Two-level decomposition algorithm for shift scheduling problems

Abstract

We propose a new two-level decomposition algorithm for shift scheduling problems. The problem determines the assignment of duties and rest days to the set of staff members to minimize the given objective function. The constraint on the set of staff members are considered. The objective of this paper is to achieve the minimization of total costs with fairness of working conditions. The proposed method decomposes the original problem into the master and the subproblems. These subproblems are iteratively solved with embedding cuts into the master problem. Computational results show that the performance of the proposed method outperforms a generalpurpose constraint logic programming solver.Shift scheduling problems has received much attention with growing service industry, social systems and infrastructures. The problem is to find an optimal assignment of duties and rest days to weekly schedules for staff members including rest days and working days. The shift scheduling problems appear in airline, railway transportations, traffic systems, nurse scheduling in health care systems [3]. It is highly desired to develop the scheduling system for solving general shift scheduling problems. In practice, to achieve fairness of working conditions for staff members is one of the difficult tasks for shift scheduling problems because there are a number of hard constraints due to several regulations for working conditions of staff members. Due to the variety of the constraints, the computational complexity of shift scheduling problems becomes increasing if the number of duties, staff members and scheduling time horizon is large.Most of the conventional methods are concentrated on the application of heuristics [5] or meta-heuristic methods [9]. However, the performance of these heuristic methods depends on the selection of parameters for their search. Also, the solution is obtained by the heuristic algorithms cannot be optimality evaluation. Recently, column generation or branch and price methods are also widely studied on shift scheduling problems [8].For shift scheduling models, the preference or its satisfaction model has been studied [6], [8]. The model with full-time and part-time workers has been developed [7].In this paper, we propose a novel two-level decomposition algorithm for shift scheduling problems to achieve fair working conditions. A two-level decomposition algorithm for crew rostering problems with fair working condition has been proposed [1]. The proposed method has the characteristic that the problem is decomposed into the master problem and the subproblems. The master problem determines the assignment of duties and the number of staff members. The main difference between this paper and reference [1] is to consider the constraint on the required number of staff members for a duty. The subproblem cannot be decomposed into several subproblems for each staff and solved difficultly by that constraint. The subproblem is a feasibility problem to check the existence of a feasible shift schedule when the solution of the ...

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