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.     

A single-machine scheduling problem with maintenance activities to minimize makespan

We study a single-machine scheduling problem with periodic maintenance activity under two maintenance stratagems. Although the scheduling problem with single or periodic maintenance and nonresumable jobs has been well studied, most of past studies considered only one maintenance stratagem. This research deals with a single-machine scheduling problem where the machine should be stopped for maintenance after a fixed periodic interval (T) or after a fixed number of jobs (K) have been processed. The objective is to minimize the makespan for the addressed problem. A two-stage binary integer programming (BIP) model is provided for driving the optimal solution up to 350-job instances. For the large-sized problems, two efficient heuristics are provided for the different combinations of T and K. Computational results show that the proposed algorithm Best-Fit-Butterfly (BBF) performs well because the total average percentage error is below 1%. Once the constraint of the maximum number of jobs (K) processed in the machine’s available time interval (T) is equal or larger than half of jobs, the heuristic Best-Fit-Decreasing (DBF) is strongly recommended.     

Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan

This paper considers single machine scheduling with an aging effect in which the processing time of a job depends on its position in a sequence. It is assumed that aging ratios are job-dependent and machine can be maintained some times in a schedule. After a maintenance activity, machine will be restored to its initial condition. The processing of jobs and the maintenance activities of machine are scheduled simultaneously. The objective is to schedule the jobs and the maintenance activities, so as to minimize the makespan. We provide a polynomial time algorithm to solve the problem.     

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.     

Multi-machine scheduling with deteriorating jobs and scheduled maintenance

In this paper, we investigate a multi-machine scheduling problem in which job processing times are increasing functions of their starting times and machines are not always available. Job processing times are assumed to follow simple linear deteriorations. Moreover, each machine is assumed to have a maintenance period which is known in advance. Both the resumable and non-resumable cases are discussed with the objective of minimizing the makespan. A lower bound and a heuristic algorithm are derived for each case. Numerical results are also provided to evaluate the efficiency of the proposed procedures.     

On a periodic maintenance problem

In this paper, a machine maintenance problem, in which n machines are to be served on a regular, periodic basis, is studied. In particular, we are interested in how the maintenance cycles of the machines can be initiated so that all service requirements can be fulfilled by k servers.     

Single machine scheduling with release dates and rejection

In this paper, we consider the single machine scheduling problem with release dates and rejection. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem is NP-hard in the ordinary sense. Then we provide two pseudo-polynomial-time algorithms. Consequently, two special cases can be solved in polynomial-time. Finally, a 2-approximation algorithm and a fully polynomial-time approximation scheme are given for the problem.     

Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: Single machine problem

We study a scheduling problem motivated by the challenges observed in the newest semiconductor manufacturing wafer fabrication facilities. As wafers are larger and heavier in these wafer fabs, it is becoming more common to use specialized material handling containers that carry multiple orders coming from different customers and to schedule the containers as jobs in the fab. The system performance is a function of the completion times of orders, which ultimately depend on both (1) how the orders are assigned to such containers (“job formation”), and (2) how the containers are scheduled in the fab (“job scheduling”). The overall problem is to find the best way to form and schedule the jobs subject to complicating constraints, including the restrictions on the number of containers that can be used at one time and on the number of wafers the containers can carry. We focus on the single machine job formation and scheduling problem with the total completion time objective. We show that this problem is quite different from conventional parallel and serial batching scenarios and prove that the uncapacitated special case is polynomially solvable and the capacitated case is strongly NP-hard. We use a dynamic programming algorithm to solve the uncapacitated problem, which not only provides tight lower bounds for the capacitated problem, but also becomes a basis for a heuristic approach for the capacitated problem. The computational results show that this approach is very effective, leading to small optimality gaps that get even smaller as the problems become larger.     

Single machine unbounded parallel-batch scheduling with forbidden intervals

In this paper we consider the single machine parallel-batch scheduling with forbidden intervals. There are some forbidden intervals in which the machine cannot be available. The jobs are processed in batches form in the remaining free time-slots without preemption, where the processing time of a batch is defined to be the maximum processing time of the jobs in this batch. We show that, when the objective is bottleneck form, maximum lateness, or makespan with release dates of jobs, the considered problem can be solved in polynomial time.     

Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect

In this paper we consider the single machine scheduling problems with exponential sum-of-logarithm-processing-times based learning effect. By the exponential sum-of-logarithm-processing-times based learning effect, we mean that the processing time of a job is defined by an exponent function of the sum of the logarithm of the processing times of the jobs already processed. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Single machine scheduling under potential disruption

We provide optimal algorithms to solve a new scheduling problem in which there is a possibility that a disruption will happen at a particular time and last for a period of time with a certain probability. The objective functions are the expected total weighted completion times and the expected maximum tardiness, respectively.     

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.     

Single machine scheduling with a general exponential learning effect

In this paper we consider the scheduling problem with a general exponential learning effect and past-sequence-dependent (p-s-d) setup times. By the general exponential learning effect, we mean that the processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the δ ? 0th power of completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Single machine scheduling with randomly compressible processing times

This work is concerned with single machine scheduling with random compression of processing times. The objective is to find the optimal sequence to minimize the cost based on earliness, tardiness and compression. The analysis is carried out under a common due date. Both absolute derivation cost and squared derivation cost are considered. For both constrained problems and unconstrained problems, it is shown that an optimal schedule must be V-shaped. Remarks on common slack model is also provided.     

Single machine scheduling under market uncertainty

This paper considers single machine scheduling problems where job processing times are known and deterministic but where the reward received upon completion of a job changes stochastically over time according to Brownian motion. The objectives of maximizing expected net-present-value (NPV), minimizing the variance of NPV and maximizing the probability of achieving a minimum benchmark NPV are considered. For non-preemptive static list policies complexity results and branch and bound procedures are presented. The branch and bound procedures are shown to be effective for problem instances with 20–25 jobs. For the problem of maximizing NPV with non-preemptive dynamic policies the optimal static schedule is shown through empirical testing to be as good as a greedy heuristic and to be near optimal when the variance is not large.     

Two-machine flow shop no-wait scheduling with machine maintenance

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is subject to mandatory maintenance. The length of the maintenance period is defined by a non-decreasing function that depends on the starting time of that maintenance. The objective is to minimize the completion time of all activities. We present a polynomial-time approximation scheme for this problem. Received: November 2004 / Received version: March 2005 AMS classification: 90B35, 90B30, 90C59 The research was partly supported by INTAS (Project 03-51-5501) All correspondence to: Vitali A. Strusevich     

Single machine scheduling with time-dependent linear deterioration and rate-modifying maintenance

We study single machine scheduling problems with linear time-dependent deterioration effects and maintenance activities. Maintenance periods (MPs) are included into the schedule, so that the machine, that gets worse during the processing, can be restored to a better state. We deal with a job-independent version of the deterioration effects, that is, all jobs share a common deterioration rate. However, we introduce a novel extension to such models and allow the deterioration rates to change after every MP. We study several versions of this generalized problem and design a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized. We show that all problems reduce to a linear assignment problem with a product matrix and can be solved by methods very similar to those used for solving problems with positional effects.     

Single machine quadratic penalty function scheduling with deteriorating jobs and group technology

This paper considers single machine scheduling problems with group technology (GT) and deteriorating jobs. We consider the case of jobs whose processing times are a simple linear function of their starting time. The two objectives of scheduling problems are to minimize the weighted sum of squared completion times and the weighted sum of squared waiting times, respectively. We also provide polynomial time algorithms to solve these problems.