Mixed-integer linear programming approach for product design for life-cycle profit

Abstract

The paper deals with the product design problem where the characteristics of new and remanufactured products must be determined. The objective of the problem is to maximize the total profit taking into account the design specifications and the selling prices for the new and remanufactured products. The amount of new and remanufactured products is to be determined and the take-back rate is considered. The problem representation leads to a mixed-integer nonlinear structure, which makes very hard to deal with the corresponding mathematical formulation. Nevertheless, the problem can be modeled as a mixed-integer linear formulation taking advantage of the high efficiency, both in terms of solution accuracy and computing time of the software tools (solvers) developed for mixed-integer linear programming (MILP). This is explored in this work and a MILP model able to accurately represent the life-cycle design while the profit is maximized is proposed. In particular, the model takes into account the effects on the demand level of specifications and prices of new and remanufactured products. The formulation deals with the representation of demands nonlinear functions (new and remanufactured products) and the existent bilinear terms are handled through piecewise linear approximation and multi-parametric disaggregation techniques. The practical behavior of the formulation is analyzed through computational experiments considering an example of a desktop computer. In addition, the performance of the formulation and the quality of the solution obtained are compared with the performance of a nonlinear approach.