Zero‐one quadratic programming algorithm for resource leveling of manufacturing process schedules

Abstract

AbstractIn industrial plant construction scheduling, it is necessary to minimize the fluctuation or the maximum peak of the fluctuation or the maximum peak value of the daily resources amount, which is calculated as the sum of daily resources for each process. Minimization of the fluctuation or the maximum peak value corresponds to leveling the pile of resources. To perform this resource leveling, we need to decide on an objective function which is a monotone function that simply increases with the degree of resources leveling and then solve the optimization problem by fixing the process start dates while minimizing the objective function. Industrial plant construction is, however, in many cases a large‐scale scheduling with an entire period of more than 1000 days and more than 100 processes, so it is very difficult to obtain a global optimization solution. In this study, we have developed an algorithm which solves a large‐scale optimization problem to level necessary resources. This algorithm can quickly search for a good suboptimal solution close to the global optimal solution of a 0–1 quadratic programming problem. The algorithm searches by repeating a pivot operation using variable selection rules for resources leveling. We applied this algorithm to largescale scheduling for an actual plant construction schedule, and successfully obtained a practical suboptimal solution within a few minutes (CPU power: 28MIPS). The results suggest that the algorithm is practical for resources leveling of large‐scale construction scheduling.