Exact Solution of Resource Leveling Problem by Exhaustive Enumeration with Parallel Programming

Resource Leveling Problem (RLP) is solved by heuristic, meta-heuristic, and mathematical methods. However, the aforementioned methods cannot guarantee the exact solution for large size problems. In this study, number of feasible schedules which can be obtained by delaying the non-critical activities without violating the precedence relationships and elongating the project completion time are computed. All of the feasible schedules which can be defined as the search domain are enumerated and the guaranteed optimum solution for the RLP is obtained by a different method from the existing methods. Exponential equation between the search domain and the number of activities on serial path is derived and the insolvability of large RLP in a reasonable time by one central processing unit is verified. Partitioning of the problem into equal sizes is provided by parallel programming so that each particle contains the same number of enumeration. In this study, four RLP in which the largest problem has 36 activities are solved by exhaustive enumeration within reasonable solution time and it is proved that the proposed method is applicable. Exact solutions of larger problems can also be obtained by the proposed method if the problem is partitioned into smaller sizes. © 2021 Turkish Chamber of Civil Engineers. All rights reserved.