A note to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity

This note considers a single machine scheduling and due-window assignment problem, in which the processing time of a job is a linear function of its starting time and the job-independent deterioration rates are identical for all jobs. We allow an option for performing a rate-modifying activity for changing the normal processing times of the jobs following this activity. The objective is to schedule the jobs, the due-window and the rate-modifying activity so as to minimize the sum of earliness, tardiness and due-window starting time and due-window size costs. We introduce a polynomial solution for the problem.     

Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

Scheduling jobs on a single machine to maximize the total revenue of jobs

In today's hyper-competitive marketplace, many products like memory chips and computers are characterized by short life cycles and rapidly declining sales prices. This implies that the amount of revenue generated as a result of completing a product (job) may be decreasing as its completion time is delayed. In such an environment, there is a decided preference for the maximization of product revenues as an important objective. Based on the assumption that the decreasing rate of revenue is dependent on their product types, we intend to develop a searching algorithm and some heuristic algorithms to locate optimal and near-optimal job sequences, respectively, and thereby maximize total earned revenue.     

Minimizing the total weighted completion time of deteriorating jobs

The paper deals with a single machine problem of scheduling jobs with start time dependent processing times to minimize the total weighted completion time. The computational complexity of this problem was unknown for ten years. We prove that the problem is NP-hard.     

Minimizing the number of tardy jobs in a single-machine scheduling problem with periodic maintenance

This research focuses on the problem of scheduling jobs on a single machine that requires periodic maintenance with the objective of minimizing the number of tardy jobs. We present a two-phase heuristic algorithm in which an initial solution is obtained first with a method modified from Moore's algorithm for the problem without maintenance and then the solution is improved in the second phase. Performance of the proposed heuristic algorithm is evaluated through computational experiments on randomly generated problem instances and results show that the heuristic gives solutions close to those obtained from a commercial integer programming solver in much shorter time and works better than an existing heuristic algorithm in terms of the solution quality.     

Branch-and-bound method for minimizing the weighted completion time scheduling problem on a single machine with release dates

In this paper, we consider a single-machine scheduling problem with release dates. The aim is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose two new lower bounds that can be, respectively, computed in O(n²) and in O(nlogn) time where n is the number of jobs. We prove a sufficient and necessary condition for local optimality, which can also be considered as a priority rule. We present an efficient heuristic using such a condition. We also propose some dominance properties. A branch-and-bound algorithm incorporating the heuristic, the lower bounds and the dominance properties is proposed and tested on a large set of instances.     

Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times

We consider a single machine scheduling problem with simple linear deterioration. Job processing times are assumed to be a simple linear function of a job-dependent growth rate and the job's starting time. We seek an optimal schedule, so as to minimize the total absolute deviation of completion times (TADC). We prove several interesting properties of an optimal schedule, and introduce two efficient heuristics which are tested against a lower bound.     

Single-machine scheduling problems with deteriorating jobs and learning effects

In this paper, we introduce a new scheduling model in which deteriorating jobs and learning effect are both considered simultaneously. By deterioration and the learning effect, we mean that the actual processing time of a job depends not only on the processing time of the jobs already processed but also on its scheduled position. For the single-machine case, we show that the problems of makespan, total completion time and the sum of the quadratic job completion times remain polynomially solvable, respectively. In addition,we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain conditions.     

Some scheduling problems with deteriorating jobs and learning effects

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper, we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. For the single-machine case, we derive polynomial-time optimal solutions for the problems to minimize makespan and total completion time. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. For the case of an m-machine permutation flowshop, we present polynomial-time optimal solutions for some special cases of the problems to minimize makespan and total completion time.     

Three scheduling problems with deteriorating jobs to minimize the total completion time

In this paper, three scheduling problems with deteriorating jobs to minimize the total completion time on a single machine are investigated. By a deteriorating job, we mean that the processing time of the job is a function of its execution start time. The three problems correspond to three different decreasing linear functions, whose increasing counterparts have been studied in the literature. Some basic properties of the three problems are proved. Based on these properties, two of the problems are solved in O(nlogn) time, where n is the number of jobs. A pseudopolynomial time algorithm is constructed to solve the third problem using dynamic programming. Finally, a comparison between the problems with job processing times being decreasing and increasing linear functions of their start times is presented, which shows that the decreasing and increasing linear models of job processing times seem to be closely related to each other.     

An O(n 2 ) algorithm for scheduling equal-length preemptive jobs on a single machine to minimize total tardiness

In this paper, we study the problem of scheduling n equal-length preemptive jobs on a single machine to minimize total tardiness, subject to release dates. The complexity status of this problem has remained open to date. We provide an O(n²) time algorithm to solve the problem.     

Minimizing the makespan in a single machine scheduling problem with a time-based learning effect

Both the building cost and the multiple-source routing cost are important considerations in construction of a network system. A spanning tree with minimum building cost among all spanning trees is called a minimum spanning tree (MST), and a spanning tree with minimum k-source routing cost among all spanning trees is called a k-source minimum routing cost spanning tree (k-MRCT). This paper proposes an algorithm to construct a spanning tree T for a metric graph G with a source vertex set S such that the building cost of T is at most 1+2/(α−1) times of that of an MST of G, and the k-source routing cost of T is at most α(1+2(k−1)(n−2)/k(n+k−2)) times of that of a k-MRCT of G with respect to S, where α>1, k=|S| and n is the number of vertices of G.     

Dispatching heuristics for the single machine weighted quadratic tardiness scheduling problem

In this paper, we consider the single machine scheduling problem with weighted quadratic tardiness costs. Several efficient dispatching rules are proposed. These include existing heuristics for the linear problem, as well as procedures suitably adapted to the quadratic objective function. Also, both forward and backward scheduling procedures are considered.The computational results show that the heuristics that specifically take into account the quadratic objective significantly outperform their linear counterparts. Also, the backward scheduling approach proves to be superior, and the difference in performance is even more noticeable for the harder instances.The best of the backward scheduling heuristics is both quite efficient and effective. Indeed, this procedure can quickly generate a schedule even for large instances. Also, its relative deviation from the optimum is usually rather low, and it performs adequately even for the more difficult instances.     

The two-machine flowshop no-wait scheduling problem with a single server to minimize the total completion time

This work studies the scheduling problem where a set of jobs are available for processing in a no-wait and separate setup two-machine flow shop system with a single server. The no-wait constraint requires that the operations of a job have to be processed continuously without waiting between two machines. The setup time is incurred and attended by a single sever which can perform one setup at a time. The performance measure considered is the total completion time. The problem is strongly NP-hard. Optimal solutions for several restricted cases and some properties for general case are proposed. Both the heuristic and the branch and bound algorithms are established to tackle the problem. Computational experiments indicate that the heuristic and the branch and bound algorithm are superior to the existing ones in term of solution quality and number of branching nodes, respectively.     

Single machine batch scheduling to minimize total completion time and resource consumption costs

In this paper we study the single-machine batch scheduling problem under batch availability, where both setup and job processing times are controllable by allocating a continuously divisible nonrenewable resource. Under batch availability a set of jobs is processed contiguously and completed together, when the processing of the last job in the batch is finished. We present polynomial time algorithms to find the job sequence, the partition of the job sequence into batches and the resource allocation, which minimize the total completion time or the total production cost (inventory plus resource costs).     

Heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose several dispatching heuristics, and analyse their performance on a wide range of instances. The heuristics include simple and widely used scheduling rules, as well as adaptations of those rules to a quadratic objective function. We also propose heuristic procedures that specifically address both the earliness and the tardiness penalties, as well as the quadratic cost function. Several improvement procedures were also analysed. These procedures are applied as an improvement step, once the heuristics have generated a schedule.     

A note on “Single machine scheduling with time-dependent deterioration and exponential learning effect”

result in a recent paper Huang, Wang, Wang, Gao, and Wang (2010) (Computers & Industrial Engineering 58 (2010) 58–63) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect.     

Dispatching heuristics for the single machine early/tardy scheduling problem with job-independent penalties

In this paper, we consider the single machine earliness/tardiness scheduling problem with job-independent penalties, and no machine idle time. Several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of each of those rules. We also consider early/tardy dispatching procedures, and a heuristic method based on existing adjacent precedence conditions. An improvement procedure that can be used to improve the schedules generated by the heuristics is also proposed.

The computational tests show that the best results are given by the early/tardy dispatching rules. These heuristics are also quite fast, and are capable of quickly solving even very large instances. The use of the improvement procedure is recommended, since it improves the solution quality, with little additional computational effort.