A unified modeling framework and improved formulations for single-hoist cyclic scheduling

Abstract

The cyclic hoist scheduling problem originates in electroplating lines, where a single or multiple hoists transport parts between processing tanks subject to technological constraints. The objective is typically to determine a cyclic sequence of hoist movements that minimizes the cycle time while satisfying travel and processing constraints. Although the problem has been widely studied for several decades, the literature contains a puzzling phenomenon: different studies often report different optimal cycle times for the same benchmark instances, which limits the comparability and reproducibility of computational results. In this paper, we revisit the modeling of cyclic hoist scheduling problems from a unified perspective. We introduce a consistent modeling approach for single-hoist problems and analyze several mixed-integer linear programming (MIP) formulations proposed in the literature. Our analysis identifies modeling inconsistencies and clarifies the relationships between existing formulations. Based on these observations, we propose straightforward constraint programming (CP) models that can serve as baseline approaches, and we also derive improved MIP~formulations. Extensive computational experiments compare the strength and performance of the investigated formulations. To support reproducible research, we also provide a publicly available library containing benchmark instances and implementations of several CP and MIP~formulations for single-hoist cyclic hoist scheduling.

Figures (6)

• Figure 1: A bi-directional line with a single hoist. Currently, carriers are soaking in tanks 2 and $N$, and another one is being transported by the hoist. Tank 3 is not included in this processing sequence, however, the carrier re-enters multifunction tank 4.
• Figure 2: An optimal single-hoist schedule ($C = 521$) for the instance of phillips1976mathematical with associated load and unload stations. The colors refer to the four carriers used in the simple cycle.
• Figure 3: Soaking either starts and ends within the same cycle ($\mathbf{y}_{i-1,i} = 1$, i.e., $\mathbf{t}_{i-1} < \mathbf{t}_i$) or it is in process at the beginning of the cycle ($\mathbf{y}_{i-1,i} = 0$, i.e., $\mathbf{t}_{i-1} > \mathbf{t}_i$).
• Figure 4: An example of a schedule with three operations that use the same tank. A later operation (red carrier) appears between two earlier operations (blue carrier) in the cyclic timeline, showing that feasible schedules are not restricted to cyclic shifts of the original operation order.
• Figure 5: The process of operation $i$ follows a 3-period pattern. The carrier inserted into the tank in a given cycle is removed three cycles later, after being soaked for a duration between $2\mathbf{C}$ and $3\mathbf{C}$.