Future Demand Uncertainty In Personnel Scheduling: Investigating Deterministic Lookahead Policies Using Optimization And Simulation

Abstract

One of the main characteristics of personnel scheduling problems is the multitude of rules governing schedule feasibility and quality. This paper deals with an issue in personnel scheduling which is both relevant in practice and often neglected in academic research: When evaluating a schedule for a given planning period, the scheduling history preceding this period has to be taken into account. On the one hand, the history restricts the space of possible schedules, in particular at the beginning of the planning period and with respect to rules a scope transcending the planning period. On the other hand, the schedule for the planning period under consideration affects the solution space of future planning periods. In particular if the demand in future planning periods is subject to uncertainty, an interesting question is how to account for these effects when optimizing the schedule for a given planning period. The resulting planning problem can be considered as a multistage stochastic optimization problem which can be tackled by different modeling and solution approaches. In this paper, we compare different deterministic lookahead policies in which a one-week scheduling period is extended by an artificial lookahead period. In particular, we vary both the length and the way of creating demand forecasts for this lookahead period. The evaluation is carried out using a stochastic simulation in which weekly demands are sampled and the scheduling problems are solved exactly using mixed integer linear programming techniques. Our computational experiments based on data sets from the Second International Nurse Rostering Competition show that the length of the lookahead period is crucial to find good-quality solutions in the considered setting.

The Second International Nurse Rostering Competition

“…), integrated in a hyperheuristic framework which implements Iterated Local Search and Multi Start techniques. -NurseOptimizers [20,21] reformulated the problem as a network flow-based MILP. The flow model associates each nurse with a directed acyclic graph in which arcs correspond to shift and days off assignments; a flow from the source to the sink can be interpreted as a roster.…”

A Dedicated Pricing Algorithm to Solve a Large Family of Nurse Scheduling Problems with Branch-and-Price

“…In the first one, the problem is formulated as a compact integer linear program (ILP) where the variables refer to working assignments and resting days. This has been investigated by Römer [Röm16] to successfully handle the stochastic problem described in INRC-II. Santos et al [San+16b] have also been able to find provable optimal solutions of many INRC-I instances and improve on the optimality gap of others.…”

Modeling and solving staff scheduling with partial weighted maxSAT

“…Although several approaches have been applied on those instances within the competition (e.g. Römer and Mellouli 2016), to the best of our knowledge they will be modeled for the first time using maxSAT.…”