Linear Goal Programming Research Articles

Uncertainty-based mine planning framework for oil sands production scheduling and waste management

ABSTRACT In oil sands mining, the production schedule must be integrated simultaneously with in-pit and ex-pit dike construction scheduling. Any extra mined ore is stockpiled for a limited duration, and the topmost layer of the overburden is used for land reclamation. An uncertainty-based mathematical programming model is developed based on mixed integer linear goal programming for oil sands production scheduling and waste management. The model aims to maximize the net present value (NPV) while meeting all required production and technical constraints. The reclamation strategy for the stockpiled ore and the destination of dike materials is determined to minimize costs. The model uses kriged estimates with a variance penalty scheme to minimize the financial risk from grade uncertainty associated with the production schedule. The uncertainty-based model is implemented for an oil sands mine case study with two scenarios. An integrated mine plan with a waste management and stockpiling strategy is generated by Scenario 1 that maximizes the NPV of the operation and minimizes dike construction and reclamation cost. Scenario 2 uses the variance penalty scheme to estimate the production schedule financial risk from grade uncertainty.

A New Hybrid LGPMBWM-PIV Method for Automotive Material Selection

Efforts are continuously being made by researchers to improve fuel efficiency and to reduce CO 2 emissions from the passenger cars. To achieve these goal, recent trend is to make the cars components light in weight for which manufacturing car roofs using natural fiber reinforced composites (NFCs) is one of the method. Several natural fibers (NFs)are available as alternative reinforcements for the fabrication of NFCs. Different NFs possess different properties and therefore, it is necessary to select the most appropriate natural fiber for fabrication of the composites which in turn will lead to the desired performance of the vehicle. Selection of the optimal natural fiber, amongst the several alternatives, is basically a multi criteria decision making (MCDM) problem as selection is based on the evaluation of several conflicting criteria. In this study, twelve alternative natural fibers (Flax, Hemp, Jute, Kenaf, Ramie, Okra, PALF, Coir, Isora, Cotton, Banana and Sisal) and six evaluation criteria (Tensile strength, Stiffness, Failure strain, Density, Degradation temperature and Moisture gain) are considered and selection of the optimal NF is made using a newly developed hybrid MCDM method i.e. Linear goal programming model for Best-Worst method (LGPMBWM) and Proximity index value method (PIV). Results of the study reveal that among all considered natural fibers, Ramie fiber is the most suitable alternative for the fabrication of composites and coir fiber is the worst candidate for the same.

Lecturer Teaching Scheduling that Minimize The Difference of Total Teaching Load Using Goal Programming

An implementation of scheduling problems is the scheduling of lecturers in educational institution. There are several considerations, including the availability of teaching time, the suitability between the subject and the lecturer’s field, and also the fairness of assignments for each lecturer. Because of these considerations, scheduling using operation research is needed to overcome the weaknesses of scheduling by conventional methods, which may not be able to cover several rules and conditions that need to be met. This scheduling problem can be solved by linear goal programming. In this work, two types of constraints need to be considered, i.e. hard and soft constraints. The hard constraints are some constraints that must be fulfilled, while the soft constraints are some constraints that hoped to be fulfilled as much as possible. In goal programming, the goal is minimizing the deviation variable, which may be able to make the soft constraints deviate from the expected value. This scheduling model is applied to the data of scheduling lecturers in the Department of Mathematics XYZ University. In this model, the main goal is minimizing the difference of total teaching load and it was achieved quite well because the total credits earned by each lecturer was quite same due to the limitation of deviation value. However, it makes the other goal wasn’t fulfilled, there are several lecturers who get schedules to teach courses outside their division.

Pareto efficient buy and hold investment strategies under order book linked constraints

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and “level II order book data”, i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the order book information makes our study much more realistic, since it is more closely related to the real behavior of many financial markets. Besides, ambiguity may be incorporated, which allows us to overcome the model-risk, since a potential discrepancy between the real (and maybe unknown) probabilities and the estimated ones is taken into account. Though the portfolio choice problem is not at all linear, its dual problem becomes a linear goal programming problem, and, consequently, the absence of duality gap allows us to solve the portfolio choice problem in an easy way. Furthermore, the double dual problem is linear too, and its solution also leads to the Pareto-efficient frontier. Lastly, we explore the influence on the Pareto-efficient frontier of the existence of “golden strategies”, i.e., investment strategies whose tail (or downside) risk is strictly lower than their price. Numerical experiments involving all the findings are implemented in a derivative market where both future contracts and call/put options may be traded.

A solving approach for fuzzy multi-objective linear fractional programming and application to an agricultural planting structure optimization problem

In this paper, an algorithm is presented to solve fuzzy multi-objective linear fractional programming (FMOLFP) problems through an approach based on superiority and inferiority measures method (SIMM). In the model for the proposed approach, each of fuzzy goals defined for the fractional objectives and some of constraints have fuzzy numbers. To achieve the highest membership value, SIMM is adopted to deal with fuzzy number in constraints, then a linear goal programming methodology is introduced to solve the problem in which the fractional objectives is fuzzy goals. A case of agricultural planting structures optimization problem is solved to illustrate the application of the algorithm. The results show that winter wheat and summer corn acreage should be 38,386.4 ha, and cotton acreage should be 20,669.6 ha. Because of high risk in cotton cultivation at present, the ratio of grain planted area to cotton planted area is unreasonable. An improved support in policy is necessary for the government to enhance the enthusiasm of farmers to plant cotton and sustain the development of cotton market in the long term.

Optimalisasi Ekspor Produk Ekonomi Kreatif Indonesia Menuju Peningkatan Dayasaing

Indonesia’s creative economy product exports have not been optimal. The purpose of this study is to optimize the goals of creative economic development in Indonesia. This research was conducted using secondary time series data for the period 2010-2017. The research method uses linear programming and goal programming. The results showed that exports of creative economy products responded to an increase in export selling prices based on the demand behavior of the exports of creative economy products. The factor of export competitiveness of Indonesia’s creative economy products lies in the use of cheaper labor costs. Exports of creative economy products do not automatically increase, if the education level of the workforce increases, but rather comes from an increase in creativity. Fashion products are efficient products compared to producing exports of craft products and culinary products. Finally, the development of the creative economy is more optimal for the purpose of increasing exports of creative economy products than for the purpose of increasing employment, namely by producing fashion products.

Using Mixed Integer Goal Programming in Final Yield Harvest Planning: A Case Study from the Mediterranean Region of Turkey

A mixed integer goal programming model is developed to address the regeneration planning problems of even-aged forests in the Mediterranean region of Turkey. The unique aspect of the goal programming formulation is to minimize deviations in scheduled wood product volumes and the size of harvest areas within each time period, as these are important goals for the management area. About 98% of the forests in Turkey are considered even-aged, and 2% are uneven-aged. Therefore, an age class method is used for the planning of even-aged forests. For the areas where this method is applied, reaching the optimal age class structure is the first priority. This involves implementing final harvests (clearcuts) to regenerate an amount of forest area into each age class. To meet the local market’s needs, forest enterprises also require the final yield to be fairly equal each year. Further, it is desired that the harvest area (regeneration area) is relatively equal each year, to address operational considerations. A linear goal programming model is developed to address the problem. The minimization of deviations from both the harvest area and harvest volume targets are incorporated as goals in the objective function of the model. Several scenarios are solved using the extended version of Lingo 16. A scenario with weights of 0.8 for area and 0.2 for volume produces the best results. Here, the total deviation for 20 years is 3.8 ha in area and 2889 m3 in volume. In the actual regeneration plan, the area deviation for 10 years is 54.72 ha (6.2% of total regeneration area), and the volume deviation is 20,472 m3 (9.8% of harvest volume). The model described through this study can be developed further and integrated into forest management planning software and processes used for the planning of even-aged forests in the Mediterranean region.

Ingredients Formulation of Analogue Rice Based on Location Spesific Flour, Case Studies in the Purworejo District

The determined of rice as staple food of Indonesians people will increase with increased of population growth. One of the efforts to meet basic food demand can be done through food diversification perform by using non-rice carbohydrate sources. Purworejo Regency is one of the regions that has a source of carbohydrate in addition to rice, which has not been further processed to be an alternative to meeting calorie needs other than rice. The purpose of this study is to obtain an optimal analog rice composition formulation in the form of a goal programming model by mixing non-rice base ingredients for analog rice production to produce analog rice that has nutritional characteristics determined with Ciherang rice. Conducting the results of making analog rice formulations with non-rice materials available in Purworejo District using a linear objective programming model. The linear goal programming optimization model uses a solver program with an objective function of the nutrient content of protein, amylose, and amylopectin to approach Ciherang rice. Analog rice optimization results were tested using similarity percentage values to determine the proximity of nutrient content with Ciherang rice. Based on the analysis of calculations from the solver program produces a mixture of white corn (94.674%) and taro beneng (5.326%) with a similarity of 98.381%. While the results of the optimization of the availability of carbohydrate sources in Purworejo District produced a mixture of taro beneng (19.462%), sago starch (20.668%) and breadfruit (59.851%) with the similar nutritional content of Ciherang rice of 89.717%.

The Effect of CAP Policy Incentives for the Environmental and Economic Performance of Cereal Farms in South-Central Bulgaria

This paper aims to assess the effects of three mechanisms of the Common Agricultural Policy incentivizing environmentally friendly farming practices, on a model cereal farm’s environmental and economic performance. Based on linear goal programming method and input data on the farm’s size, production system, crop yield and gross margin per crop, the model optimizes the farm’s production structure. The results indicate that the availability of support is essential for the economic results of cereal farms in South-Central Bulgaria. Generally, higher gross margin corresponds to higher greenhouse gas emissions and vice versa. Nevertheless, the addition of policy support decreases the degree of this dependency by improving the profitability of some less GHG-intensive crops. This allows farmers to consider more environmentally-friendly crops and production practices without having to cut profits. An optimal balance between farms’ environmental and economic performance is crucial in order for agriculture to continue to support vital ecosystem services.

Gender Differentials and Optimal Combination of Crop Enterprises under Limited Resource Conditions in South Western Nigeria: A Case Study of Cocoa-based Farming Systems

This study investigated gender differentials and an optimal combination of crop enterprises in southwestern. Specifically, it described the socio-economic characteristics of households in cocoa-based farming by gender; determine enterprise combinations of households in the cocoa-based farming systems and profile gender participation in optimal farm plan activities in cocoa-based farming systems. A multistage sampling procedure was used to select 200 respondents, comprising 147 males and 53 females. Data were collected on socioeconomic characteristics such as age, household size, years of schooling and year of farming experience among others. Data were analyzed using descriptive statistics and linear goal programming. Descriptive statistics show that majority of the respondents aged above 60 years comprising of 46.5% male and 2% females, married comprising of 69.5% male and 20% female, and had a household size of between 7 and 12 persons, with males accounting for 25.5% and females 12.5%. Most of the respondents had primary school education in the study area, with 73.8% male and 26.2% female. Goal ranking showed that food security; increased income; and reduced production cost are the most important goals among farmers in the cocoa-based farming system. The linear goal programming model shows that Cocoa and Banana; Cocoa, Oil Palm and Plantain and Cocoa, Maize, Cassava and Orange are the optimal enterprise combination. It further showed that farmers will incur a cost of N38, 833.56/ha on the three basic activities to achieve the stated goals. The shadow prices for the fully utilized resources were N9348, N1352 and N6.52 for land, hired labour and capital respectively. The result further showed that 67 percent of the goal components was achieved. Percentages of female-headed households in cocoa/banana, cocoa/oil palm/plantain and cocoa/maize/cassava/orange enterprises were 45%, 31% and 0% respectively. For the goals of food security, increased income and reduced farm production costs to be accomplished in the study area, farmers should produce 0.2 ha of cocoa/banana, 1.2 ha of cocoa/oil palm/plantain and 1.25 ha of cocoa/maize/cassava/orange in the study area. Also, conscious efforts should be made by policymakers to ensure gender equality in the access and use of productive farm resources.

A Deterministic Multi-Objective Optimization Process of Multi-Item Inventory Management in Fmcg Industry

The inventory management is the crucial part of any of the company’s, and nowadays, they find challenging to perceive out the optimal quantity level needed to overcome from shortages problem and also to reduce the wastages.In this paper, we used a multi-criteria decision-making for formulating the inventory management problem without shortages with the aim of optimizing profit and holding cost of the company simultaneously. We have also considered both ordering cost and storage cost as a non-linear function of the rapid stock level. In addition we used linear goal programming to find out the minimum optimal quantity level to put in the inventory to reduce out of stock situation. Finally, a numerical illustration of FMCG Company has been taken to show the application of proposed work.

Optimization of FADs-based tuna fishing in the Fishing Port of Pondokdadap, East Java, Indonesia

The Minister of Marine Affairs and Fisheries Regulation number 26/2014 has decreed that the distance between FADs should not be less than 10 nautical miles and should not be installed to make a fence effect. Highly dense FADs that are deployed with not enough distance between them in a certain period will change the movement pattern of tuna. This study aims to obtain information on the actual data of FADs deployed in the southern waters of East Java, to estimate the deployment area and to provide a recommendation on the ideal number of FADs deployed in these waters. The FAD deployment area has been estimated to be 219,792 km2 or 21,979,200 ha. Based on this estimation, it is calculated that the ideal number of FADs installed in these waters is 814 units. Estimates of the optimal number of tuna fishing units are carried out using linear goal programming (LGP) which suggests 380 units of sekoci (fishing vessel) as the optimal unit number that can operate annually at the Fishing Port of Pondokdadap, Malang Regency. The number of sekoci currently operating at this port is 644 units.

Consistency Analysis and Priorities Deriving for Pythagorean Fuzzy Preference Relation in the “Computing in Memory”

Pythagorean fuzzy set, characterized by membership function and non-membership function, has received increasing attention in recent years. In this paper, a new approach to decision making is proposed based on Pythagorean fuzzy preference relation and its additive consistency. Firstly, the concepts of Pythagorean fuzzy preference relations and its additive consistency are introduced, and followed by a discussion of their desirable properties. Then, a linear goal programming model is proposed to determine the consistency of PFPRs. For the PFPRs that does not satisfy the consistency, the consistency index is defined to measure the degree of consistency, and a consistency adjustment algorithm is proposed. Finally, based on the additive consistency, a new algorithm for decision making is presented. An example of CIM(Computing In Memory) is provided, and in comparison with other methods, the validity and rationality of the proposed method are verified.

An approach to probabilistic linear goal programming (PLGP)

An approach to probabilistic linear goal programming (PLGP)

Towards sophisticated decision models: Nonadditive robust ordinal regression for preference modeling

This paper addresses a methodology for decision support under multiple and correlated decision criteria. Nonadditive robust ordinal regression (NAROR) aims to build capacities that fit the decision makers’ explicit preferences and pairwise rankings of some alternatives. The capacities provide great flexibility to model decision problems accounting for interactions among the decision criteria. The feasible set of capacities helps identifying all the necessary and possible dominance relations among all the decision alternatives. In this paper we enhance the NAROR method by identifying optimal capacities through entropy maximisation. We formulate suitable optimisation problems and provide avenues for capacity simplification based on k-interactivity. We also consider the situation of large number of sparse constraints, for which we formulate a linear program based on Renyi entropy. We deal with preferences inconsistency by using multiple goal linear programming technique. The results show that the k-interactivity is an efficient way to reduce the complexity of capacities while preserving their expressiveness and representation ability, and that optimal capacities can be found by standard mathematical programming techniques.

Formulation and Ranking of Human Resources Strategies of Iran Technical and Vocational Training Organization based on Linear Goal Programming

Formulation and Ranking of Human Resources Strategies of Iran Technical and Vocational Training Organization based on Linear Goal Programming

Developing an Exact Method for Solving Non Linear Integer Goal Programming Problems

The nonlinear goal programming problem focused in this paper has a special structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, as used in linear goal program, combined with the reduced gradient method, has been developed. This strategy is used to force the appropriate non-integer basic variables within a priority level to move to their neighbourhood integer points.

Achievement Stability Set for Parametric Rough Linear Goal Programing Problem

This paper introduces an algorithm for researching the achievement stability set for parametric rough linear goal programming (PRLGP) issues with parameters in the achievement function and roughness in goal and system constraints. The proposed goal programing model has two types of uncertainty. We transform the PRLGP into an upper approximation model and a lower approximation model. Then, the Lexicographical goal programing method is utilized to solve such upper and lower approximation models iteratively to avoid the complexity of the attainment issue. This model has been applied as it enables the decision-maker to articulate the weights for goals however, for the sub-goals it shall be complicated as they possess the same measure. Finally, to clarify how to investigate the achievement stability set for the PRLGP, an algorithm and a numerical illustration was given.

A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems

This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all the linear fractional programming models on the given set of constraints were solved separately. Next, all the linear fractional objective functions were linearized, membership functions of objective functions and decision variables controlled by decision-makers at the highest level calculated, and a fuzzy multi-objective linear programming model formed and solved as linear goal programming problem by using simplex algorithm. The efficiency of the proposed algorithm was investigated using an economic example, and the obtained results compared with those obtained using an existing method.

Multiple Goal Linear Programming-Based Decision Preference Inconsistency Recognition and Adjustment Strategies

The purpose of this paper is to enrich the decision preference information inconsistency check and adjustment method in the context of capacity-based multiple criteria decision making. We first show that almost all the preference information of a decision maker can be represented as a collection of linear constraints. By introducing the positive and negative deviations, we construct the the multiple goal linear programming (MGLP)-based inconsistency recognition model to find out the redundant and contradicting constraints. Then, based on the redundancy and contradiction degrees, we propose three types of adjustment strategies and accordingly adopt some explicit and implicit indices w.r.t. the capacity to test the implementation effect of the adjustment strategy. The empirical analyses verify that all the strategies are competent in the adjustment task, and the second strategy usually costs relatively less effort. It is shown that the MGLP-based inconsistency recognition and adjustment method needs less background knowledge and is applicable for dealing with some complicated decision preference information.