This project developed a comprehensive facility design methodology which, given information on parts, workcenters, expected demand distributions over a planning horizon, material handling systems availability, and site specifications, will provide an optimal manufacturing facility design under specific constraints. The design seeks to minimize the material handling effort within the facility. To date, the problems of grouping machines into manufacturing cells and generating intra-cell layout have been addressed successfully. For the inter-cell layout problem, three highly interconnected stages have been identified: department and cell placement on the shop floor, design of the resource interconnections (material flow paths), and material handling system control. (See also Hybrid Facility Master Planning)
The design of the material flow paths has been formulated as a fixed-charge capacitated network design problem. The objective is two-fold: minimize the cumulative distance traveled by the parts and minimize the total cost of building and controlling flow paths. This problem models the tradeoff between routing cost savings and fixed charges for using path segments. Constraints include flow conservation equations and arc capacity inequalities that are introduced to prevent traffic congestion. The problem is NP-hard. Two heuristics and a dual ascent approach that determines good lower bounds and primal feasible solutions have been developed. Both heuristics are based on the linear programming relaxation of the integer programming formulation; they iteratively fix the values of the binary variables in order to obtain a feasible network design. The dual ascent approach is based on the labeling method for the uncapacitated design problem of Balakrishnan et al. (1989). The algorithm successively absorbs arc fixed costs into the dual objective and updates arc routing costs to provide a better lower bound at each iteration and a capacity-feasible network design at termination.
The material handling system control problem is viewed from a steady-state perspective, with constant production rates and transportation speeds as well as negligible pickup and delivery times. The following issues are addressed: evaluation of the number of carriers required to serve the material flow, identification of the number of unloaded carrier moves between input/output stations, and assignment of the carriers to unloaded moves. The problem is formulated as an arc-covering problem on a complete directed graph, with nodes which represent the input/output stations and arcs which represent the multiple resource connections. A breadth-first search is under development as a method of generating near-optimal solutions to this problem. The placement of departments (cells) on the shop floor has been formulated as a quadratic assignment problem which employs the results of the previous two design problems to evaluate the overall objective.
Improved shop design results in a competitive advantage through the reduction of material handling costs. An integrated approach which includes the flow path design and material handling control in the shop design is innovative in the material handling research community. The fixed-charge capacitated network design problem is generic and can be applied to several areas, including communication and transportation systems. The dual ascent approach extends the existing framework to account for arc capacities. In addition, the formulation for the flow path problem provides a strong mathematical model for a practical application and captures most of the important design attributes. Finally, the material handling control problem is introduced for the first time in the shop design stage; it is anticipated that this will further extend the applicability of the methodology, since a significant but often neglected factor is taken into consideration.
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