Updating an optimal structured scheme

Abstract

An optimal structured schedule at time t is considered for a set of jobs Z with given start and due date [d _i ,D _i ] volumes V_i (volume is defined as the number of homogeneous independent elementary operations of unit length that comprise the job), and penalty functions. The penalty for selecting an element of jobi∈Z at timet is ϕ _i (t). The schedule penalty is the total penalty of all the elements of all the jobs. An optimal schedule is a minimum-penalty schedule. We investigate the impact of changing the volume of a job from the setZ on the structure of the optimal schedule. Algorithms are proposed for handling the modified job set with both reduced and enlarged job volumes. These algorithms require ckℓ computer operations, where k is the number of jobs in the original set, ℓ is the change in job volume (expressed by the number of units), andC is a constant.