Linear Goal Programming Research Articles

Application of Sequential Linear Goal Programming Method and Modified Simplex Method for Production Planning Optimization

Production planning is an important thing in company management. Every company aims to seek maximum profit in its business activities, so it must be able to utilize its resources as optimally as possible. This study was conducted to determine whether or not any production planning that has been implemented at Istana Roti Hilyah Bakery is optimal. This research aimed to maximize revenue and profit, minimize production costs and raw material usage and optimize production quantities using the sequential linear goal programming method and the simplex modification method with the assistance of LINGO software. Based on the study's results, the revenue increased by IDR 60,000, and the profit increased by IDR 66,679. The minimization value of production costs decreased by IDR 6,679, with the production amount of White Bread as many as 60 pcs, Almond Crumble Bread as many as 45 pcs, Chocolate Crumble Bread as many as 50 pcs, Wheat Bran Bread as many as 55 pcs, Sweet Comb Bread as many as 82 pcs and Jam Comb Bread as many as 84 pcs.

A novel intuitionistic fuzzy best-worst method for group decision making with intuitionistic fuzzy preference relations

This paper proposes a new intuitionistic fuzzy best-worst method (IFBWM) for group decision making (GDM) with intuitionistic fuzzy (IF) preference relations (IFPRs). IF values (IFVs) are used to express reference comparisons of criteria. Based on the additive consistency of IFPRs, this paper proposes the definition of additive consistency of IF reference comparisons (IFRCs). Based on the deviation minimization, a linear goal programming model is established to calculate the optimal IF priority weights. By the additive consistency, the consistency index in the closed form is computed by the score function of IFVs. A new approach is devised to enhance the additive consistency of IFRCs. Thus, an IFBWM with the additive consistency of IFRCs is proposed. For GDM with IFPRs, the best criterion and the worst criterion are identified for each decision maker by constructing the score matrix of the IFPR. The individual ranking order of the criteria is obtained by using the proposed IFBWM. Then, the collective ranking order of the criteria is obtained via building a 0–1 integer programming model. Therefore, a GDM method based on the developed IFBWM with IFPRs is proposed. Four examples are analyzed to demonstrate the effectiveness and the advantages of the proposed IFBWM for GDM.

Precision nutrition for type 2 diabetes in Benin: leveraging linear goal programming to optimize diets with emphasis on adequacy, affordability, accessibility, and culture.

Nutrition and diet are critical to managing Type 2 diabetes (T2D). Low-income households often face challenges maintaining a healthy and balanced diet due to food insecurity, availability, and cost. To address this issue, we used a linear goal programming (LGP) model to develop nutritionally adequate, affordable, accessible, and culturally acceptable diets for persons with T2D in Benin, a French-speaking sub-Saharan country. The goal was to help persons with T2D manage their condition more effectively. We compiled a robust list of local commonly consumed foods in Benin, and calculated their nutritional value using West African food composition tables and food costs per serving from a market survey. Using mathematical optimization techniques, we designed dietary plans that meet the daily nutrient intake recommended by the World Health Organization (WHO) to prevent chronic diseases in normal adults. While adhering to dietary constraints of T2D, we developed optimized diet plans with varying energy levels that meet all nutrient requirements while considering availability, acceptability, and budgetary constraints. Fifty-two food items and recipes were evaluated to create six low-cost daily menus. Menu 1 was the most affordable at CFA 1,127 (USD 1.88), providing 1890 kcal of energy, while Menu 6 was the most expensive at CFA 1,227 (USD 2.05), providing 1749 kcal. All the menus met the daily WHO minimum requirements for carbohydrates, fat, cholesterol, and fiber content, while other nutrients such as protein, vitamin C, and iron reached the upper limits of the acceptable value range. Linear goal programming can be an effective tool in helping to obtain optimized adequate, accessible, and culturally acceptable diets at minimal cost by interpreting and translating dietary recommendations into a nutritional model, based on local market prices.

Firefighting Stations Allocation Model for the State of Kuwait

The objective is to determine the best re-allocations of the stations to easily reach the accident location with both the least cost and time possible, with the best firefighting effective required facilities. This objective required dividing the six governorates into 133 areas served in 6 minutes efficient response time. The final findings of this study were 30 reallocated stations, which managed effectively to cover all 133 required areas. This has been shown on included maps of the six governorates. The goal linear programming model idea was not discussed in the emergency field research of the “State of Kuwait,” specifically in the firefighting emergency service. Moreover, this modeling can be expanded to cover all other types of emergency service topics such as health, paramedics, and police stations.

Decision Making with Intuitionistic Fuzzy Best-Worst Method

Best-worst method (BWM) is an efficient multi-attribute decision-making (MADM) method. This paper puts forward two decision-making methods with intuitionistic fuzzy (IF) BWM (IF-BWM). Firstly, a new consistency definition of IF-BWM is presented. To comprehensive reflect the consistency level of original IF preference comparisons, an acceptable input-and-output-based consistency ratio (CR) of IF-BWM preference comparisons is defined to measure the consistency level of IF-BWM preference comparisons. A goal linear programming model is built to improve the consistency level of input-based CR from the original IF-BWM preference comparisons. To induce an optimal multiplicative normalized IF weight vector (IFWV), a programming model is set up. Accordingly, a novel individual IF-BWM is proposed. Using the deviation between IF values, an analytic expression of determining experts' weights is formulated. By minimizing the weighted deviation between individual multiplicative normalized IFWVs and group multiplicative normalized IFWV, a programming model is built to determine the optimal group multiplicative normalized IFWV. Subsequently, a novel group IF-BWM is put forward. Two real-life examples are furnished to reveal the validity of proposed individual IF-BWM and group IF-BWM in practice. In view of theoretical aspect, this paper fosters the theory of IF-BWM by firstly proposing an input-based CR, output-based CR, an acceptable input-and-output-based CR and group IF-BWM. The model of improving CR of IF-BWM preference comparisons is initially discussed. This paper has a certain guiding significance for the following research on IF-BWM and provides a novel perspective for an MADM problem with positive and negative preference information.

Interval-valued intuitionistic fuzzy best-worst method with additive consistency

Best-worst method (BWM) has received extensive attention because of its fewer pairwise comparisons and maintenance of consistency. Extending it to various fuzzy environments has become a hot research spot. This paper initiates a new interval-valued intuitionistic fuzzy (IVIF) BWM with additive consistency. Firstly, an IVIF fuzzy preference relation (IVIFPR) is viewed as a directed graph with IVIF weights. An approach is offered to distinguish the best and worst criteria by the defined score out-degree and accuracy out-degree of criteria. The concept of IVIF reference comparisons is introduced. The additive consistency of IVIF reference comparisons is acquired by that of IVIFPR using its left and right intuitionistic fuzzy preference relations. We derive the relationship between the IVIF reference comparisons and the IVIF priority weight vector. Based on this relationship, a linear goal programming model is constructed to generate the IVIF priority weights. Two consistency indexes are analytically obtained and the consistency ratio is then defined to check the consistency of IVIF reference comparisons. For the unacceptably additive consistency, a new approach is put forward to enhance the consistency. Thereby, the proposed IVIF BWM is summarized step by step. Three examples of applications are furnished to demonstrate its effectiveness and validation.

Developing feasible healthy diets for Ethiopian women of reproductive age: a linear goal programming approach.

To develop a healthy diet for Ethiopian women closely resembling their current diet and taking fasting periods into account while tracking the cost difference. Linear goal programming models were built for three scenarios (non-fasting, continuous fasting and intermittent fasting). Each model minimised a function of deviations from nutrient reference values for eleven nutrients (protein, Ca, Fe, Zn, folate, and the vitamins A, B1, B2, B3, B6, and B12). The energy intake in optimised diets could only deviate 5 % from the current diet. Five regions are included in the urban and rural areas of Ethiopia. Two non-consecutive 24-h dietary recalls (24HDR) were collected from 494 Ethiopian women of reproductive age from November to December 2019. Women's mean energy intake was well above 2000 kcal across all socio-demographic subgroups. Compared to the current diet, the estimated intake of several food groups was considerably higher in the optimised modelled diets, that is, milk and dairy foods (396 v. 30 g/d), nuts and seeds (20 v. 1 g/d) and fruits (200 v. 7 g/d). Except for Ca and vitamin B12 intake in the continuous fasting diet, the proposed diets provide an adequate intake of the targeted micronutrients. The proposed diets had a maximum cost of 120 Ethiopian birrs ($3·5) per d, twice the current diet's cost. The modelled diets may be feasible for women of reproductive age as they are close to their current diets and fulfil their energy and nutrient demands. However, the costs may be a barrier to implementation.

Land use allocation based on multi-goal linear programming model: a case study of Central Luzon State University

Allocating and reallocating land resources is critical to a long-term land use planning and is a key component to achieve a balanced land use system. This provides appropriate space for varied land uses while preserving the environment for future generations. It is found to be an excellent measure for development and sustainability of an area. Using multiple goal linear programming as a decision support system, this study highlighted the optimization of land use allocation at Central Luzon State University to meet the needs for sustainable development. All the seven (7) general land use classifications determined in the University: agricultural, institutional, residential, commercial, fisheries (pond/fish tanks), roads and open areas were assessed in crafting the Land Use Development and Infrastructure Plan (LUDIP) for 2021 to 2031. The findings demonstrated that the priority goals set by the CLSU constituents: (1) minimizing disaster risk, (2) maximizing land suitability, (3) maximizing research capability, maximizing social development, and maximizing economic value were achieved with the aid of Gurobi. Agricultural and commercial growth, residential, social, and infrastructure development for all constituents, research development, climate change adaptation, and cultural heritage preservation were all aided by the land use optimization in the LUDIP.

Short-term planning of a work shift for open-pit mines: A case study

This work deals with the short-term planning problem of a work shift for open-pit mines. The problem involves ore and waste fronts, shovels, heterogeneous truck fleets, and discharge points. The allocation of trucks is dynamic to allow multiple routes to be assigned to each truck. The problem consists of deciding which fronts must be mined and establishing the number of trucks, their routes, and the amount of material transported by them to each discharge point, satisfying a stripping ratio at the desired level. The objectives are to minimize the deviations from the targets for production, chemical grade, and particle size range of each control parameter at each plant and reduce the number of trucks needed for the process. To solve the problem, we developed a mixed-integer linear goal programming model and tested it using real data from an iron ore mine. The results showed that the proposed approach supports decision-makers in the sizing and allocation of truck fleets and in meeting the production and control parameter targets required by the ore processing plants according to the daily scenario, such as low availability of shovels and trucks, flexibility in ore quality, and need for increased production.

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.
 

On modeling a lexicographic weighted maxmin–minmax approach for fuzzy linear goal programming

In this paper, a novel approach for solving fuzzy goal programming is proposed. This approach utilizes the weighted maxmin and weighted minmax methods simultaneously. Relative weight is assigned to each fuzzy goal according to the preference of the decision maker. A model for each of the two methods is separately stated; hence the two models are merged into one. Moreover, the lexicographic maximization technique is applied to guarantee efficient solutions. Therefore, the proposed approach allows the decision maker to compromise between the two methods. Furthermore, the proposed approach can be implemented to concave piecewise linear membership functions. This type of membership function is represented using the min-operator. The effectiveness of the proposed approach is illustrated by a numerical example.

A nested multiple-objective optimization algorithm for managing production fleets in surface mines

The fleet management system (FMS) plays a vital role in truck and shovel open-pit mining operations. The list of expectations from the FMS ranges from data recording to making operational decisions. This article proposes a nested fleet management system (N-FMS) for open-pit mining operations. The primary contribution of the proposed FMS is connecting the operation to the strategic plan by incorporating shovel allocation and plant feed optimization. Another contribution of the proposed N-FMS is that it simultaneously optimizes the utilization of the shovel fleet and truck fleet. The proposed FMS makes decisions using two nested multiple-objective mixed-integer linear goal programming models. Results of the implementation of the developed N-FMS in a metal mining case study show that compared to a locked-in operation, the mine experienced a 14.6% improvement in its required truck fleet capacity to meet the production target.

A new integrated circular economy index and a combined method for optimization of wood production chain considering carbon neutrality

The wood industry is potentially advantageous to applying the concepts of circular economy for sustainable development and can contribute to the commitment of carbon neutrality. This study developed an integrated circular economy index based on five different quantitative indicators for assessment of the wood production chain: heat recovery rate, CO2 sequestration rate, fossil fuel substitution rate, renewable electricity usage rate, and revenue increase from the by-products. A combination of best-worst method (BWM) and linear goal programming (LGP) techniques was investigated to develop an optimal circular economy model of wood processing chain for reduction in CO2 emission. The integrated circular economy index and the combined method were tested in a case-study of a rubberwood processing chain in Vietnam. The proposed model suggests that the woodchips and biomass from the harvesting and processing of rubberwood could be collected and treated using microwave thermolysis techniques; the enzyme hydrolysis technique is appropriate for bioethanol and biomethane recovery from the sawdust; and the hot air technique is preferable in the drying process. The proposed model could result in a significant reduction of the total net carbon emission from +552,750 tons CO2eq to −1,145,940 tons CO2eq per year. This could support the achievement of Vietnam's zero CO2 emission goal and hopefully contribute to the country's commitment to carbon emission neutrality by the year 2050.

A Goal Programming Approach to Multi-Objective Farm Planning Among Small-Scale Arable Crop Farmers in Kogi State, Nigeria

Summary The purpose of this study was to develop prototype farm plans according to the multi-objective production goals of small-scale arable crop producers in Kogi State, Nigeria. A multi-stage sampling technique was used to select a total of 137 farm households in different local government areas (LGAs). A structured questionnaire complemented with interview schedule was used to collect primary data from the respondents. Descriptive statistics and linear goal programming were used for data analysis. The results obtained indicate that the optimal plan of generating an income of ₦242,076.20 requires 0.368 ha of melons, 0.044 ha of yam/maize mixture and 0.259 ha of sorghum/groundnuts. The optimal net profit was 44.05% higher than that achieved by implementing the existing plan. To meet family food requirements, the solution plan prescribed devoting 0.048 ha to cassava, 0.211 ha to sorghum, 0.368 ha to melons, 0.074ha to Bambara nuts, and 1.065 ha to sorghum/groundnuts to generate an income of ₦158,475.00. To minimize paid labour and generate an income of ₦168,325.50, the plan prescribed devoting 0.195 ha to rice, 0.502 ha to melons and 0.246 ha to Bambara nuts. Out of the three basic farm household objectives considered, meeting family food requirements and limiting labour expenditure were overachieved, whereas the objective of maximizing farm income was underachieved. A great deal of the existing staple food plan was found consistent with the prescribed optimal plan, except in the case of existing cassava and Bambara nut production which was falling short of the optimal production prescribed. The maize/groundnut production had the lowest shadow prices. However, land, labour, capital, agrochemicals, fertilizers and seeds constituted the limiting resources in the plan. It was found that these resources were not optimally allocated in the existing plan for arable crop activities. Therefore, the respondents were advised to utilize their resources as prescribed in the optimum plan, supported by farm advisory services in selecting good crop mixtures.

Evaluation of insurance companies considering uncertainty: A multi-objective network data envelopment analysis model with negative data and undesirable outputs

Uncertainty is an important issue to consider when evaluating entities in both public and private sectors. On the other hand, many operations have more than one stage process when some inputs are fed to the system to produce a number of intermediate measures. The intermediate measures are then transformed into final products in the subsequent stages. The composition method in network data envelopment analysis (NDEA) is a popular method for measuring the efficiency of a two-stage process. The composition method is fractional bi-objective programming that is solved by non-linear programming techniques such as bisection search. In this paper, the two-stage NDEA is extended with negative data and undesirable outputs. First, we propose an alternative linear model based on the goal programming technique to avoid complex non-linear calculations. Then, we use a method to transform negative data into positive and undesirable outputs into desirable ones. Finally, we develop the proposed model using the fuzzy α-cut approach in order to incorporate data uncertainty in the linear goal programming (GP) model. To validate the accuracy of the proposed model, a numerical example is solved. To show the applicability of the proposed model, a real case of 22 insurance companies is examined. We also perform a comparative analysis to specify the benchmark and inefficient companies. Comparative analysis can help managers to recognize where improvement should be investigated with priority.

A novel group BWM approach to evaluate the implementation criteria of blockchain technology in the automotive industry supply chain

The use of blockchain technology leads to improved operations and supply chain (SC) integration. Moreover, identifying and evaluating the blockchain technology application criteria in the logistics system is a Multi-Criteria Decision-Making (MCDM) challenge that requires taking into account the perspectives of experts with varying degrees of SC expertise. The purpose of this paper is to propose a novel group decision-making method based on the best-worst method (BWM) to evaluate the criteria of implementing blockchain technology in the SC. The proposed approach provides a mechanism whereby opinions of decision-makers (DMs) are aggregated in nine steps, first. Then, weights of criteria are determined using BWM individual decision-making models. Moreover, two individual decision-making methods called nonlinear goal programming based BWM II (NGPBWM II) and linear goal programming based BWM II (LGPBWM II) are extended in this study, which can be adopted in both individual and group decision-making problems. The NGPBWM II and LGPBWM II methods can be used for both individual and group decision-making. This study proposes a novel group decision-making framework. The framework has fewer constraints than previous group BWM models and can consider different best (worst) criteria by different DMs. The effectiveness of the proposed methodology is investigated employing eight numerical examples. The results reveal the high accuracy of the NGPBWM II in all eight examples. Therefore, a combination of the proposed group decision-making method and NGPBWM II is applied in a real case to evaluate the application criteria of the blockchain technology in the automotive industry SC, which was a new application for using blockchain technology in SC.

Using a Product Life Cycle Cost Model to Solve Supplier Selection Problems in a Sustainable, Resilient Supply Chain

Supplier selection constitutes a crucial component of manufacturing procurement. We developed a product life cycle cost (PLCC) model to support Taiwanese light-emitting diode (LED) manufacturers in capacity planning for sustainable and resilient supply chain (SC) management. For firms, supply chain PLCC (SCPLCC) is a key consideration, but relevant evidence is scarce. We applied two types of goal programming, namely multiobjective linear programming and revised multichoice goal programming (RMCGP), to develop a PLCC-based model that minimizes net costs, rejections, and late deliveries. Moreover, we constructed a decision-making tool for application to a case of SC sustainable procurement management in a high-tech Taiwanese LED company. Managers can resolve relevant problems by employing the two approaches of the SCPLCC model with various parameters. The implementation of RMCGP with weighted linear goal programming sensitivity analysis produced sufficient findings, according to a study of five models for practical implications. The primary findings of the current model assist business decision-makers in minimizing PLCC, reducing PLCC cost, minimizing net cost, number of rejections, number of late deliveries, achieving PLCC goals, and selecting the best supplier in the context of sustainable SC development.

Modeling of Catfish Farm Using Lexicographic Linear Goal Programming

Modeling of Catfish Farm Using Lexicographic Linear Goal Programming

Introducing a New Approach in Stand Tending Planning and Thinning Block Designation by Using Mixed Integer Goal Programming

Long-term management plans have been developed for nearly all of the forests in Turkey. These plans are applied at a sub-district management unit level and may contain guidance for both intermediate yield and final yield harvests. To implement an intermediate yield plan, which involves the scheduling of forest thinnings (stand tending), consideration in Turkey is given to the advantages of working in the same terrain and the same general area each year. Therefore, compartments are often clumped together to create thinning blocks, taking into consideration the thinning priority of the stands, road conditions, site index, age, and proximity of the compartments. Further, when preparing annual budgets and planning to meet the market’s needs, forest enterprises require an even flow of intermediate wood volume each year. In this paper, we introduce a new approach in stand tending planning designed to schedule an equal amount of intermediate wood volume each year and to create thinning blocks by minimizing the distance to pre-defined ramps (landings). We developed both linear and nonlinear goal programming models to minimize both the deviations from a harvest volume (annual intermediate yield allowable cut) target and the deviations from a target value determined for the distances (total and average) of the centroid of each compartment to the hypothetical forest ramps. By using the extended version of Lingo 16, we solved the problem with different weights for the deviations in volume and distance that ranged from 0.0 to 1.0, in 10% intervals, which created 11 scenarios. We carefully analyzed the results of each scenario by taking into consideration the wood volume and distance of compartments to the ramps. The best scenario using the linear model produced a deviation in volume scheduled for the entire decade of 6 m3, while the deviation in total distance between harvest areas and ramps was 59.7 km. Scenario 5, with weights of 0.6 for volume and 0.4 for distance, produced these results, where compartments were closest to one another. The best scenario using the nonlinear model also produced a deviation in volume of 0 m3 and the total average deviation in distance between harvest areas and ramps was 8.7 km. Scenario 3, with weights of 0.8 for volume and 0.2 for distance, produced these results. The approach and models described through this study may be appropriate for further integration into forest management planning processes developed for the planning of Mediterranean forests.

A multi-objective model for fleet allocation schedule in open-pit mines considering the impact of prioritising objectives on transportation system performance

ABSTRACT This paper deals with optimal decisions regarding truck and shovel scheduling problem in open-pit mines. A mixed-integer linear goal programming model (MILGP) is formulated for solving the problem, aiming at four major goals: (1) maximise production, (b) minimise deviations in head grade, (c) minimise deviations in tonnage to the ore destinations, and (d) minimise fuel consumption of mining trucks. This paper also examines the extent to which the priority of objectives can affect the results and efficiency of the mining operation. Implementation of the model with a copper mine case study demonstrated that the proposed model is effective and efficient.