OPTIMASI KEUNTUNGAN MENGGUNAKAN METODE KARUSH- KUHN-TUCKER (STUDI KASUS: MI ACEH PATTIMURA DI JAMBI)

Masalah pengeluaran yang tidak stabil dan produksi yang tidak optimal mendorong pelaku usaha untuk merumuskan strategi yang tepat agar usaha dapat terus berjalan dengan lancar. Hal tersebut juga terkait dengan adanya keinginan untuk memaksimalkan keuntungan. Masalah yang demikian dialami pula oleh pelaku usaha Mi Aceh Pattimura, Jambi. Adapun tujuan dari penelitian ini adalah untuk menentukan dan mengidentifikasi jumlah produksi yang optimal per hari supaya pelaku usaha Mi Aceh Pattimura memperoleh keuntungan harian yang optimal berdasarkan modal dan bahan yang tersedia. Dan pada penelitian ini, metode yang digunakan untuk menemukan keadaan optimal tersebut adalah metode Kuhn Tucker. Berdasarkan perhitungan menggunakan metode Karush-Kuhn-Tucker, diperoleh jumlah produksi optimal per hari pada usaha Mi Aceh Pattimura adalah mi aceh kuah sebanyak 15 porsi, mi aceh goreng sebanyak 6 porsi, mi aceh tumis sebanyak 19 porsi, mi aceh daging sebanyak 20 porsi, mi aceh ayam sebanyak 20 porsi, dan mi aceh udang sebanyak 20 porsi dengan keuntungan optimal yang dapat diperoleh sebesar Rp. 745.169,9279 per hari

Optimization of bantuan pangan non tunai (BPNT) distribution using bilevel linear programming in siantar martoba subdistrict pematang siantar

Bantuan Pangan Non Tunai (BPNT) is assistance that is in the second decile; in other words, KPMs who are in the first decile will also get assistance. A limited quota of BPNT recipients will result in people in categories such as the elderly group not getting this assistance. This problem arises because there is a significant increase in the population of the elderly group every year. The research method uses secondary data from data sources, namely the social service office, to develop a bilevel model for the problem of distributing food aid on cash by regularizing the bilevel model so that a linear programming model with a single objective function is obtained. In the regularization stage, the gradient descent method is used to find the optimal value of the penalty parameter. From the calculation results of the regularized model, it is found that the values of the variables  x_1= 2956,  x_2= 583, and x_3 = 250 have a value of Z = 3804. This bilevel linear programming model approach provides a strong basis for planning and decision-making related to the distribution of Non-Cash Food Assistance (BPNT) in Siantar Martoba Subdistrict. Therefore, it can be assumed that this bilevel linear programming approach can be used as a guideline for related agencies in allocating resources efficiently

Optimal configuration of energy storage system capacity in traction power supply system considering photovoltaic consumption

In order to achieve energy savings and promote on-site integration of photovoltaic energy in electrified railways, a topology structure is proposed for the integration of photovoltaic (PV) and the energy storage system (ESS) into the traction power supply system (TPSS) based on a railway power conditioner (RPC). This paper analyzes the composition and operation principles of this structure. To assess the economic benefits brought by the integration of photovoltaic and energy storage systems, a bilevel optimization model is established, with the objectives of optimizing energy storage capacity configuration and photovoltaic energy integration. The KKT (Karush–Kuhn–Tucker) method is employed to transform the model into a single-layer mixed-integer linear programming model, which is then solved using the CPLEX solver in MATLAB. The research findings indicate that, with the configuration of the ESS, the optimal PV consumption rate achieved is 96.8749%. Compared to a 100% PV consumption rate, the ESS capacity configuration is reduced by 13.14%, and the overall operational cost of the TPSS is at its lowest. The study suggests that the proposed bilevel optimization algorithm can more effectively consider PV consumption, leading to enhanced economic performance of the TPSS operation

Optimal selection of the regularization function in a generalized total variation model. Part II: Algorithm, its analysis and numerical tests

Based on the generalized total variation model and its analysis pursued in part I (WIAS Preprint no. 2235), in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on

Optimum Fund Allocation Strategy by Considering the Company's Assets and Liabilities

Investment is essentially placing some funds at present with the expectation of future profits. The basic thing that an investor needs to know is that there is a risk that follows the profit/return. In determining the proper allocation of funds, an investor needs to consider the company's assets and liabilities. Company assets can be in the form of shares, property, and others. Meanwhile, the company's liabilities include debts and other obligations. One of the sectors whose company value has stagnated or increased during the Covid-19 Pandemic is the financial sector. Securities companies are a sub-sector of the financial sector which has a fairly strong position during the Pandemic. This research aims to determine the weight of fund allocation in each company forming the optimum portfolio and to see the effect of the company's assets and liabilities on the formation of the optimum portfolio. One of the methods used is the Lagrange Multiplier method for model formulation. The results of this study show that the optimal portfolio weight of PANS companies is 16.31% with an allocation of funds amounting to Rp163.612.976,00, the optimum portfolio weight of RELI companies is 83.003% with an allocation of funds of Rp830.029.681,00, and the optimum portfolio weight of TRIM companies is 0.636% with the allocation of funds amounting to Rp6.358.243,00. In this study, it was also found that the greater the percentage difference between the company's assets and liabilities, the greater the company's optimum portfolio weight

A bilevel optimal motion planning (BOMP) model with application to autonomous parking

In this paper, we present a bilevel optimal motion planning (BOMP) model for autonomous parking. The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and the lower level is for geometry collision-free constraints. The significant feature of the BOMP model is that the lower level is a linear programming problem that serves as a constraint for the upper-level problem. That is, an optimal control problem contains an embedded optimization problem as constraints. Traditional optimal control methods cannot solve the BOMP problem directly. Therefore, the modified approximate Karush-Kuhn-Tucker theory is applied to generate a general nonlinear optimal control problem. Then the pseudospectral optimal control method solves the converted problem. Particularly, the lower level is the $J_2$-function that acts as a distance function between convex polyhedron objects. Polyhedrons can approximate vehicles in higher precision than spheres or ellipsoids. Besides, the modified $J_2$-function (MJ) and the active-points based modified $J_2$-function (APMJ) are proposed to reduce the variables number and time complexity. As a result, an iteirative two-stage BOMP algorithm for autonomous parking concerning dynamical feasibility and collision-free property is proposed. The MJ function is used in the initial stage to find an initial collision-free approximate optimal trajectory and the active points, then the APMJ function in the final stage finds out the optimal trajectory. Simulation results and experiment on Turtlebot3 validate the BOMP model, and demonstrate that the computation speed increases almost two orders of magnitude compared with the area criterion based collision avoidance method