The minimum shift design problem

Luca Di Gaspero, Johannes Gärtner, Guy Kortsarz, Nysret Musliu, Andrea Schaerf, Wolfgang Slany

Research output: Contribution to journalArticlepeer-review


The min-Shift Design problem (MSD) is an important scheduling problem that needs to be solved in many industrial contexts. The issue is to find a minimum number of shifts and the number of employees to be assigned to these shifts in order to minimize the deviation from workforce requirements. Our research considers both theoretical and practical aspects of the min-Shift Design problem. This problem is closely related to the minimum edge-cost flow problem (MECF), a network flow variant that has many applications beyond shift scheduling. We show that MSD reduces to a special case of MECF and, exploiting this reduction, we prove a logarithmic hardness of approximation lower bound for MSD. On the basis of these results, we propose a hybrid heuristic for the problem, which relies on a greedy heuristic followed by a local search algorithm. The greedy part is based on the network flow analogy, and the local search algorithm makes use of multiple neighborhood relations. An experimental analysis on structured random instances shows that the hybrid heuristic clearly outperforms our previous commercial implementation. Furthermore, it highlights the respective merits of the composing heuristics for different performance parameters.

Original languageEnglish
Pages (from-to)79-105
Number of pages27
JournalAnnals of Operations Research
Issue number1
StatePublished - 2007
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgements This work was supported by Austrian Science Fund Project No. Z29-N04 and by the Italian Ministry of Education, University and Research (MIUR) under the project PRIN 2003 “Design and implementation of a solver based on local search for the execution of declarative specifications for combinatorial problems”.


  • Greedy heuristics
  • Hybrid algorithms
  • Local search
  • Workforce scheduling


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