MSPSP Instance Library

Library of instances of the Multi-Skill Project Scheduling Problem (MSPSP).

The MSPSP is a relatively new variant on the classical Resource Constrained Project Scheduling Problem (RCPSP) with the additional consideration of multi-skilled resources. This consideration introduces a set of assignment decisions, further to the usual scheduling decisions, which result in a non-trivial layer of complexity.

This library provides all instances used in the computational experiments of a 2017 research paper as well as the author's full-results. Some additional untested instances (set 3) are also included in this library.

Data Format

Each instance is provided as an individual DataZinc file (dzn) which are naturally compatible with the modelling language MiniZinc. New instances can be created in any desired format by editing the instance generator as you see fit (refer to Python scripts in the gen-inst/ directory).

For a detailed description of the format within any one DataZinc file we refer you to format-description.pdf.

Instances

All instances can be found in the instances/ directory. The instances are divided into three primary sets, which are further divided into a total of eight subsets. Only set 1 and set 2 have been tested.

Set 1'

This data set was generated using the instance generator. A partial specification of the two subsets generated is given in the directory instances/set-1/. We refer you to Almeida et al. 2015 for a detailed specification where an equivalent set of data was originally created.

• Set 1'a: (100% solved) 216 instances with 22 activities, 4 skills and 10-30 resources.
• Set 1'b: (12.5% solved) 216 instances with 42 activities, 4 skills and 20-60 resources.

Set 2

This data set is a selection of the available benchmark instances used by the literature. For the full specification of the three subsets, including their origin, we refer you to Montoya et al. 2014. Set 2 can be considered as a selection of small and medium sized instances of the MSPSP.

• Set 2a: (73.64% solved) 110 instances with 20-51 activities, 2-8 skills and 5-14 resources.
• Set 2b: (81.82% solved) 77 instances with 32-62 activities, 9-15 skills and 5-19 resources.
• Set 2c: (100% solved) 91 instances with 22-32 activities, 3-12 skills and 4-15 resources.

Set 3

This set contains the remaining benchmark instances that were made available to us from the literature.

These instances are organised in the same way as set 2 as they have been adapted from the same instances of the RCPSP. However, their parameter values fall outside the ranges considered by Montoya et al. in set 2. As such, each subset of set 3 contains instances with a very small or very large number of activities/skills/resources. Even though these instances have as yet been untested, we anticipate that the very small instances can be trivially solved.

• Set 3a: (untested) 73 instances with 7-51 activities, 2-8 skills and 1-22 resource(s).
• Set 3b: (untested) 112 instances with 32-122 activities, 9-15 skills and 5-34 resources.
• Set 3c: (untested) 109 instances with 22-92 activities, 3-15 skills and 4-15 resources.

Instance Generator

The instance generator provided here was developed by Young et al. 2017 and was originally created by Almeida et al. 2015. It can be found in gen-inst/.

The full details of the implementation of the instance generator can be found in Almeida et al. 2015.

Solutions

The full results found by Young et al. 2017 can be found in the results/ directory. These results were obtained using the MiniZinc model which can be found in the models/ directory. A discussion of the model given here and the various formulations which were considered, can be found in Young et al. 2017.

Together with the model used to achieve the final results provided, a series of other scripts have been included in the models/support-scripts/ directory. These include shell scripts used to run the model across subsets of the data, a Python script to process the output data and other assorted shell scripts.

References

1. Kenneth D. Young, Thibaut Feydy, Andreas Schutt. Constraint Programming applied to the Multi-Skill Project Scheduling Problem. In Proceedings of Principles and Practice of Constraint Programming - CP2017, 2017.
2. Almeida, B. F., Correia, I., Saldanha-da Gama, F. An instance generator for the multi-skill resource-constrained project scheduling problem, 2015.
3. Montoya, C., Bellenguez-Morineau, O., Pinson, E., Rivreau, D. Branch-and-price approach for the multi-skill project scheduling problem. Optimization Letters 8(5), 1721–1734, 2014.