Finite capacity scheduling with multiple tools and machines

This is one of a series of papers that describe the placement sequence approach to finite-capacity scheduling of factories. We explain the concept of event networks and use input–output matrices so that complex scheduling calculations can be formalized as operations on the rows and columns of matrices. A central aim of the placement sequence approach is to achieve well-packed and stable schedules without the need for an iterative schedule improvement stage within the calculations. This means that calculations are bounded and it is feasible to apply the technique to large industrial applications. This paper addresses the issue of finite-capacity scheduling where activities can have multiple and alternative combinations of tools and machines. This is often called the alternate routing problem. We represent the tooling combinations as Boolean expressions that include the preferences between tools and machines. These are converted into an input–output matrix, which we call the tooling matrix. The description is presented partly in terms of principles and partly in terms of how to write a computer program to implement the calculations. The paper explains the principles of scheduling multiple and alternative tools and machines and then works through a detailed example of the calculations.