The Line-less Mobile Assembly System Simultaneous Scheduling and Location Problem

Line-less Mobile Assembly Systems (LMAS) operations management requires a global planning approach to benefit from the paradigm's beneficial resilience and flexibility. LMAS's unique property is the spatio-temporal assessment of assembly stations by mobile multipurpose resources. In mixed-integer programming (MIP), the simultaneous scheduling location problem (ScheLoc) combines two essential objectives desired for LMAS global planning and control: Finding optimal machine locations on the shop floor and finding optimal schedules for each of these machines subject to production and location constraints. However, recent ScheLoc formulations do not map the LMAS properties entirely and only respect either a single machine location for planar regions (P-ScheLoc) or parallel machines' locations for discrete regions (D-ScheLoc). Therefore, this paper deduces the LMAS ScheLoc problem extending recent mixed-integer programs to customized production orders and spatio-temporal station assessment with individual capabilities by mobile robots for discrete environments. The model's objective is to minimize the makespan respecting scheduling-specific, location-specific, and joining constraints. Since LMAS ScheLoc is computationally heavy, we propose the necessary criteria for input datasets. If they are not fulfilled, a solution's existence for a given problem is precluded. Further, we present an upper bound estimate for the makespan CMakeestimate for practical implementations. The analysis is executed based on an industrial sewage pump assembly use case. Test datasets exhibit different flexibility levels ultimately highlight LMAS ScheLoc's benefits.