MILP model for multi-product, multi-part and multi-hoist cycle shops

This paper addresses the cyclic multi-hoist scheduling problem. The problem arises in automated electroplating lines where multiple hoists are operating on a shared track. A number of parts are processed periodically and are categorized in different types of products. For each type of product a different processing sequence and processing time windows are supported. All parts of the same product are identical. A different number of parts for each product within a cycle is possible. The general processing sequences may be different from the location sequence of the tanks and multi functional resources are considered. A multi-degree cyclic mixed integer linear programming (MILP) model for optimizing the cycle time is presented, considering in particular the spacial dimensions of hoists and their collision. There are no restrictions concerning the start and end of loaded or empty hoist moves. The collision avoidance is formulated with the help of spacial relations of the movement. The model supports fixed and processing times with time windows.