Complete MCS-Based Search: Application to Resource Constrained Project Scheduling (original) (raw)
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More Efficient Algorithms for Constrained Project Scheduling Problems
In an earlier paper, we have described a framework to compute a destructive lower bound for a number of resource constrained project scheduling (RCPS) problems, which is based on column generation. If a certain threshold cannot be rejected, then we attempt finding a feasible solution with this value by solving an ILP. In this paper, we present two methods to speed up the computation. The first one is that we shrink the timewindows for the jobs by deriving additional release dates and deadlines from the solution that we obtained when determining the lower bound. The second method is to enforce the exact precedence delays by adding additional equalities. Our computational experiments show that each method can reduce the computation time by a factor of at most 10.
Solving resource-constrained project scheduling problems using tabu search
1998
The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.
New Benchmark Results for the Resource-Constrained Project Scheduling Problem
Management Science, 1997
This paper reports on computational results obtained with an updated version of the branch-andbound procedure previously developed by for solving the resource-constrained project scheduling problem (RCPSP). The new code fully exploits the advantages of 32-bit programming provided by recent compilers running on platforms such as Windows NT® and OS/2®: flat memory, increased addressable memory and fast program execution. We study the impact of three important variables on the computation time for the RCPSP: addressable computer memory, the search strategy (depth-first, best-first or hybrid) and the introduction of an improved lower bound. We compare the results obtained by a truncated branch-and-bound procedure with the results generated by the minimum slack time heuristic and report on the dependency of its solution quality on the allotted CPU time.
The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.
Time-constrained project scheduling
Journal of Scheduling, 2008
We propose a new approach for scheduling with strict deadlines and apply this approach to the Time-Constrained Project Scheduling Problem (TCPSP). To be able to meet these deadlines, it is possible to work in overtime or hire additional capacity in regular time or overtime. For this problem, we develop a two stage heuristic. The key of the approach lies in the first stage in which we construct partial schedules. In these partial schedules, jobs may be scheduled for a shorter duration than required. The second stage uses an ILP formulation of the problem to turn a partial schedule into a feasible schedule, and to perform a neighborhood search. The developed heuristic is quite flexible and, therefore, suitable for practice. We present experimental results on modified RCPSP benchmark instances. The two stage heuristic solves many instances to optimality, and if we substantially decrease the deadline, the rise in cost is only small.
Strong Bounds for Resource Constrained Project Scheduling: Preprocessing and Cutting Planes
Comput. Oper. Res., 2020
Resource Constrained Project Scheduling Problems (RCPSPs) without preemption are well-known N P -hard combinatorial optimization problems. A feasible RCPSP solution consists of a time-ordered schedule of jobs with corresponding execution modes, respecting precedence and resources constraints. In this paper, we propose a cutting plane algorithm to separate five different cut families, as well as a new preprocessing routine to strengthen resource-related constraints. New lifted versions of the well-known precedence and cover inequalities are employed. At each iteration, a dense conflict graph is built considering feasibility and optimality conditions to separate cliques, odd-holes and strengthened Chvatal-Gomory cuts. The proposed strategies considerably improve the linear relaxation bounds, allowing a state-of-the-art mixed-integer linear programming solver to find provably optimal solutions for 754 previously open instances of different variants of the RCPSPs, which was not possible...
This paper addresses the Resource Constrained Project Scheduling Problem (RCPSP). For its solution, a hybrid methodology, which uses a Branch and Bound basic algorithm with dominance rules, is developed and implemented, and is combined with four deterministic heuristics whose objective is to prune the search tree branches, taking into account the iterations available and, at the same time, to minimize the probability of discarding branches that contain optimal solutions. Essentially, these strategies allow the allocation of most iterations to the most promissory regions in an organized manner using only subsets with similar or the same characteristics as those of the optimal solutions at each level of the tree, thus assuring a broad search within the feasible region and, simultaneously, a good exploitation by the selective use of the subsets by level. Finally, the developed algorithm performance is analyzed by solving some of the problems of the PSPLIB test library.
An Efficient Relax-and-Solve Algorithm for the Resource-Constrained Project Scheduling Problem
Proceedings of the 11th International Conference on Operations Research and Enterprise Systems
The resource-constrained project scheduling problem (RCPSP) has a broad range of practical applications, e.g., in manufacturing, mining, and supply chain, among others(Kreter et al., 2015). Over the last 50 years, many researchers have tried to solve this challenging NP-hard problem. This paper presents an efficient and easy-to-implement relax-and-solve matheuristic to solve RCPSP. The proposed method employs constraint programming in a heuristic framework and uses CPLEX as an optimization solver. This algorithm is tested on more than 1500 instances from the standard library PSPLIB. Our experimental results show that the proposed heuristic framework outperforms the CPLEX and provides competitive results compared with the state-of-theart techniques.