An economical backup strategy for floppy disks

A variety of data files are preserved on floppy disks. Document files created using a word processor as well as a personal computer are, for instance, stored on floppy disks. Nevertheless, such flies are occasionally lost due to human errors, the life of the floppy disk and a failure of hardware devices, which are comprised in a word processor or a personal computer. This is called a floppy disk failure. One of the simplest methods for protecting us from such serious losses is to backup files on another floppy disk periodically. Frequent backup operations would spend considerable cost in operations themselves although they could reduce the loss at a floppy disk failure. On the contrary, rare backup operations would make the loss at a floppy disk failure very large although they could considerably save cost in backup operations. These observations reveal the significance of determining an adequate backup timing of files. The present study considers an economical backup strategy for floppy disks, which suggests backing up files when each 1/N of the total memory of a floppy disk is consumed. The long-run average cost of the proposed backup strategy is formulated as an objective function. It is shown that there always exists an economical integer N* that minimizes the long-run average cost. Numerical examples are also presented.