Two-Stage Stochastic Optimization Model for Personnel Days-off Scheduling Using Closed-Chained Multiskilling Structures

This paper addresses a days-off scheduling problem that incorporates multiskilling decisions using a 2-chaining policy. The generated closed-chained multiskilling structures minimize the expected training and over/understaffing costs, while assigning rest days between working days to single-skilled and multiskilled employees. This research provides a suitable methodology for a wide range of industries where the main problem is to meet the demand requirements the seven days of the week, but where the employees cannot work daily. The methodology is structured in two steps. First, we develop a deterministic mixed integer linear programming model. Second, the deterministic model is reformulated as a two-stage stochastic optimization model in order to explicitly incorporate demand uncertainty. Our methodology was applied in a case study associated to a Chilean retail store. We use real data but also simulated data to represent various demand variability scenarios. Results showed that the model was able to do the days-off scheduling decisions cost-effectively for a planning horizon of two weeks. Additionally, it was found that the levels of understaffing and overstaffing can vary between weekdays (Monday to Friday) and weekend. Finally, we also observed that the 2-chaining policy was cost-effective in all scenarios; however, when there are very high levels of demand variability, it can be interesting to explore k-chaining with k ≥ 2 and/or to hire more employees.