Modeling supplier coordination in manufacturing process validation.

Abstract

This dissertation presents a quantitative model to examine the value of coordination between an automobile manufacturing firm and its die suppliers during sheet metal stamping die tryout. Die suppliers often face extensive die rework to remove dimensional bias---the mean deviation from target of panel dimensions---caused by die design uncertainty. Yet, much of the rework is unnecessary for producing dimensionally correct assemblies at the next manufacturing stage. To determine if dimensionally correct assemblies can be made from panels with dimensions outside of specification, die suppliers must coordinate with the manufacturer. However, the resources spent in coordination are not always justified. The primary objective of this research is to quantify the amount of time and cost that can be saved by coordination in die tryout. The results include two formulations. One is used to find the minimum expected elapsed rework time with and without coordination. The other is used to find the minimum expected rework cost with and without coordination. In the time formulation, rework is deterministic and subject to assembly quality constraints. The optimal policy with coordination is obtained by solving a mixed-integer program that determines which biases to rework and the amount of rework. The optimal policy without coordination is obtained by solving a non-linear program that finds the optimal bias control limits. Several numerical examples suggest that coordination saves the most time with complex, non-rigid panels and saves the least time with simple, rigid panels. Two common organizational restrictions---the tendency of engineers to only reduce the bias and the requirement to rework the bias to zero if it is not acceptable---are shown to increase the a amount of rework time. In the cost formulation, rework is random and unconstrained. A stochastic dynamic program is used to find the optimal trade-off between rework costs during die tryout and nonconformance costs during production. In the case of a single dimension, the structure and closed form solution of the optimal policy is obtained. Numerical examples illustrate the effect of bias uncertainty, rework uncertainty and panel characteristics on the value of coordination.