The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 2. The Doctor Rostering Problem 5 Doctor 1 2 3 4 5 6 Week 1 Tuesday NDO Wednesday Thursday Friday Monday Week 2 NDO Wednesday Thursday Friday Monday Tuesday Week 3 Wednesday Thursday Friday Monday Tuesday NDO Week 4 Thursdag Friday Monday Tirsdag NDO Wednesday Week 5 Friday Monday Tirsdag NDO Wednesday Thursdag Week 6 Monday Tirsdag NDO Wednesday Thursdag Friday Table 2.1: Rolling days off, NDO: no day off 2.2 Rolling Days Off A specific requirement of this project is rolling days off (RDO). These define which weeks a doctor gets a day off and which weeks contains no day off (NDO) for each doctor. Table 2.1 illustrates the concept of rolling days off. A key point of RDO is the fact that all doctors receive weekends where they have both the predating Friday and the postdating Monday off. The RDO as a constraint is omitted from the mathematical model of this problem and is instead implemented as a program mechanism. 2.3 Literature review Previous work on the nurse scheduling problem (NSP) has been covered by many approaches, taking different angles and perspectives throughout the problem environment. In this section, I briefly review articles that has served as inspiration to this project. Nonobe and Ibaraki [18] applies a general weighted constraint satisfaction problem (WCSP) solver, using a Tabu Search (TS), to a range of problems, incl. the NSP. Also applying a weight control mechanism to each iteration of TS works well for them. They choose to handle hard and soft constraints on the same level of processing. Dias et al. [7] deals with a relatively large problem. They apply both a Genetic Algorithm (GA) heuristic and a TS for solving a problem with over 1500 nurses, 30 supervisory nurses and 30 wards and finds that the two heuristics performs equally well, with one more time efficient and slightly worse results than the other and vice versa. In Bard and Purnomo [2] the authors discuss the issue of sudden shortages appearing due to the fluctuation in patients needing health care. The problems handled are relatively large, scheduling more than 120 nurses.
Chapter 2. The Doctor Rostering Problem 6 Resende and Ribeiro [20] and Resende and Feo [19] considers the Greedy Random- ized Adaptive Search Procedure (GRASP). The GRASP described by the authors is the main source of inspiration for the metaheuristic chosen in this project. They also implement various improvements to their GRASP, incl. reactive GRASP, automated RCL adjustments, variable neighborhoods, path-relinking, optimising memory-usage as well as allowing for efficient cooperative parallel strategies. They show that the use of GRASP along with these improvements can significantly improve the time required to find a near-optimal solution compared to basic GRASP. Where Resende and Ribeiro [20] investigates the use of GRASP on the set covering problem, Resende and Feo [19] covers the effect of various hybridisations to GRASP. Burke et al. [5] reviews the state of Nurse Scheduling Problem research. In their review, they describe how different authors have approached the NSP, including bibliographic reviews and research papers on various algorithms for solving the NSP. Silvestro and Silvestro [22] argues that self-scheduling . . . can easily lead to over- or understaffing, that the schedule is made for the convenience of staff, and that there are no formal procedures for conflict solving. Opposite to this, Hung [14] argues that self-scheduling leads to greater staff-satisfaction and improves co-operation. Both are different approaches to viewing the subject. Sil- vestro and Silvestro [22] concludes that the benefits of self-scheduling relies on the size and complexity of the problem. It can work well in smaller wards where the constraints remain relatively simple. Burke et al. [5] also notes how finding the optimal solution is largely meaningless, when most hospital administrators want to get high quality results in a short amount of time. The administrators prefer quick generation of schedules that satisfy all hard constraints and as many soft constrains as possible. Another observation made by Burke et al. [5] is that optimal solutions in the literature tend to simplify the problem, making them inapplicable for real world problems. In their section covering TS, they note how Dowsland [8] allows search to go back and forth from the feasible region, which is an important feature as todays problems in large health care institutions tend to be nearly impossible to solve, while maintaining fea- sibility. Contrary to this, Burke et al. [3] develops a model in which search remains in the feasible part of the solution space. They describe PLANE, a commercial nurse rostering system which employs a hybrid TS, embodying a TS coupled with either a diversification mechanism or a shuffling technique to model human scheduling behavior. Comparing their hybrid algorithm to a basic Steepest Descent (SD) search- or TS algorithm, they find that their hybrid search algorithm performs overall better than the
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Bibliography 118 [10] Michael R. Ga
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