An efficient pseudo-polynomial algorithm for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem

Abstract

Several algorithms for finding a lower bound on the makespan for the Resource Constrained Project Scheduling Problem (RCPSP) were proposed in the literature. However, fast computable lower bounds usually do not provide the best estimations and the methods that obtain better bounds are mainly based on the cooperation between linear and constraint programming and therefore are time-consuming. In this paper, a new pseudo-polynomial algorithm is proposed to find a makespan lower bound for RCPSP with time-dependent resource capacities. Its idea is based on a consecutive evaluation of pairs of resources and their cumulated workload. Using the proposed algorithm, several bounds for the PSPLIB benchmark were improved. The results for industrial applications are also presented where the algorithm could provide good bounds even for very large problem instances.

A Multi-Objective Scheduling Algorithm for Multi-Mode Resource Constrained Projects in the Presence of Uncertain Resource Availability

“…Kassandra et al (2018) presented a single-objective model for solving the problem of scheduling constrained resource projects with the goal of reducing the completion time of the project and solving their model with the help of FFA algorithm. Arkhipov et al (2019) used a polynomial algorithm to find the limit of the time schedule of constrained resource projects with the goal of reducing project time. Wang et al (2019) proposed a model for routing high-speed trains in China and provided a generic general model for solving the problems of maintenance of fast trains with the aim of reducing the repair time of these trains with a two-day horizons.…”

A new upper bound based on Dantzig-Wolfe decomposition to maximize the stability radius of a simple assembly line under uncertainty

“…On the one hand, finding good upper bounds informs the decision maker on what can be expected in terms of robustness for a particular problem instance. More generally, it is common to search for lower bounds in the case of minimization problems, as in Arkhipov et al (2019). On the other hand, the MILP formulation of SALBP-S requires the availability of an upper bound on the objective function value (see constraint (3) in Section 5).…”

A hyper-heuristic based ensemble genetic programming approach for stochastic resource constrained project scheduling problem

“…It is an NP-hard problem (Blazewicz, Lenstra, & Kan, 1983) with a wide range of industrial application scenarios, such as semiconductor wafer fabrication (Wang, Zhang, & Wang, 2018), software development (Chen & Zhang, 2013), and aircraft assembly (Shan et al, 2017). And most often, the objective of RCPSP is to minimise the project makespan (Arkhipov, Battaïa, & Lazarev, 2019;Hartmann & Briskorn, 2010), i.e., the completion time of the last activity in the project.…”