760 research outputs found
Optimal Algorithms for Scheduling under Time-of-Use Tariffs
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.Comment: 17 pages; A preliminary version of this paper with a subset of
results appeared in the Proceedings of MFCS 201
Single-machine scheduling with stepwise tardiness costs and release times
We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems
Single machine scheduling with job-dependent machine deterioration
We consider the single machine scheduling problem with job-dependent machine
deterioration. In the problem, we are given a single machine with an initial
non-negative maintenance level, and a set of jobs each with a non-preemptive
processing time and a machine deterioration. Such a machine deterioration
quantifies the decrement in the machine maintenance level after processing the
job. To avoid machine breakdown, one should guarantee a non-negative
maintenance level at any time point; and whenever necessary, a maintenance
activity must be allocated for restoring the machine maintenance level. The
goal of the problem is to schedule the jobs and the maintenance activities such
that the total completion time of jobs is minimized. There are two variants of
maintenance activities: in the partial maintenance case each activity can be
allocated to increase the machine maintenance level to any level not exceeding
the maximum; in the full maintenance case every activity must be allocated to
increase the machine maintenance level to the maximum. In a recent work, the
problem in the full maintenance case has been proven NP-hard; several special
cases of the problem in the partial maintenance case were shown solvable in
polynomial time, but the complexity of the general problem is left open. In
this paper we first prove that the problem in the partial maintenance case is
NP-hard, thus settling the open problem; we then design a -approximation
algorithm.Comment: 15 page
A linear programming-based method for job shop scheduling
We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation
completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach
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