Linear Goal Programming Method 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.

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.

Linear Goal Programming Method for Optimal Decision Making of Multi-Criteria Assignment Problems

The decision making process is the essence of the administrative process and its means of achieving the goals of the service organizations or productivity because the decision contributes mainly to enable them to carry out their administrative activities efficiently and effectively. The assignment process is one of the most important problems affecting the organizations performance because to determine the administrative composition of the organization. The correct decision making to the assignment problem and the right person in the right place will increase the efficiency and effectiveness of the organization. The previous methods to solve these problems depend on a single criterion such as cost, profit, time and so on. In this paper, three models were formulated for the of multi-criteria assignment problem. The first model multiple objective for present assignment problem when the assignment matrix is square, while the second and third models are a non-square assignment problem. The second model is the number of rows is greater than the number of columns while the third model where the number of columns larger than the rows. The second model is applied to the assignment problem of unit managers in the college of Administration and Economics based on two criteria: deferring the employee's desire to leader of task and the other criterion of assignment cost and using goal programming method. The data were collected by questionnaire.

A linear goal programming method to recover risk neutral probabilities from options prices by maximum entropy

We develop a new methodology to retrieve risk neutral probabilities (equivalent martingale measure) with maximum entropy from quoted option prices. We assume the no arbitrage hypothesis and model the efficient market hypothesis by means of a maximum entropic risk neutral distribution. The method is free of parametric assumption except for the simulation of the distribution support, for which purpose we can choose any stochastic model. Firstly, we innovate in the minimization of a different f-divergence than Kullback–Leibler’s relative entropy, resulting in the total variation distance. We minimize it by means of linear goal programming, thus guaranteeing a fast numerical resolution. The method values non-traded assets finding a RNP minimizing its f-divergence to the maximum entropy distribution over a simulated support—the uniform distribution—calibrated to the benchmarks prices constraints. Our second innovation is that in an incomplete market, we can increase the f-divergence from its minimum to obtain any asset price belonging to the interval satisfying the non-existence of an arbitrage portfolio, without presupposing any utility function for the decision maker. We exemplify our methodology by means of synthetic and real-world cases, showing that our methodology can either price non-traded assets or interpolate and extrapolate a volatility surface.

Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1) Taylor’s polyno-mial linearization approximation, (2) the method of variable change, and (3) a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a) using the optimal value of the objective functions as the decision makers’ aspirations, and (b) the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.

The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems

Most of real world decision making problems have multiple objectives, which cannot be optimized simultaneously due to the conflicting nature of the objectives. Such problems can be solved by various methods to obtain the best-compromise solutions. Modified Sequential Linear Goal Programming (MSLGP) method can be used to solve Multiple Objective Linear programming Problems. In this paper, the use of existing single objective Linear Programming (LP) techniques is there, and the information required for MSLGP in each iteration are taken from the previous iteration. In this study, there is a great Revised Multi-phase Simplex Algorithm, which is used to solve MSLGP Accordingly within small number of computations as much as possible. This method is illustrated by some numerical examples, and provides ‘best compromise’ solution.

Nonlinear structural optimization using goal programming

This paper presents a method for solving nonlinear structural optimization problems using goal programming techniques. The method can be used as a conceptual design tool since goal programming removes the difficulty of having to define one equation as the objective function and the rest as constraints. The developed algorithm uses the linear goal programming techniques with successive linearization for the nonlinear equations to obtain the solution for the nonlinear goal optimization problems. The linear goal programming method with the steps required to obtain the goal programming solution are discussed. The linearization of the general nonlinear optimization problem along with the flow chart of the algorithm are presented. In order to demonstrate the formulation of the nonlinear goal optimization problem and the use of the method, as a design tool, an illustrative example of a three-bar truss structure is included.