Hybrid stage shop scheduling

The proposed hybrid stage shop scheduling (HSSS) model, inspired from a real case in the high-fashion industry, aims to fully exploit the potential of parallel resources, splitting and overlapping concurrent operations among teams of multifunctional machines and operators on the same job. The HSSS formally extends mixed shop scheduling (a combination of flowshop and open shop), which is able to model routing flexibility, and hybrid shop scheduling, which provides resource flexibility. To also include operational flexibility through alternative plans obtained by reordering operations linked by undefined or arbitrary (immaterial) precedence constraints, the proposed model integrates process planning and group shop scheduling. A mixed integer linear programming model and a theory based on disjunctive graphs have been proposed to explore the composite relations between nodes involving immaterial relations and deploying their routing rules. A constructive O(resources  jobs 2) algorithm to generate a feasible plan/schedule in the most general case has been developed and applied to a case study. We consider a rather general model of mixed shop in which a set of operations for a given set of jobs has to be scheduled on a set of machines, which includes two extensions to the standard scheduling problem as defined by Dauzère-Pérès, Roux, and Lasserre (1998): 1. An operation can be processed by one resource chosen in a given set (resource flexibility); for the sake of generality, we use the standard term resource from the scheduling theory instead of machine. 2. The routing of products in the shop floor is not necessarily linear , i.e. an operation can have more than one predecessor and more than one successor on the routing (nonlinear routing). The mixed shop type considered here is a hybrid (or flexible) shop type combination of flowshop and open shop. A hybrid flowshop is a flowline with parallel resources. In a flowshop, the sequence of operations of each job (routing) is linear and prede-fined; in an open shop the sequence of operations is immaterial (or undefined). An overview of resource constraints in scheduling and planning problems is available from Baptiste, Laborie, Le Pape, and Nuijten (2006). In a mixed shop, the set of constraints between operations is partitioned into two sets: flowshop type set and open shop type set (Masuda, Ishii, & Nishida, 1985). 1.1. Integration of process planning and shop scheduling Mixed shop is the paradigm for the integration of process planning and shop scheduling (Tan & Khoshnevis, …