Efficient scheduling to minimize calibrations

Integrated Stockpile Evaluation (ISE) is a program to test nuclear weapons periodically. Tests are performed by machines that may require occasional calibration. These calibrations are expensive, so finding a schedule that minimizes calibrations allows more testing to be done for a given amount of money. This paper introduces a theoretical framework for ISE. Machines run jobs with release times and deadlines. Calibrating a machine requires unit cost. The machine remains calibrated for T time steps, after which it must be recalibrated before it can resume running jobs. The objective is to complete all jobs while minimizing the number of calibrations. The paper gives several algorithms to solve the ISE problem for the case where jobs have unit processing times. For one available machine, there is an optimal polynomial-time algorithm. For multiple machines, there is a 2-approximation algorithm, which finds an optimal solution when all jobs have distinct deadlines.