Finite capacity scheduling – packed placement sequence schedule

This is one of a series of papers which describe the placement sequence approach to finite capacity scheduling of factories. A central aim of the placement sequence approach is to achieve well-packed and stable schedules, with multiple and alternative tools and machines, without the need for an iterative schedule improvement stage within the calculations. This means that calculations are bounded and the technique is suitable for large industrial applications. In this paper we treat schedule packing as the main goal and show how to build a ‘packed placement sequence schedule’. We use a two-stage process to choose the machines and placement sequence constraints. The first stage is a backward infinite capacity schedule and the second stage is a backward finite capacity schedule. While building the backward finite schedule we schedule using the order of event times from the infinite capacity schedule, and read the machine loading from the infinite capacity schedule so we can spread the load and push jobs away from the most heavily loaded machines in the finite capacity schedule. The final result is a well-packed, backward, finite capacity schedule. The paper explains the method, discusses the issues, and works through a detailed example of the calculations.