Multicriteria scheduling of two-subassembly products with batch availability and precedence constraints

This article studies the multicriteria problems of scheduling a set of n products on a fabrication facility, focusing on batch availability and precedence constraints. Each product is composed of two distinct subassemblies: a common subassembly, shared across all products, and a unique subassembly unique to each product. The common subassemblies are processed together in batches, with each batch requiring an initial setup, while unique subassemblies are handled individually. The availability of a common subassembly is contingent upon the completion of its entire batch (i.e., batch availability), whereas a unique subassembly becomes available immediately after its processing. The product completion time is determined by the availability of both subassemblies. Strict (weak) precedence means that if a product precedes another, then the latter can start only after the former is completed (the latter cannot start earlier than the former). We propose O(n⁴)-time algorithms to simultaneously optimize makespan and maximum cost, as well as to lexicographically optimize two maximum costs and makespan under strict or weak precedence constraints.