Order acceptance and scheduling with machine availability constraints

We consider an order acceptance and scheduling model with machine availability constraints. The manufacturer (machine) is assumed to be available to process orders only within a number of discontinuous time intervals. To capture the real-life behavior of a typical manufacturer who has restrictions of time availability to process orders, our model allows the manufacturer to reject or outsource some of the orders. When an order is rejected or outsourced, an order-dependent cost of penalty will occur. The objective is to minimize the makespan of all accepted orders plus the total penalty of all rejected/outsourced orders. We study the approximability of the model and some of its important special cases.     

Approximability of two-machine no-wait flowshop scheduling with availability constraints

We consider in this paper the two-machine no-wait flowshop scheduling problem in which each machine may have an unavailable interval. We present a polynomial time approximation scheme for the problem when the unavailable interval is imposed on only one machine, or the unavailable intervals on the two machines overlap.     

Single machine scheduling problem with two synergetic agents and piece-rate maintenance

This paper attempts to study on the single machine scheduling problems with two synergetic agents, each has a set of nonpreemptive jobs and a regular objective function depending on the completion times of its jobs only. It is not only necessary to satisfy the constraints of each agents objective function, it is necessary to minimize an aggregate increasing objective function of two agents’ objective function. Furthermore, this paper proposes a new kind of machine maintenance: piece-rate maintenance, which depicts the scenario that machine maintenance is implemented once every a fixed number of jobs is completed. Hence, it explores into the single machine scheduling problems with two synergetic agents and piece-rate maintenance. If the regular objective function of each job is polynomial, it can be observed that these problems are all polynomially solvable.     

Parallel machine scheduling with machine availability and eligibility constraints

In this paper we consider the problem of scheduling n independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the makespan. Each machine is not continuously available at all times and each job can only be processed on specified machines. A network flow approach is used to formulate this scheduling problem into a series of maximum flow problems. We propose a polynomial time binary search algorithm to either verify the infeasibility of the problem or solve it optimally if a feasible schedule exists.     

Approximation algorithm for minimizing total latency in machine scheduling with deliveries

We study the problem of minimizing total latency in machine scheduling with deliveries, which is defined as follows. There is a set of n jobs to be processed by a single machine at a plant, where job J_i is associated with its processing time and a customer i located at location i to which the job is to be delivered. In addition, there is a single uncapacitated delivery vehicle available. All jobs (vehicle) are available for processing (delivery) at time 0. Our aim is to determine the sequence in which the jobs should be processed in the plant, the departure times of the vehicle from the plant, and the routing of the vehicle, so as to minimize the total latency (job delivery time). We present a 6e16.309691-approximation algorithm for the problem.     

An FPTAS for scheduling with resource constraints

We study a basic scheduling problem with resource constraints: A number of jobs need to be scheduled on two parallel identical machines with the objective of minimizing the makespan, subject to the constraint that jobs may require a unit of one of the given renewable resources during their execution. For this NP-hard problem, we develop a fully polynomial-time approximation scheme (FPTAS). Our FPTAS makes a novel use of existing algorithms for the subset-sum problem and the open shop scheduling problem.     

Parallel machine scheduling with nested processing set restrictions

We consider the problem of scheduling a set of n independent jobs on m parallel machines, where each job can only be scheduled on a subset of machines called its processing set. The machines are linearly ordered, and the processing set of job j   is given by two machine indexes _aj$a_j$ and _bj$b_j$; i.e., job j   can only be scheduled on machines _aj,_aj+1,…,_bj$a_j\text{,}{a}_j+1\text{,}\dots \text{,}{b}_j$. Two distinct processing sets are either nested or disjoint. Preemption is not allowed. Our goal is to minimize the makespan. It is known that the problem is strongly NP-hard and that there is a list-type algorithm with a worst-case bound of 2-1/m$2-1/m$. In this paper we give an improved algorithm with a worst-case bound of 7/4. For two and three machines, the algorithm gives a better worst-case bound of 5/4 and 3/2, respectively.     

A single machine scheduling problem with availability constraints and sequence-dependent setup costs

We study a single machine scheduling problem with availability constraints and sequence-dependent setup costs, with the aim of minimizing the makespan. To the authors’ knowledge, this problem has not been treated as such in the operations research literature. We derive in this paper a mixed integer programming model to deal with such scheduling problem. Computational tests showed that commercial solvers are capable of solving only small instances of the problem. Therefore, we propose two ways for reducing the execution time, namely a valid inequality that strengthen the linear relaxation and an efficient heuristic procedure that provides a starting feasible solution to the solver. A substantial gain is achieved both in terms of the linear programming relaxation bound and in terms of the time to obtain an integer optimum when we use the enhanced model in conjunction with providing to the solver the solution obtained by the proposed heuristic.     

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.     

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.     

A note on “scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan”

In a recent paper, Chen [J.S. Chen, Scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan, European Journal of Operational Research 190 (2008) 90–102] proposes a heuristic algorithm to deal with the problem Scheduling of Nonresumable Jobs and Flexible Maintenance Activities on A Single Machine to Minimize Makespan  . Chen also provides computational results to demonstrate its effectiveness. In this note, we first show that the worst-case performance bound of this heuristic algorithm is 2. Then we show that there is no polynomial time approximation algorithm with a worst-case performance bound less than 2 unless P=NP$P=\mathit{NP}$, which implies that Chen’s heuristic algorithm is the best possible polynomial time approximation algorithm for the considered scheduling problem.     

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.     

Parallel-machine scheduling with non-simultaneous machine available time

We consider a problem of scheduling n independent jobs on m parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem.     

The bounded single-machine parallel-batching scheduling problem with family jobs and release dates to minimize makespan

We consider the problem of scheduling family jobs with release dates on a bounded batching machine to minimize the makespan. A polynomial-time approximation scheme for the identical job size model and an approximation algorithm with a worst-case ratio of for the non-identical job size model will be derived.     

On-line scheduling to minimize average completion time revisited

We consider the scheduling problem of minimizing the average-weighted completion time on identical parallel machines when jobs are arriving over time. For both the preemptive and the nonpreemptive setting, we show that straightforward extensions of Smith's ratio rule yield smaller competitive ratios than the previously best-known deterministic on-line algorithms.     

Makespan minimization in open shops: A polynomial time approximation scheme

In this paper, we demonstrate the existence of a polynomial time approximation scheme for makespan minimization in the open shop scheduling problem with an arbitrary fixed numberm of machines. For the variant of the problem where the number of machines is part of the input, it is known that the existence of an approximation scheme would implyP = NP. Hence, our result draws a precise separating line between approximable cases (i.e., withm fixed) and non-approximable cases (i.e., withm part of the input) of this shop problem. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Supported by the DIMANET/PECO Program of the European Union.Supported by a research fellowship of the Euler Institute for Discrete Mathematics and its Applications. This research was done while Gerhard Woeginger was with the Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands.     

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.      

Single machine scheduling subject to precedence delays

A single-machine scheduling problem with precedence delays is analyzed. A set of n tasks is to be scheduled on the machine in such a way that the makespan is minimized. The executions of the tasks are constrained by precedence delays, i.e., a task can start its execution only after any of its predecessors has completed and the delay between the two tasks has elapsed. In the case of unit execution times and integer lengths of delays, the problem is shown to be NP-hard in the strong sense. In the case of integer execution times and unit length of delays, the problem is polynomial, and an O(n²) optimal algorithm is provided. Both preemptive and non-preemptive cases are considered.