New competitive results for the stochastic resource-constrained project scheduling problem: exploring the benefits of pre-processing We study the resource-constrained project scheduling problem with stochastic activity durations. We introduce a new class of scheduling policies for solving this problem, which make a number of a-priori sequencing decisions in a pre-processing phase while the rema...

It is shown that the Precedence Constrained K-Processor Scheduling problem is W [2]-hard. This means that there does not exist a constant c, such that for all xed K, the Precedence Constrained K-Processor Scheduling problem can be solved in O(nc) time, unless an unlikely collapse occurs in the parameterized complexity hierarchy introduced by Downey and Fellows (see [5]). That is, if the problem...

It is shown that the Precedence Constrained K-Processor Scheduling problem is W2]-hard. This means that there does not exist a constant c, such that for all xed K, the Precedence Constrained K-Processor Scheduling problem can be solved in O(n c) time, unless an unlikely collapse occurs in the parameter-ized complexity hierarchy introduced by Downey and Fellows (see 5]). That is, if the problem ...

We show a close connection between structural hardness for k-partite graphs and tight inapproximability results for scheduling problems with precedence constraints. Assuming a natural but nontrivial generalisation of the bipartite structural hardness result of [1], we obtain a hardness of 2 − for the problem of minimising the makespan for scheduling precedence-constrained jobs with preemption o...

We consider the resource constrained project scheduling problem (RCPSP) with precedence. All resources are renewable and the objective is to find a schedule that meets all resource and precedence constraints and minimizes the makespan. We propose a heuristic deterministic greedy algorithm solving this problem with the time complexity depending on the number of activities as n log n. The main id...

It is a basic scheduling problem to sequence a set of precedence-constrained tasks to minimize the number of setups, where the tasks are partitioned into classes that require the same setup. We prove a conjecture in (Ph.D. Thesis, School of ISyE, Georgia Institute of Technology, August 1986; Oper. Res. 39 (1991) 1012) that no polynomial-time algorithm for this problem has constant worst-case pe...