Grammar-Based Column Generation for Personalized Multi-Activity Shift Scheduling

Abstract

W e present a branch-and-price algorithm to solve personalized multi-activity shift scheduling problems.The subproblems in the column generation method are formulated using grammars and solved with dynamic programming. The expressiveness of context-free grammars is exploited to easily model restrictions over shifts, allowing the branch-and-price algorithm to solve large-scale problem instances. We present computational experiments on two types of multi-activity shift scheduling problems and compare our approach with existing methods in the literature. These experiments show that our approach can efficiently solve large-scale instances and is flexible enough to model different classes of problems.

Home healthcare integrated staffing and scheduling

“…Context-free grammars have been successfully used in the context of personnel scheduling. Applications include the solution of multi-activity and multi-task shift scheduling problems (Côté et al, 2013;Boyer et al, 2012) and multi-activity tour scheduling problems (Restrepo et al, 2017(Restrepo et al, , 2016.…”

“…To do so, we present a two-stage stochastic programming model where first-stage decisions correspond to the sta ng and scheduling of caregivers at each geographic district, and second-stage decisions are related to the temporary reallocation of caregivers to neighboring districts, to contact caregivers to work on a day-o↵, and to allow under-covering and over-covering of demand. Second, although other authors have already benefit from the expressiveness of context-free grammars to build short-term schedules with a planning horizon of one day (see Restrepo et al (2017); Côté et al (2013)), we believe that our work is the first that uses context-free grammars to build schedules over long time horizons (i.e., one month or more) guaranteeing horizontal work regulations such as the minimum rest time between consecutive shifts and the allocation of a minimum and a maximum number of shifts to each work sequence. Context-free grammars allow to easily incorporate horizontal regulations as a set of recursive rewriting rules (or productions) to generate patterns of strings (Hopcroft et al, 2001), in our case, to generate caregiver schedules.…”

Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation

“…The pricing subproblem for an employee consists in finding a feasible shift with the minimum cost. In [7], it is shown that the set of feasible shifts can be described by context-free grammars. This description allows one to solve a pricing subproblem by dynamic programming which runs linearly in the number of hyper-arcs of the graph modeling transitions, which is what we implemented.…”

ASP, The Art and Science of Practice: Academia-Industry Interfacing in Operations Research in Montréal

“…Together, they enhanced the prototype and launched Omega Optimization. Omega Optimization's core product, originally called OpTime, is thus closely associated with the research of its founders (Rousseau et al 2002, Côté et al 2103. ExPretio is a privately owned company headquartered in Montreal and specializing in revenue-optimization and pricing solutions in the airline and railway industries.…”

“…Together, they enhanced the prototype and launched Omega Optimization. Omega Optimization's core product, originally called OpTime, is thus closely associated with the research of its founders (Rousseau et al 2002, Côté et al 2103. …”