A Bi-Objective Optimization Approach using the LP-Metric Method Applied to Single-Row Facility Layout Problem

In the manufacturing industry, material handling costs account for a significant portion of total manufacturing costs, ranging from 15 % to 70 %. The efficient arrangement of facilities within a manufacturing system can reduce these costs by 10 % to 30 %. This is where the facility layout problem comes into play, which involves arranging physical spaces for multiple departments within a given space. Traditionally, the facility layout planning has been solved using intuition and the artistic skills of a human designer. However, when quantitative considerations are involved, computers have an advantage over humans. This work focuses on computerized procedures for solving the facility layout planning, including single-row facility layout, multi-row facility layout, and multi-floor facility layout planning. Facility design has become increasingly important since the mid-1990s due to the emergence of new technologies and intensified industrial competition. Efficient and suitable facility layouts can help companies grow and reduce costs. In this work, we focus on the single facility layout, which involves assigning a set of departments with equal or unequal areas to a single row. This is an NP-hard problem that requires arranging facilities of varying lengths and widths. Our goal is to develop a mathematical model that finds the optimal arrangement of facilities along a single row to minimize material handling travel distance while maximizing adjacency by increasing the overall placement rating. This model can be used to solve practical problems and help manufacturing companies reduce costs and increase efficiency. In summary, facility layout design is a crucial aspect of manufacturing systems, and efficient layout design can significantly reduce material handling costs. The facility layout planning is a complex problem that can be solved using computerized procedures, and our work focuses on developing a mathematical model to solve the single facility layout, which can help manufacturing companies improve their facility layouts and reduce costs.