Developing a non-gradient based mixed-discrete optimization approach for comprehensive product platform planning (CP³)

The Comprehensive Product Platform Planning (CP³) framework presents a flexible mathematical model of the platform planning process, which allows (i) the formation of sub-families of products, and (ii) the simultaneous identification and quantification of platform/scaling design variables. The CP³ model is founded on a generalized commonality matrix that represents the product platform plan, and yields a mixed binary-integer nonlinear programming problem. In this paper, we develop a methodology to reduce the high dimensional binary integer problem to a more tractable integer problem, where the commonality matrix is represented by a set of integer variables. Subsequently, we determine the feasible set of values for the integer variables in the case of families with 3 - 7 kinds of products. The cardinality of the feasible set is found to be orders of magnitude smaller than the total number of unique combinations of the commonality variables. In addition, we also present the development of a generalized approach to Mixed-Discrete Non-Linear Optimization (MDNLO) that can be implemented through standard non-gradient based optimization algorithms. This MDNLO technique is expected to provide a robust and computationally inexpensive optimization framework for the reduced CP³ model. The generalized approach to MDNLO uses continuous optimization as the primary search strategy, however, evaluates the system model only at the feasible locations in the discrete variable space.