We are concerned with the precedence-constrained knapsack problem (PCKP), which is a knapsack problem defined on a directed acyclic graph (DAG). It is often the case that the original problem includes redundant constraints, and by eliminating these we obtain a PCKP of (much) smaller size. We show that such a reduction can be explained in terms of the ‘transitive reduction’ of the DAG associated...

ÐGiven a set of precedence constrained parallel tasks with their processor requirements and execution times, the problem of scheduling precedence constrained parallel tasks on multicomputers with contiguous processor allocation is to find a nonpreemptive schedule of the tasks on a multicomputer such that the schedule length is minimized. This scheduling problem is substantially more difficult t...

The use of neighborhood search techniques to address a practical issue faced by agricultural investors is examined in this study. problem named as land investment with precedence constraints and it has an essential impact on agriculture issues. tackled can be viewed variant the well-known classical 0-1 knapsack where are imposed pairs items. Precedence take into account relation between This pa...

x{ Scope and Purpose. | We consider a scheduling problem in a two-processor system where (i) every job can be processed on only one machine and where (ii) there are chain-type precedence relations among the jobs. The goal is to minimize the makespan. This continues the work of Chang and Lee 1], Jansen 4] and of Kellerer and Woeginger 5]. Abstract. | We consider a special case of the precedence ...

In this paper we study an extension of the classical Resource-Constrained Project Scheduling Problem (RCPSP) with minimum makespan objective by introducing a further type of precedence constraints denoted as “Feeding Precedences” (FP). This kind of problem happens in that production planning environment, like make-to-order manufacturing, when the effort associated with the execution of an activ...

In this paper the multiple projects resourceconstrained project scheduling problem is considered. Several projects are to be scheduled simultaneously with sharing several kinds of limited resources in this problem. Each project contains non-preemptive and deterministic duration activities which compete limited resources under resources and precedence constraints. Moreover, there are the due dat...