Mixed-Integer Linear Programming Approach for Life-Cycle Carpet Profit

Abstract

This paper proposes an mixed-integer linear programming (MILP) model to accurately represent a product life-cycle design considering profit maximization. The model that takes into account the effects on the demand lev-el and a measure of the customer utility considering recycled raw materials and prices of the traditional and modular products. Demand functions for traditional and modular products are considered. Given the presence of bilinear terms in the formulation (for example due to the multiplication of product price for the demand), the multi-parametric disaggregation technique is used to obtain a line-ar model. The developed model is applied to a company that produces tradition-al carpets and it wants to manufacture carpets based on a new modular design where recycled materials must be incorporated. The objective of the company is to maximize the total profit taking into account the design specifications and the selling prices for traditional and modular carpets. In addition, the amount of square meters of traditional carpets must be determined and the take-back rate must be considered. The practical behavior of the formulation is analyzed through computational experiments exploring the analyzed case-study.