Conditions for the existence of continuous schedules of duration five

Each device must perform one operation with each of two demands assigned to it. The assignments are such that the maximum number of operations for one demand equals five, the partial precedence limitations are missing, simultaneous servicing of two or more demands by the same device or of one demand by two or more devices is forbidden, and the duration of each operation equals a unit. The necessary and sufficient conditions are obtained for the existence of a schedule of duration five conforming to the specified assignments and such that each device performs its operations during two consecutive intervals of unit duration. Hence follows the polynomial solvability of the problem under discussion.