An integer linear programming model and a modified branch and bound algorithm for the project material requirements planning problem

Abstract

This study presents a novel integer linear programming (ILP) model and a modified branch and bound (MBB) algorithm to minimize the total project inventory cost for the project material requirements planning (PMRP) problem. Twelve two-step lot-sizing rules are compared with the ILP model based on an experiment involving the single-material and two-material requirement problems. According to the results of the experiment, the ILP model outperforms the twelve two-step lot-sizing rules with an average reduction in the total project inventory cost of about 28.54%. This study further assesses the performance of the twelve two-step lot-sizing rules with respect to several important parameters of the PMRP problem. The results indicate that the performance of the twelve two-step lot-sizing rules is significantly affected by the rule itself, the network density, and the value of the percentage of activities with material requirements (PERC). On the other hand, the effectiveness of the MBB algorithm is also evaluated by comparing it with the ILP model. The results of the comparison reveal that the solution obtained by the MBB algorithm is very close to the optimal solution, and that the proposed algorithm does not consume much computational time. The approaches presented in this study, in which project scheduling and lot sizing are considered simultaneously, could provide project managers with useful tools for making better PMRP decisions.