Optimized Design of Laundry Cleaning Based on Linear Programming

Abstract

This paper presents an optimized design for laundry cleaning, utilizing linear programming and Python and SPSS software programming. It aims to achieve cost-effective and good cleaning effects under different conditions. The core challenge addressed in this paper is
balancing cost-effectiveness and cleaning effectiveness. First, a mathematical model is developed to describe dirt solubilization in water and
the relationship between wash frequency and water consumption. Second, a cost-effective cleaning scheme is identified, considering water
rates and other factors. Additionally, factors such as clothing types and quantities, dirt types, detergent types, and the constraint of mixing
certain clothing items during washing are taken into account. By solving the laundry cleaning mathematical problems using an optimization
model in mathematical modeling, factor analysis is conducted considering various factors including a given amount of dirt, water, dirt solubility in water (function), wash frequency, water consumption per wash, dirt type, detergent type, detergent solubility in dirt, detergent unit
price, water rates, and the constraint of certain clothing items not being able to be washed together. The goal is to achieve a lower-cost laundry cleaning solution that is both effective and tidy.