scholarly journals Light Robust Goal Programming

2019 ◽  
Vol 24 (4) ◽  
pp. 85 ◽  
Author(s):  
Mensah ◽  
Rocca
Keyword(s):  
Decision Maker ◽  
Goal Programming ◽  
Aspiration Levels ◽  
Conflicting Objectives ◽  
Optimal Value ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
Programming Techniques ◽  
Ellipsoidal Uncertainty ◽  
Optimal Values

Robust goal programming (RGP) is an emerging field of research in decision-making problems with multiple conflicting objectives and uncertain parameters. RGP combines robust optimization (RO) with variants of goal programming techniques to achieve stable and reliable goals for previously unspecified aspiration levels of the decision-maker. The RGP model proposed in Kuchta (2004) and recently advanced in Hanks, Weir, and Lunday (2017) uses classical robust methods. The drawback of these methods is that they can produce optimal values far from the optimal value of the “nominal” problem. As a proposal for overcoming the aforementioned drawback, we propose light RGP models generalized for the budget of uncertainty and ellipsoidal uncertainty sets in the framework discussed in Schöbel (2014) and compare them with the previous RGP models. Conclusions regarding the use of different uncertainty sets for the light RGP are made. Most importantly, we discuss that the total goal deviations of the decision-maker are very much dependent on the threshold set rather than the type of uncertainty set used.

Resolving multiple goal conflicts with interactive goal programming

1987 ◽  
Vol 17 (11) ◽  
pp. 1401-1407 ◽  
Author(s):  
Krishna P. Rustagi ◽  
B. Bruce Bare
Keyword(s):  
Utility Function ◽  
Decision Maker ◽  
Goal Programming ◽  
Efficient Solutions ◽  
Compromise Solution ◽  
Multiple Use ◽  
Two Phase ◽  
Conflicting Objectives ◽  
Analytical Phase ◽  
Goal Conflicts

A two-phase interactive goal programming procedure is described, which is potentially useful for resolving multiple-use conflicts where multiple and conflicting objectives exist. In the analytical phase, the procedure locates efficient solutions that are proportionally equidistant from the established goal targets. In the decision phase, these results are presented to the decision maker who either accepts the compromise solution provided by the analyst or revises the goal targets and enters into another iteration. The important features of the procedure are (i) the decision maker is not required to explicitly specify any weights or utility function to express preference among objectives; (ii) the results of each iteration are presented to the decision maker graphically, using value paths to allow easy visualization of the extent of compatibility or conflict among the different objectives; and (iii) the analyst explores efficient basic as well as nonbasic solutions in search of the best compromise solution. An illustrative example is included to demonstrate the application of the procedure.

scholarly journals Robust data envelopment analysis via ellipsoidal uncertainty sets with application to the Italian banking industry

2020 ◽  
Vol 43 (2) ◽  
pp. 491-518
Author(s):  
Emmanuel Kwasi Mensah
Keyword(s):  
Classification Scheme ◽  
Banking Industry ◽  
Data Envelopment ◽  
Uncertainty Sets ◽  
New Models ◽  
Dea Models ◽  
Uncertainty Set ◽  
Ellipsoidal Uncertainty ◽  
The Relationship ◽  
Decision Making Units

AbstractThis paper extends the conventional DEA models to a robust DEA (RDEA) framework by proposing new models for evaluating the efficiency of a set of homogeneous decision-making units (DMUs) under ellipsoidal uncertainty sets. Four main contributions are made: (1) we propose new RDEA models based on two uncertainty sets: an ellipsoidal set that models unbounded and correlated uncertainties and an interval-based ellipsoidal uncertainty set that models bounded and correlated uncertainties, and study the relationship between the RDEA models of these two sets, (2) we provide a robust classification scheme where DMUs can be classified into fully robust efficient, partially robust efficient and robust inefficient, (3) the proposed models are extended to the additive DEA model and its efficacy is analyzed with two imprecise additive DEA models in the literature, and finally, (4) we apply the proposed models to study the performance of banks in the Italian banking industry. We show that few banks which were resilient in their performance can be robustly classified as partially efficient or fully efficient in an uncertain environment.

ÇOK AMAÇLI ÜRETİM SÜREÇLERİNİN BULANIK KARAR ORTAMINDA İNCELENMESİ: BULANIK HEDEF PROGRAMLAMA VE BİR UYGULAMA

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Nurullah UMARUSMAN
Keyword(s):  
Decision Maker ◽  
Goal Programming ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Objective Functions ◽  
Multiobjective Linear Programming ◽  
Aspiration Levels ◽  
Ideal Solutions ◽  
Fuzzy Goals ◽  
Fuzzy Goal

If the aspiration levels of the goals are set realistically by the decision maker in Goal Programming, the deviations from the goals could occur too high as a result of the solution.  It leads the decision maker to make incorrect decisions. It is also the case for Fuzzy Goal Programming. When the fuzzy goals and their tolerance levels are not defined properly, there will be deviations from the goals. Additionally, if there are constraint functions besides the goals in the problems of either Goal Programming or Fuzzy Goal Programming, the solutions will deviate greatly from the incorrectly defined goal values as the solutions are realized based on the constraints. It is because the goals are limited by the constraints. This study firstly defines the positive and negative ideal solutions of objective functions in the problem organized in Multiobjective Linear Programming model for a business which manufactures hand crafted furniture. Afterwards, each objective is transformed into fuzzy goals using positive and negative ideal solutions.

scholarly journals Sistem Pendukung Keputusan Pengalokasian Spare Part

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Rita Wiryasaputra ◽  
Sri Hartati
Keyword(s):  
Decision Making ◽  
Decision Support ◽  
Decision Maker ◽  
Goal Programming ◽  
Spare Part ◽  
Entropy Method ◽  
Ideal Solution ◽  
Decision Support Model ◽  
Main Concept ◽  
Conflicting Objectives

AbstrakEra informasi yang semakin berkembang mempengaruhi lingkungan bisnis. Pengaruhnya dapat dilihat pada proses pengambilan keputusan. Proses pengambilan keputusan terhadap sejumlah alternatif dan sejumlah tujuan diselesaikan dengan sebuah sistem. Sistem  yang bermodelkan Multi Attribute Decision Making (MADM) dan Multi Objective Decision Making (MODM). Model MODM digunakan untuk menyelesaikan perancangan alternatif terbaik dan model MADM digunakan untuk menyelesaikan penyeleksian terhadap beberapa alternatif dalam jumlah yang terbatas. Salah satu pendekatan model MADM adalah TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). Konsep utama TOPSIS adalah alternatif preferensi terbaik memiliki jarak terpendek dari solusi ideal positif dan memiliki jarak terjauh dari solusi ideal negatif. Hasil metode TOPSIS adalah perankingan terhadap sejumlah alternatif. Salah satu masukan dari metode TOPSIS adalah nilai pembobotan kriteria. Nilai pembobotan kriteria dapat diberikan secara langsung oleh pengambil keputusan atau dihitung melalui sebuah metode. Penelitian akan menghitung nilai pembobotan kriteria dengan metode Entropy. Tujuannya adalah untuk memberikan objektifitas pembobotan kriteria. Penelitian mengangkat kasus tentang pengalokasian spare part ke sejumlah store. Alternatif terbaik dengan sumber daya yang terbatas, beberapa tujuan yang saling bertentangan didekati dengan metode Goal programming. Pengambilan keputusan akan lebih terarah karena sistem menghasilkan perankingan store spare part, dan menampilkan  informasi alokasi spare part.  Kata kunci— Sistem Pendukung Keputusan, Entropy, TOPSIS, Goal Programming AbstractThe capabilities of computrized systems facilitate decision support in a number of ways, such as speed computations, increased productivity ,improved data management and others. Decisions are often made by individuals. There may be conflicting objectives even for a  decision maker. The conflicting objectives can be solved by goal programming. Research of spare part allocation focuses on an individual decision maker and presents the solving problem with Multiple Criteria Decision Making (MCDM). A lot of MCDM approaches have been developed and applied to diverse fields, like engineering, management, economic, etc. As one of the known classical MCDM approaches, TOPSIS method is known to be a common method to get the preliminary outcome.  The main concept of TOPSIS is the best alternative has the shortest distance from the positive ideal solution and has the longest distance from the negative ideal solution.  Before the stores are ranked with TOPIS method, the management assigned a weightage to each store using Entropy method.  Keywords— Decision Support Model, Entropy, TOPSIS, Goal Programming.

scholarly journals A Hybrid Methodology to Minimize Freshwater Consumption during Shrimp Shell Waste Valorization Combining Multi-Contaminant Pinch Analysis and Superstructure Optimization

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1887
Author(s):  
Viviana Quintero ◽  
Arturo Gonzalez-Quiroga ◽  
Angel Darío Gonzalez-Delgado
Keyword(s):  
Process Integration ◽  
Preliminary Design ◽  
Water Network ◽  
Hybrid Strategy ◽  
Shrimp Shell ◽  
Optimal Value ◽  
Shell Waste ◽  
Programming Techniques ◽  
Shrimp Shell Waste ◽  
Freshwater Consumption

The conservation and proper management of natural resources constitute one of the main objectives of the 2030 Agenda for Sustainable Development designed by the Member States of the United Nations. In this work, a hybrid strategy based on process integration is proposed to minimize freshwater consumption while reusing wastewater. As a novelty, the strategy included a heuristic approach for identifying the minimum consumption of freshwater with a preliminary design of the water network, considering the concept of reuse and multiple pollutants. Then, mathematical programming techniques were applied to evaluate the possibilities of regeneration of the source streams through the inclusion of intercept units and establish the optimal design of the network. This strategy was used in the shrimp shell waste process to obtain chitosan, where a minimum freshwater consumption of 277 t/h was identified, with a reuse strategy and an optimal value of US $5.5 million for the design of the water network.

PRODUCTIVE LONGEVITY OF COWS: INFLUENCE OF METABOLITES OF METABOLISM ON REPRODUCTIVE FUNCTION

2020 ◽  
pp. 19-22
Author(s):  
Е.О. КРУПИН ◽  
Ш.К. ШАКИРОВ
Keyword(s):  
Life Expectancy ◽  
Ketone Bodies ◽  
Reproductive Function ◽  
Lactation Period ◽  
Protein Ratio ◽  
Protein Mass ◽  
Service Period ◽  
Optimal Value ◽  
Mass Fractions ◽  
Optimal Values

Дана оценка причин выбраковки дойных коров из стад, определена продолжительность их жизни, установлены соотношения МДЖ и МДБ в молоке коров и на основании этого выявлены взаимосвязи с содержанием кетоновых тел в молоке и некоторыми показателями воспроизводства. Наиболее часто животные выбывают из стада в связи с гинекологическими заболеваниями — 45,9%, за первые 100 дней лактации — 42,05%. Продолжительность жизни коров, выбракованных вследствие инфекционных и инвазионных болезней, является минимальной и составляет 4 года, у коров, выбывших по причине внутренних незаразных и хирургических болезней, на 15 и 20% больше. При соотношении массовых долей жира и белка (СЖБ) 1,10 и менее содержание бета-гидроксимасляной кислоты (БОМК) в молоке достоверно (на 80%, P<0,01) превышает данный показатель у животных с оптимальными значениями СЖБ. У коров с оптимальным СЖБ уровень ацетона в молоке был выше порогового на 28,57%, а у животных с низкими значениями СЖБ достоверное превышение составило 42,85% (P<0,05). Особи с СЖБ ниже оптимальных значений в первые 100 дней характеризовались более длительным периодом лактации в целом на 8,57%, в то время как у животных с оптимальным СЖБ ее продолжительность приближалась к стандартной и составила 308,13 дня (P<0,001), межотельный период был на 5,39% менее продолжительным (P<0,001). При оптимальных значениях СЖБ длительность сервис-периода равнялась 112,91 дня, что на 14,73% короче (P<0,001) продолжительности сервис-периода у животных с низкими значениями СЖБ. The analysis of the reasons for leaving dairy cows from the herd was carried out. The life expectancy of cows has been determined. The ratios of fat to protein mass fractions in cow's milk have been established. The relationship between the content of ketone bodies in milk and reproductive indicators in animals was revealed. Most often, animals leave the herd due to gynecological diseases (45.9%), and in the first 100 days of lactation (42.05%). The life expectancy of cows culled due to infectious and invasive diseases is minimal and amounts to 4 years. For cows abandoned due to internal non-communicable and surgical diseases, life expectancy was 15 and 20% longer. When the ratio of mass fractions of fat to protein was 1.10 or less, the content of beta-hydroxybutyric acid in milk significantly (by 80%, P<0.01) exceeded this indicator in animals with optimal values of the ratio of fat to protein. In cows with an optimal fat to protein ratio, the acetone level in milk was 28.57% above normal. In animals with a low value of the ratio of fat to protein, the significant excess was 42.85% (P<0.05). Animals with a ratio of fat to protein below the optimal value were characterized by a longer lactation period in general by 8.57%. In animals with an optimal fat-to-protein ratio, the duration of lactation approached the standard one and was 308.13 days (P<0.001), and the interbody period was 5.39% shorter (P<0.001). With optimal values of the fat-to-protein ratio, the duration of the service period was 112.91 days, which is 14.73% shorter (P<0.001) than the duration of the service period in animals with low values of the fat-to-protein ratio.

scholarly journals Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4642
Author(s):  
Li Dai ◽  
Dahai You ◽  
Xianggen Yin
Keyword(s):  
Robust Optimization ◽  
Dirichlet Process ◽  
Forecast Error ◽  
Optimization Methods ◽  
Optimization Method ◽  
Gaussian Mixture ◽  
Data Driven ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
Simulation Results

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

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