Linear constraint programming for cost-optimized configuration of modular assembly systems

In this paper, we develop an optimization model for providing a logical layout for reconfigurable assembly systems from a library of available equipment modules. The design problem addresses the challenges in equipment selection to build workstations and subsequently the entire assembly system. All the available equipment modules are assumed to be modular and each of them retains a subset of skills (capabilities). The set of all available equipment modules, their skills, mode of physical connectivity (ports) and costs are known. The objective is to minimize the overall equipment cost without violating their physical connectivity (ports) constraints and the precedence constraints of the assembly process requirements. The analysis of the problem and the state-of-art review steered us to the following: (1) the design problem is very closely related to the assembly line balancing problems; (2) a few Genetic Algorithm (GA) based approaches are already available for the capital cost optimization of multi-part flow-line (MPFL) configurations that includes the operational precedence constraints; (3) to our knowledge, this is the first work to combine the equipment physical connectivity constraints with task precedence in order to provide a valid and optimal configuration solution. A formalized mathematical model is developed to select suitable subsets of equipment modules and group them into workstations to construct an optimal logical layout. A number of scenarios based on an industrial case study are simulated and the results are analysed to evaluate the performance of the proposed models.