A two-stage stochastic optimization model for the retail multiskilled personnel scheduling problem: a k-chaining policy with $k \ge 2$

<abstract> <p>Considering an uncertain demand, this study evaluates the potential benefits of using a multiskilled workforce through a k-chaining policy with $k \ge 2$. For the service sector and, particularly for the retail industry, we initially propose a deterministic mixed-integer linear programming model that determines how many employees should be multiskilled, in which and how many departments they should be trained, and how their weekly working hours will be assigned. Then, the deterministic model is reformulated using a two-stage stochastic optimization (TSSO) model to explicitly incorporate the uncertain personnel demand. The methodology is tested for a case study using real and simulated data derived from a Chilean retail store. We also compare the TSSO approach solutions with the myopic approaches' solutions (i.e., zero and total multiskilling). The case study is oriented to answer two key questions: how much multiskilling to add and how to add it. Results show that TSSO approach solutions always report maximum reliability for all levels of demand variability considered. It was also observed that, for high levels of demand variability, a k-chaining policy with $k \ge 2$ is more cost-effective than a 2-chaining policy. Finally, to evaluate the conservatism level in the solutions reported by the TSSO approach, two truncation types in the probability density function (pdf) associated with the personnel demand were considered. Results show that, if the pdf is only truncated at zero (more conservative truncation) the levels of required multiskilling are higher than when the pdf is truncated at 5th and 95th percentiles (less conservative truncation).</p> </abstract>