Optimal Algorithms for Scheduling under Time-of-Use Tariffs

by   Lin Chen, et al.

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time-slots to be used for scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for.


page 1

page 2

page 3

page 4


A Polynomial Time Constant Approximation For Minimizing Total Weighted Flow-time

We consider the classic scheduling problem of minimizing the total weigh...

Optimally rescheduling jobs with a LIFO buffer

This paper considers single-machine scheduling problems in which a given...

An Approximate Pareto Set for Minimizing the Maximum Lateness and Makespan on Parallel Machines

We consider the two-parallel machines scheduling problem, with the aim o...

Scheduling a single machine with compressible jobs to minimize maximum lateness

The problem of scheduling non-simultaneously released jobs with due date...

A novel Hopfield neural network approach for minimizing total weighted tardiness of jobs scheduled on identical machines

This paper explores fast, polynomial time heuristic approximate solution...

Multitasking Scheduling with Shared Processing

Recently, the problem of multitasking scheduling has attracted a lot of ...

Shared Processor Scheduling of Multiprocessor Jobs

We study shared processor scheduling of multiprocessor weighted jobs whe...

Please sign up or login with your details

Forgot password? Click here to reset