Optimisation of the aggregation and execution rates for intersecting operation sets: an example of machining process design

A sequence of multiple parts is processed on a multi-position transfer line of conveyor type. This sequence consists of identical subsequences (batches). The sets of operations executed for each part at each position are given and these sets for different parts can intersect. Some operations executed at one position can be aggregated into blocks of operations. Each block is executed at a uniform rate (in particular, feed per minute) by a common drive unit. The set of potentially feasible blocks is specified. We consider the situation when the sets of operations for different blocks do not intersect and each potential block can be executed either completely aggregated (i.e. as one block) or completely disaggregated (individually). Aggregation reduces the investment costs, but can increase the consumption of tools due to excluding the individual selection of rates for aggregated operations. The accepted option of the aggregation and the rates of operations remain invariable during the line functioning. The problem is to select the optimal option of aggregation and rates of all operations that minimise the total batch processing cost while ensuring the required line productivity. A mathematical model of the problem and a two-level decomposition method for its solution are proposed. The statement of the problem and the results of its solution are illustrated on a real industrial example. The developed model and method can be applied to solve similar problems arising in other domains.