A partition-based branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

Abstract

The concept of partially renewable resources provides a general modeling framework that can be used for a wide range of different real-life applications. In this paper, we consider a resource-constrained project duration problem with partially renewable resources, where the temporal constraints between the activities are given by minimum and maximum time lags. We present a new branch-and-bound algorithm for this problem, which is based on a stepwise decomposition of the possible resource consumptions by the activities of the project. It is shown that the new approach results in a polynomially bounded depth of the enumeration tree, which is obtained by kind of a binary search. In a comprehensive experimental performance analysis, we compare our exact solution procedure with all branch-and-bound algorithms and state-of-the-art heuristics from the literature on different benchmark sets. The results of the performance study reveal that our branch-and-bound algorithm clearly outperforms all exact solution procedures. Furthermore, it is shown that our new approach dominates the state-of-the-art heuristics on well known benchmark instances.

Generation schemes for the resource-constrained project scheduling problem with partially renewable resources and generalized precedence constraints

“…In order to better benchmark the results of our generation schemes, they are compared to those of the presented MIP formulation as well as to those of the best-performing branch-andbound procedure of Watermeyer and Zimmermann (2022). All solution methods are coded in C++.…”

“…They present a branch-and-bound procedure which is based on the resource relaxation. As part of their further research they also developed a partition-based branch-and-bound procedure (Watermeyer & Zimmermann, 2022) as well as a constructive branch-and-bound procedure (Watermeyer & Zimmermann, 2023). To the best knowledge of the authors, apart from the schedule-generation scheme of Watermeyer and Zimmermann (2023) there exist no appropriate heuristic solution methods for the RCPSP/max-π so far.…”

New resource-constrained project scheduling instances for testing (meta-)heuristic scheduling algorithms

“…After more than 15 years of CPU time in total, the authors were able to generate a set of 623 hard instances (known as the CV set) which were believed to be unsolvable to optimality with the current state-of-the-art algorithms available at the time of publication. The authors expressed their hope that future researcher should come up with new and better algorithms that could solve these unsolvable instances, Since the publication of this new set in 2020, researchers have already proposed new solution methods and were able to close 174 of the 623 instances, leaving only 449 instances open for future researchers with new algorithms (Watermeyer and Zimmermann, 2021).…”

Efficient Optimal and Suboptimal Joint Access Point Association and Radio Resource Allocation in WLANs

“…The BnB searching approach is a well-known tool for solving NP-hard combinatorial optimization problems. It has been successfully used to solve problems such as the traveling salesman problem [35,36], structured prediction in computer vision [37], feature selection in machine learning [38,39], the resourceconstrained project duration problem with partially renewable resources in operations management [40], etc. Typically, a BnB searching for a combinatorial problem consists of branching and bounding steps [41].…”