Multi-period technician scheduling with experience-based service times and stochastic customers

Introduce a new multi-period technician scheduling problem.Present a Markov decision process model for the problem.Approximate the value of todays assignments on the ability to serve future demand.Demonstrate approximate Bellman equation can be solved as a mixed integer program.Show proposed approach leads to higher quality solutions than myopic approach. This paper introduces the multi-period technician scheduling problem with experience-based service times and stochastic customers. In the problem, a manager must assign tasks of different types that are revealed at the start of each day to technicians who must complete the tasks that same day. As a technician gains experience with a type of task, the time that it takes to serve future tasks of that type is reduced (often referred to as experiential learning). As such, while the problem could be modeled as a single-period problem (i.e. focusing solely on the current days tasks), we instead choose to model it as a multi-period problem and thus capture that daily decisions should recognize the long-term effects of learning. Specifically, we model the problem as a Markov decision process and introduce an approximate dynamic programming-based solution approach. The model can be adapted to handle cases of worker attrition and new task types. The solution approach relies on an approximation of the cost-to-go that uses forecasts of the next days assignments for each technician and the resulting estimated time it will take to service those assignments given current period decisions. Using an extensive computational study, we demonstrate the value of our approach versus a myopic solution approach that views the problem as a single-period problem.