approach. The findings suggest that the design solution produced by each social equity theory matches its essence in social science, differing considerably from the cost-based design solution. According to the general results, we can infer that each social equity theory has its own merits. Implementing Rawls’ theory brings about a greater coverage percentage in rural areas, while utilitarianism results in a higher allocation of vaccine doses to social groups compared to the Sadr and Rawls theories. Finally, Sadr’s theory outperforms Rawls’ in terms of both the allocation and cost perspective. These insights would help decision-makers leverage the right equity approach in the COVID-19 vaccine context, and be better prepared for any pandemic crisis that the future may unfold.

ANALISIS PORTOFOLIO OPTIMAL MENGGUNAKAN METODE LEXICOGRAPHIC GOAL PROGRAMMING DENGAN PENDEKATAN VaR – GEV

The stock portfolio is a combination of several stocks that can help reduce investment risk. Risk can be measured using Value at Risk. This study aims to form an optimal portfolio in which stock risk is estimated using VaR with Generalized Extreme Value distribution followed by selecting the optimal portfolio forming stock using the Lexicographic Goal Programming method. The result of this research is that a portfolio with three selected stocks is formed, namely BBRI with a proportion of 63%, KLBF with a proportion of 25% and MNCN with a proportion of 12%. From the optimal portfolio formed, the expected return is 0.00005106 and the risk is 0.0187.

A Robust Bi-objective Optimization Model for Resource Levelling Project Scheduling Problem with Discounted Cash Flows

Due to limited financial resources and high costs of infrastructure projects, project stakeholders seek to gain maximum profits with optimal resource utilization as well as cost and time minimization. Therefore, this study presents a multi-mode resource-constrained project scheduling model considering the uncertain parameters of cost and time together with the goals of maximizing the net present value and minimizing resource usage fluctuation. Also, the assumptions related to the real-world projects regarding multi-mode activities, limitation of renewable resources, and the deadline of project are incorporated into the proposed model. Moreover, a robust scheduling method is presented to better deal with the inherent uncertainties of projects regarding cost and time. The model is solved with the exact method named lexicographic goal programming (LGP). Due to the NP-hardness of the problem, two metaheuristic algorithms named Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are applied to solve various medium and large size problems. The obtained results indicate the high efficiency of the two metaheuristic algorithms in solving the problem and the better performance of the MOPSO algorithm compared with NSGA-II in terms of five indices. Furthermore, the model is implemented in an offshore equipment installation phase of a wellhead platform project. Finally, the sensitivity analysis of the proposed robust model is performed considering different conservation levels, and the results are evaluated by Monte Carlo simulation with three normal, uniform and triangular distributions. The findings demonstrate that the robustness of the model against the variations of uncertain parameters.

Modeling of Catfish Farm Using Lexicographic Linear Goal Programming

Modeling of Catfish Farm Using Lexicographic Linear Goal Programming

Lexicographic goal programming approach for a short-term mining planning problem

This article addresses a short-term mining planning problem. There are four objectives to be minimized: the deviations in grades and ore proportion in particle size ranges of the plant goals, the deviation in the waste mass to achieve the stripping rate, and the number of truck trips between mining fronts and discharges. The problem was solved through the lexicographical goal programming (LGP) method, which generates solutions that can guarantee a more comprehensive analysis of the decision-making process. The LGP method was tested by using several scenarios of a Brazilian mining company. These scenarios differ in the number of excavators and the tolerances concerning meeting the plants' ore grades. In the results, the impact on the values of the other objectives is analysed of varying the number of excavators and the tolerances in the plants' grade targets.

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.

A set partitioning based goal programming model for the team formation problem

AbstractIn this paper, we offer a multi‐objective set‐partitioning formulation for team formation problems using goal programming. Instead of selecting team members to teams, we select suitable teams from a set of teams. This set is generated using a heuristic algorithm that uses the social network of potential team members. We then utilize the proposed multi‐objective formulation to select the desired number of teams from this set that meets the skill requirements. Therefore, we ensure that selected teams include individuals with the required skills and effective communication with each other. Two real datasets are used to test the model. The results obtained with the proposed solution are compared with two well‐known approaches: weighted and lexicographic goal programming. Results reveal that weighted and lexicographic goal programming approaches generate almost identical solutions for the datasets tested. Our approach, on the other hand, mostly picks teams with lower communication costs. Even in some cases, better solutions are obtained with the proposed approach. Findings show that the developed solution approach is a promising approach to handle team formation problems.

Designing a Quality System using the Goals Programming Method -An Applied Research

Due to the continuous development in society and the multiplicity of customers' desires and their keeping pace with this development and their search for the quality and durability of the commodity that provides them with the best performance and that meets their needs and desires, all this has led to the consideration of quality as one of the competitive advantages that many industrial companies compete for and which are of interest to customers and are looking for. The research problem showed that the Diyala State Company for Electrical Industries relies on some simple methods and personal experience to monitor the quality of products and does not adopt scientific methods and modern programs. The aim of this research is to design a system to monitor the production quality of the transformer (400/11 KVA) through the use of a method that helps to make decisions of a quantitative multi-objective nature, which is the method of lexicographic goal programming that the researcher used to integrate the preferences of the decision-maker in monitoring the quality of the production of the transformer (400/11 KVA). Using the two programs (Excel and Lingo) in constructing and solving the mathematical model that was applied in the sections (outer and inner iron core, winding and isolating, final assembly and quality control). The results obtained were efficient, as they achieved the least possible deviations from all the target values ​​for all goals

Physical Internet: First results and next challenges

Physical Internet: First results and next challenges

A new approach to multi-objective transportation problem forbinding relationship between warehouse to consumer and consumer to consumer

A special type of multi-objective transportation problem with emphasis on consumer to consumer relationship is presented. The objective is to minimise total transportation cost along with source to consumer and consumer to consumer association/relationship in vicinity of the source. A lexicographical goal programming model has been applied. Two phase approach has been made. In the first phase the total transportation cost is minimised. In the second phase, overall independence value of the consumer to consumer association/relation is minimised. This model can give a better result than a single objective transportation model. That is because the source to consumer association/relationship is considered in the first priority to get the lowest cost and the vicinity of consumers in the periphery of the source. In the second priority grouping is made for consumers to be served in the same warehouse, provided the capacity of the source is sufficient to meet the consumer's demand.

A new approach to multi-objective transportation problem forbinding relationship between warehouse to consumer and consumer to consumer

A special type of multi-objective transportation problem with emphasis on consumer to consumer relationship is presented. The objective is to minimise total transportation cost along with source to consumer and consumer to consumer association/relationship in vicinity of the source. A lexicographical goal programming model has been applied. Two phase approach has been made. In the first phase the total transportation cost is minimised. In the second phase, overall independence value of the consumer to consumer association/relation is minimised. This model can give a better result than a single objective transportation model. That is because the source to consumer association/relationship is considered in the first priority to get the lowest cost and the vicinity of consumers in the periphery of the source. In the second priority grouping is made for consumers to be served in the same warehouse, provided the capacity of the source is sufficient to meet the consumer's demand.

Achieving compromise solutions in nurse rostering by using automatically estimated acceptance thresholds

Despite the multi-objective nature of the nurse rostering problem (NRP), most NRP formulations employ a single evaluation function that minimizes the weighted sum of constraint violations. When solving the NRP in practice, the focus should be on obtaining compromise solutions: those with appropriate trade-offs between different constraints. Due to the real-world characteristics of the problem, appropriate trade-offs may vary substantially across instances, and quantifying these trade-offs does not necessarily translate well into a single evaluation function. This paper introduces a new multi-objective approach for the NRP that promotes controlled trade-offs and guides the solver towards acceptable compromise solutions. The method consists of two phases. The first phase quantifies the characteristics of acceptable compromise solutions by estimating acceptance thresholds that implicitly incorporate trade-offs. This quantification is performed automatically by drawing upon the instance at hand and identifying appropriate trade-offs. The second phase solves the NRP by employing these acceptance thresholds in a lexicographic goal programming framework. By automatically estimating instance-specific acceptance thresholds, we not only require minimal information from the user but also obtain a realistic prediction for solution quality. A case study shows that the methodology produces rosters with little or no deviations from acceptance thresholds, within only a few minutes. Furthermore, this methodology provides the user with clear reasoning behind the trade-offs made, as opposed to methods employing a single evaluation function.