Two-agent single-machine scheduling to minimize the weighted sum of the agents’ objective functions

Scheduling with two competing agents on a single machine has become a popular research topic in recent years. Most research focuses on minimizing the objective function of one agent, subject to the objective function of the other agent does not exceed a given limit. In this paper we adopt a weighted combination approach to treat the two-agent single-machine scheduling problem. The objective that we seek to minimize is the weighted sum of the total completion time of the jobs of one agent and the total tardiness of the jobs of the other agent. We provide two branch-and-bound algorithms to solve the problem. In addition, we present a simulated annealing and two genetic algorithms to obtain near-optimal solutions. We report the results of the computational experiments conducted to test the performance of the proposed algorithms.     

Heuristics for minimizing maximum lateness on a single machine with family-dependent set-up times

We address the problem of scheduling a single machine subject to family-dependent set-up times in order to minimize maximum lateness. We present a number of local improvement heuristics based on the work of previous researchers, a rolling horizon heuristic, and an incomplete dynamic programming heuristic. Extensive computational experiments on randomly generated test problems compare the performance of these heuristics. The rolling horizon procedures perform particularly well but require their parameters to be set based on problem characteristics to obtain their best performance.     

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.     

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.     

Heuristics for scheduling problems with an unavailability constraint and position-dependent processing times

We study a single machine scheduling problem, where the machine is unavailable for processing for a pre-specified time period. We assume that job processing times are position-dependent. The objective functions considered are minimum makespan, minimum total completion time and minimum number of tardy jobs. All these problems are known to be NP-hard even without position-dependent processing times. For all three cases we introduce simple heuristics which are based on solving the classical assignment problem. Lower bounds, worst case analysis and asymptotic optimality are discussed. All heuristics are shown numerically to perform extremely well.     

A cooperative dispatching approach for minimizing mean tardiness in a dynamic flowshop

Cooperative Dispatching is a real-time scheduling methodology, which consults downstream machines before making a job dispatching decision on any given machine. This paper proposes such an approach for minimizing the mean tardiness in a dynamic flowshop where new jobs arrive continuously, at random points in time, throughout the production cycle. Cooperative Dispatching is based on the idea that individual machines act self-interestedly, with the objective of optimizing their local performance criteria. A consulted machine attempts to influence upstream dispatching decisions in a manner that promotes its ability to minimize its total local tardiness. A machine's influence in the dispatching decision depends on current congestion and due-date tightness levels in the shop. A multiple regression model is proposed to help determine the weight a consulted machine's preferences will carry in the dispatching decision. Conflicting demands from the different machines are resolved by a minimum regret decision procedure, which aims to minimize the aggregate deviation from the consulted machines' preferences. The winning candidate that ultimately emerges from this procedure is the job that is dispatched. A comparative analysis to evaluate the performance of cooperative dispatching, compared to six other dispatching rules that are commonly favoured for tardiness-based criteria, is performed by means of simulation, using randomly generated test problems. Computational results indicate that Cooperative Dispatching outperforms the other dispatching rules, across a broad range of flowshop congestion and due-date tightness levels.     

Single-machine scheduling with deteriorating jobs under a series–parallel graph constraint

This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series–parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.     

Scheduling rules to minimize total tardiness in a parallel machine problem with setup and calendar constraints

Quality control lead times are one of most significant causes of loss of time in the pharmaceutical and cosmetics industries. This is partly due to the organization of laboratories that feature parallel multipurpose machines for chromatographic analyses. The testing process requires long setup times and operators are needed to launch the process. The various controls are non-preemptive and are characterized by a release date, a due date and available routings. These quality processes lead to significant delays, and we therefore evaluate the total tardiness criterion. Previous heuristics were defined for the total tardiness criterion, parallel machines, and setup such as apparent tardiness cost (ATC) and ATC with setups (ATCS). We propose new rules and a simulated annealing procedure in order to minimize total tardiness.     

Minimizing Mean Completion Time in a Batch Processing System

We consider batch processing jobs to minimize the mean completion time. A batch processing machine can handle up to $B$ jobs simultaneously. Each job is represented by an arrival time and a processing time. Jobs processed in a batch have the same completion time, i.e., their common starting time plus the processing time of their longest job. For batch processing, non-preemptive scheduling is usually required and we discuss this case. The batch processing problem reduces to the ordinary uniprocessor system scheduling problem if $B=1$. We focus on the other extreme case $B=+\infty$. Even for this seemingly simple extreme case, we are able to show that the problem is NP-hard for the weighted version. In addition, we establish a polynomial time algorithm for a special case when there are only a constant number of job processing times. Finally, we give a polynomial time approximation scheme for the general case.     

Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem

We consider the single machine multi-operation jobs total completion time scheduling problem. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a set-up time. A job completes when all of its operations have been processed. The objective is to minimize the sum of the job completion times. In the literature, the computational complexity of this problem is posed as open. We show that the problem is strongly NP-hard even when the set-up times are common and the processing time of each operation is 0 or 1.     

Pareto and scalar bicriterion optimization in scheduling deteriorating jobs

In the paper two problems of a single machine bicriterion scheduling of a set of deteriorating jobs are considered. The jobs are independent, nonpreemptable and are ready for processing at time 0$0$. The processing time _pj$p_j$ of each job is a linear function of the starting time _Sj$S_j$ of the job, _pj=1+_αjSj$p_j=1+{\alpha }_j{S}_j$, where _Sj?0$S_j?0$ and _αj>0${\alpha }_j>0$ for j=0,1,...,n$j=0,1,...,n$.     

Scheduling jobs on parallel machines with setup times and ready times

In this research we are interested in scheduling jobs with ready times on identical parallel machines with sequence dependent setups. Our objective is to minimize the total weighted tardiness. As this problem is NP-Hard, we develop a heuristic to solve this problem in reasonable time. Our approach is an extension of the apparent tardiness cost with setups (ATCS) approach by [Lee, Y. H., Pinedo, M. (1997). Scheduling jobs on parallel machines with sequence dependent setup times. European Journal of Operational Research, 100, 464–474.] to allow non-ready jobs to be scheduled – meaning we allow a machine to remain idle for a high priority job arriving at a later time. To determine the scaling parameters for our composite dispatching rule (called ATCSR), we first develop a ‘grid approach’ that considers multiple values for the scaling parameters, generates multiple schedules, and chooses the best schedule for the solution. This experimentation was then used to develop regression equations to predict the values of the scaling parameters that would yield the highest quality solution. The grid and regression versions of ATCSR provide better performance than grid and empirically based formula versions of ATCS, BATCS, and X-RM which are the prominent algorithms in the literature.     

Notes on “some single-machine scheduling problems with general position-dependent and time-dependent learning effects”

This paper provides a continuation of the idea presented by Yin et al. [Yin et al., Some scheduling problems with general position-dependent and time-dependent learning effects, Inform. Sci. 179 (2009) 2416-2425]. For each of the following three objectives, total weighted completion time, maximum lateness and discounted total weighted completion time, this paper presents an approximation algorithm which is based on the optimal algorithm for the corresponding single-machine scheduling problem and analyzes its worst-case bound. It shows that the single-machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties. It also shows that the problems of minimizing the total tardiness, discounted total weighted completion time and total weighted earliness penalty are polynomially solvable under some agreeable conditions on the problem parameters.     

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.     

Unrelated parallel-machine scheduling with deteriorating maintenance activities

We study the problem of unrelated parallel-machine scheduling with deteriorating maintenance activities. Each machine has at most one maintenance activity, which can be performed at any time throughout the planning horizon. The length of the maintenance activity increases linearly with its starting time. The objective is to minimize the total completion time or the total machine load. We show that both versions of the problem can be optimally solved in polynomial time.