Two-machine flow-shop scheduling with equal processing time on the second machine for minimizing total weighted completion time

We consider the classical two-machine flow-shop scheduling for minimizing the total weighted completion time. For this problem, the computational complexity of a version in which the jobs have a common processing time on the second machine, has not been addressed. We show that the problem is unary NP-hard, answering an open problem posed in Zhu et al. (2016). Then we present an approximation algorithm for the problem with worst-case performance ratio at most 2.     

Approximation algorithms for single machine scheduling with one unavailability period

In this paper, we investigate the single machine scheduling problem with release dates and tails and a planned unavailability time period. We show that the problem admits a fully polynomial-time approximation scheme when the tails are equal. We derive an approximation algorithm for the general case and we show that the worst-case bound of the sequence yielded by Schrage’s algorithm is equal to 2 and that this bound is tight. Some consequences of this result are also presented.      

Approximation algorithms for scheduling problems with a modified total weighted tardiness objective

We study the approximability of minimum total weighted tardiness with a modified objective which includes an additive constant. This ensures the existence of a positive lower bound for the minimum value. Moreover the new objective has a natural interpretation in just-in-time production systems.     

Single machine scheduling with semi-resumable machine availability constraints

This paper considers the semi-resumable model of single machine scheduling with a non-availability period. The machine is not available for processing during a given time interval. A job cannot be completed before the non-availability period will have to partially restart after the machine has become available again. For the problem with objective of minimizing makespan, the tight worst-case ratio of algorithm LPT is given, and an FPTAS is also proposed. For the problem with objective of minimizing total weighted completion time, an approximation algorithm with worst-case ratio smaller than 2 is presented. Two special cases of the latter problem are also considered, and improved algorithms are given.     

Approximation algorithms for UET scheduling problems with exact delays

In this paper we consider coupled-task single-machine and two-machine flow shop scheduling problems with exact delays, unit processing times, and the makespan as an objective function. The main results of the paper are fast 7/4- and 3/2-approximation algorithms for solving the single- and two-machine problems, respectively.     

An approximate algorithm for a high-multiplicity parallel machine scheduling problem

We consider a high-multiplicity parallel machine scheduling problem where the objective is to minimize the weighted sum of completion times. We suggest an approximate algorithm and we prove that it is asymptotically exact. The algorithm exploits a convex quadratic relaxation of the problem to fix a partial schedule, consisting of most jobs, and then assigns the residual jobs following a simple and general rule. The quality of the obtained solution is evidenced by some numerical tests.     

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Parallel machine scheduling with nested job assignment restrictions

We derive a polynomial time approximation scheme for a special case of makespan minimization on unrelated machines.     

Approximation algorithms for problems in scheduling with set-ups

In this paper, we present new approximation results for the offline problem of single machine scheduling with sequence-independent set-ups and item availability, where the jobs to be scheduled are independent (i.e., have no precedence constraints) and have a common release time.We present polynomial-time approximation algorithms for two versions of this problem. In the first version, the input includes a weight for each job, and the goal is to minimize the total weighted completion time. On any input, our algorithm produces a schedule whose total weighted completion time is within a factor 2 of optimal for that input.In the second version, the input includes a due date for each job, and the goal is to minimize the maximum lateness of any job. On any input, our algorithm produces a schedule with the following performance guarantee: the maximum lateness of a job is at most the maximum lateness of the optimal schedule on a machine that runs at half the speed of our machine.     

Two-agent scheduling to minimize the total cost

Two agents, each having his own set of jobs, compete to perform their own jobs on a common processing resource. Each job of the agents has a weight that specifies its importance. The cost of the first agent is the maximum weighted completion time of his jobs while the cost of the second agent is the total weighted completion time of his jobs. We consider the scheduling problem of determining the sequence of the jobs such that the total cost of the two agents is minimized. We provide a 2-approximation algorithm for the problem, show that the case where the number of jobs of the first agent is fixed is NP-hard, and devise a polynomial time approximation scheme for this case.     

A branch-and-bound algorithm for single-machine scheduling with batch delivery minimizing flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimizing the sum of flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show significant improvements over an existing dynamic programming algorithm.     

Improved algorithm for broadcast scheduling of minimal latency in wireless ad hoc networks

A wide range of applications for wireless ad hoc networks are time-critical and impose stringent requirement on the communication latency. One of the key communication operations is to broadcast a message from a source node. This paper studies the minimum latency broadcast scheduling problem in wireless ad hoc networks under collision-free transmission model. The previously best known algorithm for this NP-hard problem produces a broadcast schedule whose latency is at least 648（rmax/rmin）^2 times that of the optimal schedule, where rmax and rmin are the maximum and minimum transmission ranges of nodes in a network, respectively. We significantly improve this result by proposing a new scheduling algorithm whose approximation performance ratio is at most （1 ＋ 2rmax/rmin）^2＋32, Moreover, under the proposed scheduling each node just needs to forward a message at most once.     

On the machine scheduling problem with job delivery coordination

This paper examines two scheduling problems with job delivery coordination, in which each job demands different amount of storage space during transportation. For the first problem, in which jobs are processed on a single machine and delivered by one vehicle to a customer, we present a best possible approximation algorithm with a worst-case ratio arbitrarily close to 3/2. For the second problem, which differs from the first problem in that jobs are processed by two parallel machines, we give an improved algorithm with a worst-case ratio 5/3.     

On-line scheduling of unit time jobs with rejection: minimizing the total completion time

We consider on-line scheduling of unit time jobs on a single machine with job-dependent penalties. The jobs arrive on-line (one by one) and can be either accepted and scheduled, or be rejected at the cost of a penalty. The objective is to minimize the total completion time of the accepted jobs plus the sum of the penalties of the rejected jobs.We give an on-line algorithm for this problem with competitive ratio . Moreover, we prove that there does not exist an on-line algorithm with competitive ratio better than 1.63784.     

Approximation of the supply scheduling problem

The supply scheduling problem consists in finding a minimum cost delivery plan from a set of providers to a manufacturing unit, subject to given bounds on the shipment sizes and subject to the demand at the manufacturing unit. We provide a fully polynomial time approximation scheme for this problem.     

Hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization

In this paper, a HGA (hybrid genetic algorithm) is proposed for permutation flowshop scheduling problems (PFSP) with total flowtime minimization, which are known to be NP-hard. One of the chromosomes in the initial population is constructed by a suitable heuristic and the others are yielded randomly. An artificial chromosome is generated by a weighted simple mining gene structure, with which a new crossover operator is presented. Additionally, two effective heuristics are adopted as local search to improve all generated chromosomes in each generation. The HGA is compared with one of the most effective heuristics and a recent meta-heuristic on 120 benchmark instances. Experimental results show that the HGA outperforms the other two algorithms for all cases. Furthermore, HGA obtains 115 best solutions for the benchmark instances, 92 of which are newly discovered.     

A 2-approximation algorithm for interval data minmax regret sequencing problems with the total flow time criterion

In this paper we discuss a minmax regret version of the single-machine scheduling problem with the total flow time criterion. Uncertain processing times are modeled by closed intervals. We show that if the deterministic problem is polynomially solvable, then its minmax regret version is approximable within 2.