We consider the problem of servicing a number of objects in a discrete time environment. In each period, we may select an object that will receive a service in the period. Each time an object is serviced, we incur a servicing cost dependent on the time since the object's last service. Problems of this type appear in many contexts, e.g., multiproduct lot-sizing, machine maintenance, and several problems in telecommunications. We assume that at most one object can be serviced in a given period. For the general problem with m objects, which is known to be NP-Hard, we describe properties of an optimal policy; and for the speciÿc case of m = 2 objects, we determine an optimal policy.
In other variants of the periodic scheduling problem (see, e.g., REF ), the processing of each job incurs a service cost, depending on the time that elapsed since the last service of this job, and the goal is to minimize the cost of the schedule; however, the cost increases with job delays − implying that an optimal solution requires some fairness.
Periodic Scheduling with Service Constraints
Operations Research
Computer Science Mathematics