A branch-and-bound procedure for the resource-constrained project scheduling problem with partially renewable resources and general temporal constraints

Abstract

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.

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

“…These procedures can be categorized in a relaxation-based and a constructive approach. The relaxation-based branch-and-bound algorithm in Watermeyer and Zimmermann (2020a) reduces the possible resource usages of the activities of the project in each decomposition step. This procedure is continued until the optimal solution of the restricted resource-relaxation of problem (P) is either feasible or does not exist.…”

“…In this paper, we present a new relaxation-based enumeration scheme for the RCPSP/max-. This approach mainly differs from classical procedures in project scheduling, which enumerate based on relaxations (see, e.g., Watermeyer and Zimmermann 2020a;De Reyck and Herroelen 1998;Fest et al 1999), in the sense that the optimal solution of the relaxation is not removed by the decomposition step. The main advantages of the new approach compared to the existing enumeration schemes for partially renewable resources, which are described in detail below, are as follows.…”

“…Recently, Watermeyer and Zimmermann (2020a) introduced an extension of the RCPSP/ that additionally considers minimum and maximum time lags between the start times of the activities in order to cover even more aspects of real-life projects. For this problem, which is denoted by RCPSP/max-, Zimmermann (2020a, 2020b) have proposed two branch-and-bound algorithms that are based on different enumeration schemes.…”

“…For this problem, which is denoted by RCPSP/max-, Zimmermann (2020a, 2020b) have proposed two branch-and-bound algorithms that are based on different enumeration schemes. The exact solution procedure in Watermeyer and Zimmermann (2020a) can be classified as a relaxation-based branch-and-bound algorithm that reduces the possible resource consumptions by the activities of the project step by step, where the resource-relaxation of the RCPSP/max-represents the starting point. An alternative approach is considered in Watermeyer and Zimmermann (2020b), which schedules the activities of the project successively in combination with an unscheduling step.…”

A Type-2 Fuzzy Optimization Model for Project Portfolio Selection and Scheduling Incorporating Project Interdependency and Splitting

“…The only type of interdependency modeled was mutual exclusiveness. Watermeyer and Zimmermann (2020) considered partially renewable resources and general temporal constraints for the RSPSP problem. They developed a branch-and-bound method to solve the model with the aim of project duration minimization.…”