Part batching and scheduling in a flexible cell to minimize setup costs

In this paper we consider the problem of batching parts and scheduling their operations in flexible manufacturing cells. We consider the case in which there is only one processor and no more than k parts may be present in the system at the same time. The objective is to minimize the total number of setups, given that each part requires a sequence of operations, and each operation requires a given tool. We prove that even for k=3 the problem is NP-hard and we develop a branch-and-price scheme for its solution. Moreover, we present an extensive computational experience. Finally, we analyze some special cases and related problems.