In this paper, we consider the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints. For the first time, the concept of partially renewable resources is embedded in the context of projects with general temporal constraints. While partially renewable resources have already broadened the area of applications for project scheduling, the extension by general temporal constraints allows to consider even more relevant aspects of real projects. We present a branch-and-bound procedure for the problem with the objective to minimize the project duration. To improve the performance of the solution procedure, new consistency tests, lower bounds, and dominance rules are developed. Furthermore, new temporal planning procedures, based on forbidden start times of activities, are presented which can be used for any project scheduling problem with general temporal constraints independent on the considered resource type. In a performance analysis, we compare our branch-and-bound procedure with the mixed-integer linear programming solver IBM CPLEX 12.8.0 on adaptations of benchmark instances from the literature. In addition, we compare our solution procedure with the only available branch-andbound procedure for partially renewable resources. The results of the computational experiments prove the efficiency of our branch-and-bound procedure.

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.

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