This paper addresses the single-product assembly system design problem (ASDP) which seeks to minimize total cost by optimally integrating design (selecting the machine type to locate at each activated station) and operating issues (assigning tasks to observe precedence relationships and cycle time restrictions). We propose an effective branch-and-cut approach for solving single-product ASDPs, adapting inequalities known to be valid for embedded line balancing structures to form inequalities that are valid for the ASDP. The implementation also involves a specialized preprocessor, a heuristic, separation procedures, and an enumeration scheme. Computational tests establish benchmark results for this first implementation of cutting planes for solving the ASDP.

This paper establishes a foundation for a cutting plane approach to solve a class of problems that are important to assembly systems, including assembly line balancing (ALB), workload smoothing (WS) and assembly system design (ASD). We describe relationships among the integer programming formulations of these problems and recast their relaxations as node packing problems (NPPs). Exploiting the well-known structure of the NPP and other relationships among the assembly problems, we derive several families of valid inequalities and show conditions under which they also define facets for the associated ALB, WS and ASD polytopes.