On the periodic service scheduling problem with non-uniform demands

This paper introduces the Periodic Service Scheduling Problem with Non-uniform Demands, in which the best service policy for a set of customers with periodically recurring demand through a given finite planning horizon has to be determined. Service to customers is provided at every time period by a set of potential service providers, each of them with an activation cost and a capacity. The decisions to be made include the servers to be activated at each time period together with a service schedule and server allocation for every customer that respect the periodicity of customer demand and the capacity of the activated servers, which minimize the total cost of the activated servers. We give a first Integer Linear Programming formulation with one set of decision variables associated with each of the decisions of the problem. Afterwards, we develop a logic-based Benders reformulation where one set of variables is projected out and constraints that guarantee the feasibility of the solutions are introduced. The separation problem for the new set of constraints is studied, and an exact Branch & Logic-Benders-Cut algorithm for the reformulation is proposed together with several variations and enhancements. The particular cases in which all servers are identical and in which all parameters are time-invariant are also studied. Extensive computational experiments assess the superiority of the logic-based Benders reformulation over the first formulation.