A new decentralized approach for the lot sizing problem of durable products with demand substitution

This study proposes a heuristic approach for the solution of the multi-item dynamic lot sizing problem of durable product with end-of-use constraints. The difficulty in solving this problem is to decompose it into item-level subproblems while ensuring the feasibility of the solution. The proposed technique aims to resolve this issue by combining the capabilities of Lagrangean relaxation to decompose the problem into smaller problems, and genetic algorithm to update the Lagrangean multipliers. We report computational results to demonstrate the effectiveness of our approach.