Scheduling with variable time slot costs

Abstract

Abstract:In this article, we study a class of new scheduling models where time slot costs have to be taken into consideration. In such models, processing a job will incur certain cost which is determined by the time slots occupied by the job in a schedule. The models apply when operational costs vary over time. The objective of the scheduling models is to minimize the total time slot costs plus a traditional scheduling performance measure. We consider the following performance measures: total completion time, maximum lateness/tardiness, total weighted number of tardy jobs, and total tardiness. We prove the intractability of the models under general parameters and provide polynomial-time algorithms for special cases with non-increasing time slot costs.

Acquisition planning and scheduling of computing resources

“…Lee et al [18] studied the same problem with the hierarchical bicriteria structure and developed approximation algorithms with worst -case performance analyses. A different job processing cost, which is determined by the time slots used by the job, is considered by Wan and Qi [27] for single-machine scheduling. The nonclassical objective function considered in this paper is different from the above ones with respect to the following three characteristics: (i) The package acquisition cost function is a piecewise linear function; (ii) The incurred cost is associated with packages rather than jobs; (iii) The acquisition cost for each package is a function of the schedule makespan in the package.…”

Optimal Algorithms and a PTAS for Cost-Aware Scheduling

“…Such a framework has been proposed recently in [11] and [7]. It models additional cost for operating servers or machines that vary over time such as, e.g., labor cost that may vary by the day of the week, or the hour of the day [11], or electricity cost fluctuating over day time [7].…”

“…Such a framework has been proposed recently in [11] and [7]. It models additional cost for operating servers or machines that vary over time such as, e.g., labor cost that may vary by the day of the week, or the hour of the day [11], or electricity cost fluctuating over day time [7]. On the one hand, the latter have economically a huge impact on facilities with enormous power consumption such as large data centers, and on the other hand, these fluctuations reflect the imbalance between generation and consumption of electricity on a daily or weekly basis.…”

“…Scheduling with time-varying reservation cost (aka variable time slot cost) has been studied explicitly in [11] and [7]. The seminal paper [11] is concerned with several non-preemptive single machine problems, which are polynomial-time solvable in the classical setting, such as minimizing the total completion time, lateness, and total tardiness, or maximizing the weighted number of on-time jobs. These problems are shown to be strongly NP-hard when taking reservation cost into account, while efficient algorithms exist for restricted reservation cost functions.…”

“…These problems are shown to be strongly NP-hard when taking reservation cost into account, while efficient algorithms exist for restricted reservation cost functions. In particular, the problem 1 | | C j + E is strongly NP-hard, and it is efficiently solvable when the reservation cost is increasing or convex non-increasing [11]. The research focus in [7] is on online flow-time mini-mization using resource augmentation.…”