The minimum shift design problem

Abstract

The min-SHIFT DESIGN problem (ÅË ) 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 (Å ), a network flow variant that has many applications beyond shift scheduling. We show that ÅË reduces to a special case of Å and, exploiting this reduction, we prove a logarithmic hardness of approximation lower bound for ÅË . On the basis of these results, we propose a hybrid heuristic for the problem which relies on a greedy heuristic with a min-cost max-flow subroutine based on the network flow analogy followed by a local search algorithm that makes use of multiple neighborhood relations. An experimental analysis on structured random instances shows that the hybrid heuristic clearly outperforms our previous commercial implementation and highlights the respective merits of the composing heuristics for different performance parameters.

Nurse rostering: models and algorithms for theory, practice and integration with other problems

“…hourly intervals, on each day. Both task-based modelling and flexible modelling require shift design as a preprocessing step which derives the appropriate input for rostering [42].…”

A Benders decomposition-based matheuristic for the Cardinality Constrained Shift Design Problem

“…The paper argues for the use of heuristics and describes a local search approach that minimizes the number of shifts active, while minimizing under and overcover as well as the average number of duties per week. Furthermore, in Di Gaspero et al (2007) the objective function is almost identical to Musliu et al (2004), i.e. it includes an aspect minimizing the number of shifts.…”

Automated Shift Design and Break Scheduling

“…Additionally, their method orders moves and applies these first to regions with larger conflicts (larger over/under-staffing). The proposed solution methods have been used since several years in the commercial software package OPA of XIMES Inc. Di Gaspero et al [14,10] proposed the application of hybrid approaches based on local search and min-cost max-flow techniques. The hybrid algorithm improved results reported in [19] on benchmark examples.…”

“…A hybrid local search approach for shift design has been presented in [10]. This solver comprises two stages, namely a greedy construction for the initial solution followed by a tabu search procedure [16] that iteratively improves it.…”

“…Shift design and break assignment problems are known also under other names, for example as shift design [19,10], shift scheduling [3,2,25,28], and break scheduling [4,5,20,31]. Such problems arise at airports, call centers, and in the service industry in general, and have been extensively investigated in Operations Research and Artificial Intelligence.…”