Improved benders-and-price algorithm for the multi-product assembly routing problem with time windows: A domain decomposition strategy for the benders-master model

Abstract

To meet the optimization requirements of many-to-one assembly systems comprising a plant and multiple suppliers, the multi-product assembly routing problem with time windows (MPARPTW) is investigated in this study. Besides optimizing the assembly of different types of products in a plant to satisfy the periodic market demand within a specific planning horizon, MPARPTW factors in the vehicle routes for collecting many components from suppliers to meet the inventory requirements that are imposed by the production. The MPARPTW is formulated as a mixed-integer linear programming model to minimize the setup, production, transportation, and inventory costs. The model is solved using an improved Benders-and-Price algorithm that combines Benders decomposition and branch-and-price algorithm. The MPARPTW model is decomposed into a lot-sizing Benders-master (BM) model and a vehicle-routing Benders-sub (BS) model. A domain decomposition strategy is developed in this study to further decompose the BM model, thereby generating Benders cuts efficiently and increasing the convergence speed. Numerical experiments are designed to test the performance of the proposed algorithm. Within a limited maximum computing time (compared with the off-the-shelf solver), the improved algorithm reduces the average cost and computing time by 0.6% and 59.3%, respectively. The significance of the proposed model and algorithm in determining the plant investment directions is demonstrated. Moreover, compared with the conventional algorithm, the improved algorithm exhibits overall improvements. In large-scale instances, the cost is reduced by 1.8% on average and 4.2% maximum. The computing time yields average and maximum reductions of 35.2% and 76.0%, respectively.