Optimal Collaborative Design in Supply Chains

Background

A product has a design space described by a set D of variables. Each variable in D is a design parameter. Type of processor used in a smart appliance is a design parameter. We assume that each parameter is associated with a discrete domain of possible values, and a naturally continuous parameter is discretized. A partial design is an assignment of values to variables in a proper subset of D, and a complete design assigns values to all variables in D.

A design is subject to a set of constraints. For instance, if length of a computer case is L and length of the motherboard is L', then L>L’ should hold. A constraint involves a subset S ⊂ D of variables and specifies allowable assignments for S. A design is valid if it satisfies all constraints.

Different valid designs result in products with different performances. Maximum speed is a performance measure of a car. For simplicity, we refer to performance of a product resultant from a design as performance of the design. Performance space of a product is described by a set M of variables, each being a performance measure. We assume that each measure is associated with a discrete domain.

Performance of a product also depends on environment in which it operates. For instance, high level of humidity may cause a computer to fail. We describe such environmental factors by a set T of discrete variables.

People differ in preference over a given product performance. Subjective preference of stake-holders (manufacturer or end-user) over design is represented by utility functions (Keeney & Raiffa, 1976). For clarity, we assume that utility is directly dependent on performance of product, not directly on design parameters. Hence, we denote the utility function U(M). An overview of methods for utility function assessment is given in (Farquhar, 1984).