Product Configuration from a Mathematical Optimization Perspective
Abstract: The optimal truck configuration for a certain customer is very specific and depends on for what transport mission and in which operating environment the truck is to be used. In addition, the customers normally specify other feature requirements ranging from visual appearance to advanced driver support systems. For this reason, the truck configurations that are made available for the customers are highly specialized. To achieve this in a cost efficient way, the manufacturer must be able to produce these configurations with a limited set of technical solutions. This is done by the use of a common architecture, in which technology is shared such that the same parts are used in different combinations, leading to a relatively small number of parts but a large number of possible configurations. This thesis presents an approach to the configuration problem by analyzing it from a mathematical optimization perspective. By assuming that a truck can be described by a number of quality measures, which different customers may appreciate differently, the problem of deciding on a good product offer can naturally be formulated within a multi-objective optimization framework. The areas within product development in which mathematical optimization can be applied are many and most often fundamentally different. In this thesis several subproblems of the whole product development problem are formulated in mathematical terms, and in the appended papers, the resulting mathematical models are considered in generalized forms. As established in the different papers, not just one optimization discipline is relevant in the product development context. The disciplines considered include multi-objective optimization, clustering, robust optimization, continuous global optimization, and nonlinear integer programming with an extension to a special type of non-sortable discrete variables. For a large number of objectives-typical in many real-world applications-multi-objective optimization becomes cumbersome; the first appended paper provides a method for problem reduction such that the representation of the Pareto optimal set is kept as accurate as possible. The second paper considers a simplification of the configuration problem of finding appropriate sets of technical solutions that are to be combined into configurations, by assuming that the decision variables are continuous and box-constrained. Clearly, real-world problems often involve uncertainties in models and/or data. In the third appended paper, a new measure of robustness of solutions to multi-objective optimization problem is developed. The preferences of the decision maker are estimated by an utility function on which the robustness measure is based. In the fourth appended paper, optimization with respect to a type of non-sortable discrete variables is addressed. Theoretical and methodological investigations are performed, and by a reformulation of the problems as nonlinear integer programming problems mathematical optimization techniques are shown to be applicable. In the last appended paper, we explore a new principle for continuous global optimization of computationally expensive functions by, for each new function evaluation, minimizing the resulting worst-case optimality gap. The main contribution of this thesis is the interpretation and formulation of a product development problem, including subproblems, in a mathematical optimization framework. The thesis has been written in close cooperation with Volvo 3P.
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