Multi-objective optimization of production: A case study on simplex, goal programming, and pareto front models

Farmers are the essential factor in the productivity chain. However, they can also be the weakest one since the distribution chain of sales transactions took a long way in Indonesia, involving farmers, collectors, wholesalers, retailers in traditional markets, and consumers. It makes consumers buy an agricultural product at a high price from farmers' uncertain stock. A distribution chain needs an optimization model involving good decision-making from organizations or governments in planning, production, warehouse, and transportation. Simulation-based optimization aims to provide adequate stock for consumers' needs and farmers' profits to minimize production costs. The Proposed Framework Integrated Three Methods is Optimization Simplex using POM QM, Optimization Goal Programming Using POM QM, Pareto Front using Phyton based and publicly available via github.This research focuses on optimization using the simplex method to fulfil the objective function with a maximum limit of more than one variable as the parameters: market demand, stock, harvest season, and price. It is also necessary to do re-optimization using goal programming to minimize the achievement deviation of the goal function and Pareto front as a model of optimizing the solution of multiple problems or Multi-Objective Optimization using linear programming. It is the development of the previous research which aims at finding the answer to the product optimization problem by cutting the distribution channel into four; farmers sell products to KUD (Cooperatives Village Unit), and KUD holds buying and selling process between farmers. Consumers and distributors sell products to consumers, and consumers purchase the product from KUD. The research shows the optimization results of the average price are up to 8913060, and the middle market hole is up to 17741000.