Matrix Approach and Scheduling for Cooperation Requirement Planning in Industrial Robots

Abstract

Recently, companies have been shifting from lean manufacturing to cell manufacturing using industrial robots. Nof et al. have proposed cooperation requirement planning (CRP) among multiple industrial robots and tasks in the production process. CRP comprises two parts, CRP-I and CRP-II. CRP-I establishes the conditions for ensuring cooperation among multiple industrial robots, whereas CRP-II formulates an operation plan for optimizing the manufacturing objectives using the conditions established by CRP-I. Nof’s study describes a method for formulating a consistent operation plan based on a two-step method procedure where conditions are set by CRP-I and optimized by CPR-II in multiple industrial robots. Furthermore, the matrix approach is a method of representing the relationship between inputs and outputs and examining operational plans. The present study focuses on CRP with multiple industrial robots and proposes a mathematical model using a matrix approach (Matsui’s equation) that includes scheduling method. The proposed mathematical model demonstrates the possibility of reducing the abovementioned two operation steps (CRP-I and CRP-II) to one and includes the scheduling theory by adding one additional matrix to Matsui’s equation. Furthermore, the mathematical model can compare the corrected values obtained for two cases involving CRP with multiple industrial robots based on this modified matrix approach with the standard values obtained from the original approach. The matrix approach examines the operation plans of multiple industrial robots by comparing the standard values and corrected values. This paper presents a mathematical model and development from the conventional two-stage method (CRP-I and CRP-II) to a one-stage method (matrix approach) of Matsui based on the cooperation requirement planning of multiple industrial robots.