Abstract
Personnel scheduling problems can be decomposed into two stages. In the first stage for each employee the working days have to be fixed. In the second stage for each day of the planning period an intraday scheduling problem has to be solved. It consists of the assignment of shifts to the employees who have to work on the day and for each working period of an employee a task assignment such that the demand of all tasks for personnel is covered. In Robinson et al. (Burke and Trick (Eds.), Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, 18th August–20th August 2004, Pittsburgh, PA, USA, pp. 561–566, 2005), the intraday problem has been formulated as a maximum flow problem. The assumptions are that, employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day. In this work, we extend the network flow model to cover the case where not all employees are qualified to perform all tasks. The model is further extended to be able to calculate shifts of employees for the given day, assuming that an earliest starting time, a latest finishing time, and a minimal working time are given. Labour cost can be also taken into account by solving a minimum cost network flow problem.
Highlights
Personnel scheduling problems represent an important operational management activity in many organizations [8]
In [7], the staff scheduling and rostering process is defined as starting with the determination of staffing requirement, where demand is modeled based on duty requirements
In this work we extend the network flow model presented by Robinson et al [10] by concerning the additional preemption requirement, aiming to further raise the generality of personnel scheduling models
Summary
Personnel scheduling problems represent an important operational management activity in many organizations [8]. Demand modeling could be separated naturally, leaving the scheduling of shifts and task assignment relatively independent. A network flow model for a special non-preemptive personnel scheduling problem is discussed in [11]. Robinson et al [10] formulated the intraday problem as a maximum flow problem under the following assumptions: employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day. Robinson et al [10] describe a tabu search heuristic to schedule the set of shifts for the employees for a given time horizon of several days. Feasibility can be checked and corresponding task assignments can be calculated by solving a maximum flow problem for each day.
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