Batch Scheduling of Unique and Common Components for a Three-Stage Hybrid Flow Shop Processing Different Product Types with Multiple Due Dates to Minimize Total Actual Flow Time

A three-stage hybrid flow shop consists of machining, assembly, and differentiation stages processing different product types, each of which is considered as a job. The machining stage processed the unique and common components of a job on unrelated parallel machines. The unique component is specific for a certain product processed individually, while the common components are the same for all products processed in batches with a setup between consecutive batches. The assembly stage starts when the components of a job are available. The differentiation stage consists of dedicated parallel machines processing types of products. The problem is to determine an integrated schedule of the three-stage hybrid flow shop system processing different product types considering multiple due dates with the objective of minimizing total actual flow time. The total actual flow time allows parts to arrive in the shop at the starting time of processing and deliver the completed products at their respective due dates. This problem is formulated in a nonlinear programming model and solved by a proposed algorithm adopting an SPT-based heuristic for the initial solution and a variable neighborhood descent method with insert and swap move operators for optimizing the solution. An illustrative example is used to test the model considering multiple due date conditions. The result shows the ability of the algorithm to solve the problem.