Cyclical schedules for the Joint Replenishment Problem with dynamic demands

The Joint Replenishment Problem (JRP) involves production planning for a family of items. The items have a coordinated cost structure whereby a major setup cost is incurred whenever any item in the family is produced, and an item-specific minor setup cost is incurred whenever that item is produced. This paper investigates the performance of two types of cyclical production schedules for the JRP with dynamic demands over a finite planning horizon. The cyclical schedules considered are: (1) general cyclical schedules – schedules where the number of periods between successive production runs for any item is constant over the planning horizon – and (2) power-of-two schedules – a subset of cyclical schedules for which the number of periods between successive setups must be a power of 2. The paper evaluates the additional cost incurred by requiring schedules to be cyclical, and identifies problem characteristics that have a significant effect on this additional cost.