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Resource-constrained project scheduling (RCPSP)

A heuristic procedure for solving the "Resource-Constrained Project Scheduling Problem " (RCPSP with a renewable resource and a single mode) is used. A formal description of the procedure is described by Kolisch/Drexl (1996), p. 38. The objective of the model is the minimization of the makespan. Opposite to the infinite loading problem, offset times between tasks are not considered.

The procedure is based on a dynamic partitioning of the set of tasks into the subsets "Completed" (Cn), "Active" (An), "Assignable" (Dn). Beginning with a planning period t=0, all assignable tasks are scheduled on the resources as early as possible. After scheduling all assignable tasks with respect to the actual planning period t is increased and so forth. The set of assignable tasks can be sorted according to the following priority rules:

  • Shortest processing time
  • Number of immediate successors
  • Total slack time
  • Capacity requirement
  • Rank positional weight
  • Total number of successors

The project is defined with the help of the graph editor:

The procedure is run with a single click. The complete protocol of all calculations is shown in the lower right list. Click on this list with the left mouse button to copy the protocol into the clipboard.

You may wish to display a gantt chart which may be printed:

You can also display a resource utilisation graph which may be printed:

The following symbols are also used in the infinite scheduling module:

i index of tasks
D(i) duration of task i
FAZ(i) earliest start time of task i
FEZ(i) earliest finish time of task i
SAZ(i) lastest start time of task i
SEZ(i) latest finish time of task i
GP(i) slack time of task i

Additional symbols with respect to the resources:

r index of resources
r(i) number of resource used by task i
k(i,r) resource requirement of resource r by task i
Kap(r) (renewable capacity of resource k
t current planning time
An set of tasks in process at time t
Cn set of tasks completed at time t
Dn set of tasks available for starting at time t


  • deterministisc processing times
  • renewable resources


- Kolisch, R. and A. Drexl, Adaptive Search for Solving Hard Project Scheduling Problems, in: Naval Research Logistics 43(1996), pp. 23-40

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