A comparative study between integrated and non-integrated approaches to the two-dimensional bin packing problem with minimization of total completion time of orders

This paper addresses a Two-Dimensional Bin Packing Problem (2D-BPP) integrated with production scheduling, in which the objective is to minimize the total completion time of customer orders. Each order is composed of a subset of rectangular items that must be allocated into identical bins according to non-exact two-stage orthogonal guillotine packing patterns. Two new approaches to the problem are proposed. The first is an integrated Integer Linear Programming (ILP) formulation that simultaneously determines the packing patterns and the production schedule. The second is a non-integrated two-step approach in which the classical 2D-BPP is first solved to generate packing patterns, and then a scheduling model is used to sequence these patterns to minimize the total completion time. Computational experiments were conducted using benchmark instances from the literature. The integrated model reduced the average total completion time by approximately 38% and 20% relative to the classical and two-step approaches, respectively. These results highlight the benefits of integrating packing and scheduling decisions in production environments involving customized orders.