Weighted Goal Programming Model Research Articles

Integer weighted goal programming model for a multi-product company: a case study in the Nigerian food industry

Production planning is a complicated task that requires cooperation among multiple functional units in any organization. The management of production companies have several goals or target which they intend to achieve for their company. Henceforth, this research work presents a weighted Goal programming model for the production problem of a Nigerian food manufacturing company. The goals of the work include minimization of the underachievement of the profit goal, minimization of the underachievement of production target of the breads (burger, sardine, banana, hot dog roll, coconut, mixed fruit) and minimization of the overachievement of the machine production time. The data was collected from the production and sales department of the case company. The data included the quantity of each raw material (flour, sugar, salt, milk, nutmeg, water, butter, yeast, preserver, improver) used in producing one unit of each bread type (burger, sardine, banana, hot dog roll, coconut, mixed fruit), profit per unit of bread, time used in producing 1 unit of bread, quantity target of 1 unit of bread. The goals of this work are 8 goals which include profit goal, machine time goal, production goal of burger bread, sardine bread, banana bread, hot dog roll bread, coconut bread, mixed fruit bread. From the results obtained using LINGO optimization software, 6 goals out of 8 target goals were achieved. The achieved goals include production goal of burger, sardine, banana, hot dog roll, coconut, mixed fruit bread while the goals not achieved includes machine time goal and profit goal.

Site selection optimization for 100% renewable energy sources.

The increase in the use of Renewable Energy Sources (RES) provides many advantages such as reducing the environmental problems and sustainability. In this study, a long-term optimum RES settlement strategic plan is conducted for 81 provinces in Turkey by considering real data. Biomass energy, solar energy, hydroelectric energy, geothermal energy, and wind energy are considered RES sources. Energy consumption until the 2050year is estimated with the regARIMA method, and then a weighted goal programming model was developed in which the outputs of the regARIMA method and risk analysis are integrated. The results of the regARIMA method are tested, and the test results indicate that an R2 value close to 1 indicates that the model is suitable, a low and negative MPE value is neutral, and a MAPE value below 4% indicates high accuracy of the model. Using GAMS 23.5 optimization software program, the developed weighted goal programming model is solved optimally. In this integrated model developed, the objectives of minimizing the installation time, minimizing the investment cost, minimizing the annual cost, maximizing the carbon emission reduction, maximizing the usage time, and minimizing the risk are considered. When the results obtained regarding the number of installations according to the model are examined, the decisions are made for 53% wind energy, 23% biomass energy, 13% hydroelectric energy, 9% solar energy, and 2% geothermal energy. Computational results show that the effective solutions are obtained by minimizing the sum of goals values, covering all provinces in Turkey, and considering real data.

Financial Management of Non - Banking Finance Companies - An AHP Based Weighted Goal Programming Model

Financial Management of Non - Banking Finance Companies - An AHP Based Weighted Goal Programming Model

Sustainable sourcing strategy for mega construction projects: An empirical analysis

AbstractTime and cost overruns are the prominent issues faced by mega construction projects. To minimize cost overruns for the projects, a stepwise approach is suggested for the formulation of a sustainable sourcing strategy. Initially, weights are derived for the existing suppliers using the analytic hierarchy process to select the best set of suppliers. Multiple conflicting variables are considered for deriving the weights. Based on the derived weights, the supply network cost optimization model is developed for optimal order quantity allocation to the selected suppliers to maximize total purchasing value (TPV). A multi‐objective weighted goal programming model is used to minimize deviations in the TPV. Finally, the full factorial design of the experiment concept is employed to identify the significant factors impacting deviations in TPV. The methodology developed is verified using a case study approach. Mega‐construction project organization case was considered for analysis. Demand for the product, materials procurement cost, quality, and supplier lead time are found to be the significant factors impacting deviations in TPV. The developed approach can provide valuable insights to practitioners for the formulation of a sustainable sourcing strategy.

Design of humanitarian supply chain system by applying the general two-stage network DEA model

PurposeThe recent COVID-19 outbreak and severe natural disasters make the design of the humanitarian supply chain network (HSCN) a crucial strategic issue in a pre-disaster scenario. The HSCN design problem deals with the location/allocation of emergency response facilities (ERFs). This paper aims to propose and demonstrate how to design an efficient HSCN configuration under the risk of ERF disruptions.Design/methodology/approachThis paper considers four performance measures simultaneously for the HSCN design by formulating a weighted goal programming (WGP) model. Solving the WGP model with different weight values assigned to each performance measure generates various HSCN configurations. This paper transforms a single-stage network into a general two-stage network, treating each HSCN configuration as a decision-making unit with two inputs and two outputs. Then a two-stage network data envelopment analysis (DEA) approach is applied to evaluate the HSCN schemes for consistently identifying the most efficient network configurations.FindingsAmong various network configurations generated by the WGP, the single-stage DEA model does not consistently identify the top-ranked HSCN schemes. In contrast, the proposed transformation approach identifies efficient HSCN configurations more consistently than the single-stage DEA model. A case study demonstrates that the proposed transformation method could provide a more robust and consistent evaluation for designing efficient HSCN systems. The proposed approach can be an essential tool for federal and local disaster response officials to plan a strategic design of HSCN.Originality/valueThis study presents how to transform a single-stage process into a two-stage network process to apply the general two-stage network DEA model for evaluating various HSCN configurations. The proposed transformation procedure could be extended for designing some supply chain systems with conflicting performance metrics more effectively and efficiently.

Weighted Goal Programming model for Storage Space Allocation problem in a container terminal

Storage Space Allocation Problem (SSAP) is defined as the temporary assignment of unloading/loading containers to the storage blocks during a planning period with the aim of balancing the workload between the blocks. Despite the widespread literature on this topic, several previous studies neglected the practical and implementation aspect of their solutions. The aim of this paper is to formulate and solve the real-life SSAP at the Sfax seaport situated in Tunisia. A Weighted Goal Programming (WGP) based-methodology is proposed as a multi-objective resolution approach. In this proposed approach, three objectives have been accorded including: (i) the balance between the containers unloaded in the blocks, (ii) the balance between the containers unloaded and loaded simultaneously, and (iii) the minimization of the storage cost of the loading/unloading containers for each period. Experimental results show that the proposed approach provides good results and can be effective and practical for the studied Sfax seaport case study.

An ensemble experiment of mathematical programming models to assess socio-economic effects of agricultural water pricing reform in the Piedmont Region, Italy

The Piedmont Region in NW Italy has recently deployed an ambitious and pioneering agricultural water pricing reform aimed at integrating and effectively enforcing EU's Water Framework Directive principles of cost recovery, polluter-pays and affordability. This paper develops a multi-model ensemble framework encompassing 5 mathematical programming models (2 Positive Mathematical Programming models, 2 Positive Multi-Attribute Utility Programming models and 1 Weighted Goal Programming model) that represent the observed behavior of socioeconomic agents to: 1) simulate the impacts of the Piedmontese water pricing reform on land use allocation and management, water conservation, profit and water tariff revenue; 2) sample modeling uncertainty through the ensemble spread; and 3) explore potential tipping points through use of scenario-discovery techniques. Our research suggests that the key challenge to the reform lies in the management of rice fields, an extensive (17% of the agricultural area), water-demanding and relatively low-added-value crop that nonetheless delivers significant ecosystem services (e.g. water retention) of historical and cultural relevance to the region. The ensemble experiment suggests that rice agriculture rapidly dwindles in the price range 0.012–0.074 EUR/m3 depending on the model. Before reaching this tipping point, agricultural water pricing can reduce withdrawals up to 1.7%–9.5%, while reducing profit between 4.9% and 5.6% and achieving a 57- to 65-fold increase in water tariff revenue.

Seleção de projetos de investimentos correntes em uma ferrovia através de programação por metas

Selecionar alternativas de investimentos correntes de acordo com recursos financeiros disponíveis configura-se como um problema clássico de otimização e dentre as diversas técnicas existentes destaca-se a Programação por Metas, uma técnica de programação por objetivos múltiplos. Esse artigo irá apresentar um modelo de programação por me-tas ponderada, aplicado na seleção de uma carteira de projetos de investimentos ferro-viários, utilizando o suplemento Solver do Microsoft Excel. Os resultados obtidos mos-traram que o modelo é uma importante ferramenta de apoio a tomada de decisão e que, com os ajustes necessários, pode ser utilizado para selecionar projetos de outras naturezas.

An integrated optimization model for selection of sustainable suppliers based on customers’ expectations

Due to intensification of market competence and customers increasing socio-environmental concerns, sustainability has become a focal point for most organizations. Thus incorporation of customer sustainable expectations into the conventional supplier selection process has become necessary for manufacturers to sustain in the competitive market. To cope with this issue, it is necessary to model the customers’ opinions and expectations into the strategic supplier selection and order allocation decision making, an area not delved upon much in the literature. Therefore, the aim of the study is to develop an analytical model for manufacturing firm for selection of suppliers based on customers’ expectations which are reflected as retailers’ expectation level and also for bringing in financial and socio-environmental stability to the whole SC. The research methodology adopted involves 1) use of fuzzy-TOPSIS technique using Z numbers for evaluation of suppliers based on traditional as well as social environmental attributes which reflect customer's social and green expectations, 2) development of a novel bi-objective mathematical model for selecting suppliers meeting the expectation levels, allocating orders proportionate to the performance scores of the suppliers, rewarding or penalizing the suppliers as per their sustainable performance, 3) Transformation of the bi-objective model into a weighted goal programming model for attaining a trade-off solution between the objectives of minimization of cost and maximization of sustainable value of purchase. To exemplify the efficacy of the model, case of electronics sector is presented. The findings of the result suggest that penalty and reward value incorporated in the cost objective system is effective in enhancing the sustainable performance of the suppliers and can prove to be an effective strategy for DMs. The study recommends that the proposed mathematical model can considerably aid the manufacturer in integrating supplier selection and order allocation decisions while optimizing the performance of the customer oriented supply chain.

Using Weighted Goal Programming Model for Planning Regional Sustainable Development to Optimal Workforce Allocation: An Application for Provinces of Iran

Due to the urbanization and economic growth, planning of regional sustainable development has become one of the major challenges in the world. The key indicators such as gross domestic product (GDP), electricity and energy consumption and greenhouse gas emission (GHG) are considered in sustainable development planning. This paper determines number of required workforce in diferent sectors of each province in Iran considering targets/goals for sustainable development indicators in the 2030 macroeconomic and regional planning. First, the relative goals are designed for GDP, electricity, energy and GHG emission and then, two weighted goal programming models are applied to allocate the optimal workforce among four sectors: agriculture, industry, services and transportation. The frst model minimizes recruitment of new workforce and allows current workforce exchange among the four sectors in each province in order to achieve the goals, while the second model indicates equitable distribution of new workforce recruitment in diferent sectors within each province. In both models, the workforce changes have been investigated based on achieving the desirable growth rates of GDP, GHG, electricity and energy consumption as planned by the government. Based on the results of this paper, policy makers can manage workforce and the government can make optimized decisions to macroeconomic and regional planning.

A Weighted Goal Programming Model for the DASH Diet Problem: Comparison with the Linear Programming DASH Diet Model

A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.

A Weighted Goal Programming model for planning sustainable development applied to Gulf Cooperation Council Countries

The United Nations agenda for sustainable development by the year 2030 proposes 17 sustainable development goals which include access to affordable, reliable and clean energy, sustained economic growth with full productive employment and, urgent action to mitigate environmental degradation. Planning for sustainable development requires integrating conflicting criteria on economy, energy, environment and social aspects. In this paper, we introduce a Weighted Goal Programming model involving criteria on the economic development (GDP), the electricity consumption, the greenhouse gas emissions, and the total number of employees to determine optimal labor allocation across various economic sectors. The proposed model is validated with data from the six members of the Gulf Cooperation Council (namely Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates). The results of the model aim to provide empirical evidence and insights to decision makers and policy analysts in developing optimal strategies able to simultaneously satisfy energy demand, economic growth, labor development and reduction in greenhouse gas emissions to achieve sustainability targets by the year 2030.

Multi-criteria model for sustainable development using goal programming applied to the United Arab Emirates

Sustainable development requires implementing suitable policies integrating several competing objectives on economic, environmental, energy and social criteria. Multi-Criteria Decision Analysis (MCDA) using goal programming is a popular and widely used technique to study decision problems in the face of multiple conflicting objectives. MCDA assists policy makers by providing clarity in choosing between alternatives for strategic planning and investments. In this paper, we propose a weighted goal programming model that integrates efficient allocation of resources to simultaneously achieve sustainability related goals on GDP growth, electricity consumption and GHG emissions. We validate the model with application to key economic sectors of the United Arab Emirates to achieve sustainable development goals by the year 2030. The model solution provides a quantitative justification and a basis for comparison in planning future energy requirements and an indispensable requirement to include renewable sources to satisfy long-term energy requirements.

Scheduling elective surgeries: the tradeoff among bed capacity, waiting patients and operating room utilization using goal programming.

Scheduling of surgeries in the operating rooms under limited competing resources such as surgical and nursing staff, anesthesiologist, medical equipment, and recovery beds in surgical wards is a complicated process. A well-designed schedule should be concerned with the welfare of the entire system by allocating the available resources in an efficient and effective manner. In this paper, we develop an integer linear programming model in a manner useful for multiple goals for optimally scheduling elective surgeries based on the availability of surgeons and operating rooms over a time horizon. In particular, the model is concerned with the minimization of the following important goals: (1) the anticipated number of patients waiting for service; (2) the underutilization of operating room time; (3) the maximum expected number of patients in the recovery unit; and (4) the expected range (the difference between maximum and minimum expected number) of patients in the recovery unit. We develop two goal programming (GP) models: lexicographic GP model and weighted GP model. The lexicographic GP model schedules operating rooms when various preemptive priority levels are given to these four goals. A numerical study is conducted to illustrate the optimal master-surgery schedule obtained from the models. The numerical results demonstrate that when the available number of surgeons and operating rooms is known without error over the planning horizon, the proposed models can produce good schedules and priority levels and preference weights of four goals affect the resulting schedules. The results quantify the tradeoffs that must take place as the preemptive-weights of the four goals are changed.

Optimal design of the renewable energy map of Greece using weighted goal-programming and data envelopment analysis

Renewable energy forms have been widely used in the past decades highlighting a “green” shift in energy production. An actual reason behind this turn to renewable energy production is EU directives which set the Union’s targets for energy production from renewable sources, greenhouse gas emissions and increase in energy efficiency. All member countries are obligated to apply harmonized legislation and practices and restructure their energy production networks in order to meet EU targets. Towards the fulfillment of 20–20–20 EU targets, in Greece a specific strategy which promotes the construction of large scale Renewable Energy Source plants is promoted. In this paper, we present an optimal design of the Greek renewable energy production network applying a 0–1 Weighted Goal Programming model, considering social, environmental and economic criteria. In the absence of a panel of experts Data Envelopment Analysis (DEA) approach is used in order to filter the best out of the possible network structures, seeking for the maximum technical efficiency. Super-Efficiency DEA model is also used in order to reduce the solutions and find the best out of all the possible. The results showed that in order to achieve maximum efficiency, the social and environmental criteria must be weighted more than the economic ones.

Modelling Investment Optimization on Smallholder Farms through Multiple Criteria Decision Making and Goal Programming: A Case Study from Ethiopia

We use data from the Ethiopia Rural Household Survey and the Ethiopian Central Statistics Agency to demonstrate a set of techniques for estimating optimal investment allocation in smallholder farming. The approaches treat farming tasks, constraints, and investments as a portfolio problem, characterized by multiple competing objectives. We formulate several versions of the multi-objective problem and solve them in three alternative ways; 1) using a scalarized Markowitz portfolio optimization, 2) using a weighted goal programming model, and 3) a multi-horizon goal programming model, estimating all model parameters using real data. The main benefit of the goal programming formulation is the possibility to simplify in a single criterion problem complex situations in which the Decision Maker (DM) faces a trade-off between two or more objectives. We discuss the importance of portfolio allocations for smallholder farmers in minimizing risk and increasing return, and discuss how these approaches provide a framework that can be extended to practical applications in smallholder farming.

An Optimization Modeling Approach to Awarding Large Fire Support Wildfire Helicopter Contracts from the US Forest Service

The US Forest Service used contracted helicopter services as part of its wildfire suppression strategy. An optimization decision-modeling system was developed to assist in the contract selection process. Three contract award selection criteria were considered: cost per pound of delivered water, total contract cost, and quality ratings of the aircraft and vendors. Discrete optimization decision models were developed and solved to optimize each of these objectives or contract selection criteria independently. These solutions provided the basis for a weighted goal programming model that minimized the percent deviation from each of the three, incorporating relative preference or priority weights on deviations from the goals. Managers chose to assign a greater relative importance to the quality rating than the two cost measures, resulting in a solution with higher quality aircraft, but at a cost of $55 million more than if total cost had been the only contract selection criteria. These optimization models show promise as a means of supporting agency decisionmaking regarding firefight- ing helicopter contracts. FOR .S CI. 58(2):130 -138.

Biomass energy production in agriculture: A weighted goal programming analysis

Energy production from biomasses can be an important resource that, when combined with other green energies such as wind power and solar plants, can contribute to reduce dependency on fossil fuels. The aim of this study is to assess how agriculture could contribute to the production of bio-energy. A multi-period Weighted Goal Programming model (MpWGP) has been applied to identify the optimal land use combinations that simultaneously maximise farmers' income and biomass energy production under three concurrent constraints: water, labour and soil availability. Alternative scenarios are considered that take into account the effect of climate change and social change. The MpWGP model was tested with data from the Rovigo county area (Italy) over a 15-year time period.Our findings show that trade-off exists between the two optimisation targets considered. Although the optimisation of the first target requires traditional agricultural crops, which are characterised by high revenue and a low production of biomass energy, the latter would be achievable with intensive wood production, namely, high-energy production and low income. Our results also show the importance of the constraints imposed, particularly water availability; water scarcity has an overall negative effect and specifically affects the level of energy production.

Conserving natural resources in olive orchards on sloping land: Alternative goal programming approaches towards effective design of cross-compliance and agri-environmental measures

Olive farming on sloping land in southern Europe is facing multiple challenges and it is reasonable to believe that farmers will opt for the abandonment of some systems and intensification or change to organic production of other systems. The issues at stake surpass financial farm viability and two EU policy instruments – cross-compliance and agri-environmental measures (AEM) – are available to address environmental objectives. This paper explores how cross-compliance and AEM policy options may lead to shifts in olive production systems and their social and environmental effects in Trás-os-Montes, NE Portugal over 25 years under two sets of conditions of uncertainty: decision-making by land users and market scenarios. Uncertainty in decision-making is addressed by employing five alternative goal programming models. The models include Linear Programming (LP), Weighted Goal Programming (WGP) and MINMAX Goal Programming (MINMAX GP), the GP variants of which are moreover formulated from a societal (S) and farmer (F) perspective. Uncertainty in market prospects is addressed by projecting olive oil and labour prices and trends in farm subsidies, distinguishing four price combinations in market scenarios. The models were validated by their capability to reproduce the initial configuration of olive production systems. Six policy options are evaluated under the complete ranges of uncertainty factors in a total of 6 × 5 × 4 = 120 model runs. Results show overall large effects of farmer decision-making and market scenarios. The cross-compliance and AEM policy instruments have an unequivocal effect on environmental performance and help to maintain work in rural areas. However, farmer income levels are insensitive to the policies, all work is absorbed by family labour and important environmental issues linked to more intensive systems such as pollution are not addressed. In a case study with the WGP (F) model which best reproduced the initial configuration of production systems, cross-compliance was moreover found to burden farmers under adverse market conditions, while AEM contributed to farmer’s objectives under favourable market conditions. A solution would be to focus cross-compliance regulations on intensive systems and offer appropriate AEM for traditional or abandoned orchards. Both policy instruments proved effective, but there is scope for removing substantial overlap between them.

A HYBRID SIMULATED ANNEALING ALGORITHM FOR SOLVING MULTI-OBJECTIVE CONTAINER-LOADING PROBLEMS

In this article, we explored a new approach to solution of multi-objective container-loading problems mostly encountered in transportation and wholesaling industries. Our goal is to load the items (boxes) that would provide the highest total weight to the container in the best possible way. These two objectives (weight maximization and volume utilization) are conflicting because the volume of a box is usually not proportional to its weight. A weighted goal programming model is formulated and presented. A simulated annealing (SA) algorithm accompanied by a heuristic filling procedure is then proposed to solve the model. The proposed algorithm has been first tested on a set of benchmark problems available in the literature and then used for real-world data provided by a distribution company. The computational results have validated significance and usefulness of the proposed approach.