Maximum Tardiness Research Articles

Single machine scheduling problems with generalised due-dates and job-rejection

We study single machine scheduling problems. Generalised due dates are assumed, i.e. job due dates are specified according to the positions of the jobs in the sequence, rather than their identity. Thus, assuming that due dates are numbered in a non-decreasing order, the jth due date refers to the job assigned to the jth position. In addition, we allow the option of job rejection, i.e. not all jobs must be processed. In this case, the scheduler is penalised for each rejected job, and the total rejection cost becomes part of the objective function. Two objective functions are considered: maximum tardiness plus rejection cost, and total tardiness plus rejection cost. Both problems are proved to be NP-hard. Pseudo-polynomial dynamic programmes and efficient heuristics are introduced and tested numerically.

A parallel-machine scheduling problem with two competing agents

ABSTRACTScheduling with two competing agents has become popular in recent years. Most of the research has focused on single-machine problems. This article considers a parallel-machine problem, the objective of which is to minimize the total completion time of jobs from the first agent given that the maximum tardiness of jobs from the second agent cannot exceed an upper bound. The NP-hardness of this problem is also examined. A genetic algorithm equipped with local search is proposed to search for the near-optimal solution. Computational experiments are conducted to evaluate the proposed genetic algorithm.

Effect of routing flexibility and sequencing rules on performance of stochastic flexible job shop manufacturing system with setup times: Simulation approach

Routing flexibility is a major contributor towards flexibility of a flexible job shop manufacturing system. This article focuses on a simulation-based experimental study on the effect of routing flexibility and sequencing rules on the performance of a stochastic flexible job shop manufacturing system with sequence-dependent setup times while considering dynamic arrival of job types. Six route flexibility levels and six sequencing rules are considered for detailed study. The performance of manufacturing system is evaluated in terms of flow time related and due date–related measures. Results reveal that routing flexibility and sequencing rules have significant impact on system performance, and the performance of a system can be increased by incorporating routing flexibility. Furthermore, the system performance starts deteriorating as the level of route flexibility is increased beyond a particular limit for a specified sequencing rule. The statistical analysis of the results indicates that when flexibility exists, earliest due date rule emerges as a best sequencing rule for maximum flow time, mean tardiness and maximum tardiness performance measures. Furthermore, smallest setup time rule is better than other sequencing rules for mean flow time and number of tardy jobs performance measures. Route flexibility level two provides best performance for all considered measures.

Minimizing sum of the due date assignment costs, maximum tardiness and distribution costs in a supply chain scheduling problem

In production systems, manufacturers face important decisions that affect system profit. In this paper, three of these decisions are modelled simultaneously: due date assignment, production scheduling, and outbound distribution scheduling. These three decisions are made in the sales, production planning and transportation departments. Recently, many researchers have devoted attention to the problem of integrating due date assignment, production scheduling and outbound distribution scheduling. In the present paper, the problems of minimizing costs associated with maximum tardiness, due date assignment and delivery for a single machine are considered. Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Programming (MIP) are used for the solution. This problem is NP-hard, so two meta-heuristic algorithms, an Adaptive Genetic Algorithm (AGA) and a Parallel Simulated Annealing algorithm (PSA), are used for solution of large-scale instances. The present paper is the first time that crossover and mutation operators in AGA and neighbourhood generation in PSA have been used in the structure of optimal solutions. We used the Taguchi method to set the parameters, design of experiments (DOE) to generate experiments, and analysis of variance, the Friedman, Aligned Friedman, and Quade tests to analyse the results. Also, the robustness of the algorithms was addressed. The computational results showed that AGA performed better than PSA.

Exact algorithms for single-machine scheduling problems with a variable maintenance

This paper deals with four single-machine scheduling problems (SMSPs) with a variable machine maintenance. The objectives of the four SMSPs are to minimize mean lateness, maximum tardiness, total flow time and mean tardiness, respectively. These four SMSPs are important in the literature and in practice. This study proposes an exact algorithm with the computational complexity O(n2) for each of the four SMSPs. In addition to the given jobs, the machine maintenance activity between two consecutive jobs is optimally scheduled.

Resource consumption minimization with a constraint of maximum tardiness on parallel machines

In response to the effects of global warming and environmental concerns, energy consumption has become a crucial issue. In this study, we consider a parallel-machine scheduling problem where the objective is to minimize the sum of resource consumption and outsourcing cost given that the maximum tardiness of all jobs does not exceed a given bound. We show that the problem is polynomially solvable for the pre-emption case and strongly NP-hard for the non-preemption case. A branch-and-bound algorithm and a hybrid metaheuristic algorithm are proposed to obtain exact and approximate solutions. Some experimental results are given to evaluate the algorithms.

Hybrid Black Hole Algorithm for Bi-Criteria Job Scheduling on Parallel Machines

Nature-inspired algorithms are recently being appreciated for solving complex optimization and engineering problems. Black hole algorithm is one of the recent nature-inspired algorithms that have obtained inspiration from black hole theory of universe. In this paper, four formulations of multi-objective black hole algorithm have been developed by using combination of weighted objectives, use of secondary storage for managing possible solutions and use of Genetic Algorithm (GA). These formulations are further applied for scheduling jobs on parallel machines while optimizing bi-criteria namely maximum tardiness and weighted flow time. It has been empirically verified that GA based multi-objective Black Hole algorithms leads to better results as compared to their counterparts. Also the use of combination of secondary storage and GA further improves the resulting job sequence. The proposed algorithms are further compared to some of the existing algorithms, and empirically found to be better. The results have been validated by numerical illustrations and statistical tests. Index Terms—Auxiliary archive, Black Hole algorithm, Genetic algorithm, Job scheduling, Nature-inspired algorithm, Tardiness, Weighted flow time.

Meta-Heuristic Algorithms to Solve Bi-Criteria Parallel Machines Scheduling Problem

Parallel machine scheduling problems are classified as NP-hard problems. The direct solutions for these problems are not available and meta-heuristic algorithms are required to be used to find near-optimal solutions. In this paper, the formulations of multi-objective Artificial Bee Colony algorithm by using combination of weighted objectives, secondary storage for managing possible solutions and Genetic algorithm have been developed and applied to schedule jobs on parallel machines optimizing bi-criteria namely maximum tardiness and weighted flow time. The results obtained indicate that proposed algorithm outperforms other multi-objective algorithms in optimizing bi-criteria scheduling problems on parallel machines. Further, the sequential optimization of bi-criteria using Early Due Date (EDD) followed by Genetic Algorithm (GA) has also been investigated. The efficiencies of the proposed algorithms have been verified by numerical illustrations and statistical tests.

An uncertain multi-objective programming model for machine scheduling problem

This paper discusses a parallel machine scheduling problem in which the processing times of jobs and the release dates are independent uncertain variables with known uncertainty distributions. An uncertain programming model with multiple objectives is obtained, whose first objective is to minimize the maximum completion time or makespan, and second objective is to minimize the maximum tardiness time. A genetic algorithm is employed to solve the proposed uncertain machine scheduling model, and its efficiency is illustrated by some numerical experiments.

Bi-criteria parallel machine scheduling using nature-inspired hybrid flower pollination algorithm

Parallel machine scheduling and its complex combinatorial optimisation problems are widely studied. A lot of research has been carried out in this area to determine how to effectively schedule parallel execution of different jobs to be carried out using different machines in order to achieve the optimisation criteria. In this paper, the formulations of multi-objective flower pollination algorithm obtained by the combination of weighted objectives or secondary storage for managing possible solutions along with their hybrids with genetic algorithm have been developed and applied to the problem of scheduling jobs on machines running in parallel in order to optimise bi-criteria, namely, maximum tardiness and weighted flow time. It has been empirically verified that multi-objective flower pollination algorithm using secondary storage and hybridised with genetic algorithm leads to better results as compared to the existing algorithms. The results obtained have been verified by numerical illustrations and statistical tests.

A multi-objective decision-making framework using preference selection index for assembly job shop scheduling problem

Assembly job shop scheduling problem (AJSSP) is an important NP-hard scheduling problem very difficult to solve because of its complex precedence relationship between jobs and product structures. In the present work, a systematic multi-attribute decision-making methodology namely, preference selection index method is adopted for ranking priority dispatching rules for scheduling an assembly job shop. A simulation model of an assembly job shop with seven work stations and one assembly station is developed for the purpose of experimentation. Eight priority dispatching rules from literature are identified and incorporated in the simulation model. Performance measures considered for analysis include mean flow time, maximum flow time, mean tardiness, maximum tardiness and machine utilisation. Products with single level assembly structure, two level assembly structure and three level assembly structure are examined to demonstrate and to check the applicability of the proposed methodology. The best performing priority dispatching rules are determined in a multi-objective environment.

A branch and bound algorithm to minimize the single machine maximum tardiness problem under effects of learning and deterioration with setup times

This paper sheds light on minimizing the maximum tardiness with processing and setup times under both learning effect and deterioration. In this paper, all the jobs have processing and setup times under effects of learning and deterioration. By the effects of learning and deterioration, we mean that the processing time of a job is defined by an increasing function of its execution start time and position in the sequence. We provide a branch and bound algorithm to minimize the maximum tardiness under effects of learning and deterioration with setup times. Computational experiments show that the proposed algorithm can solve instances up to 800 jobs in reasonable time.

Bi-criteria parallel machine scheduling using nature-inspired hybrid flower pollination algorithm

Parallel machine scheduling and its complex combinatorial optimisation problems are widely studied. A lot of research has been carried out in this area to determine how to effectively schedule parallel execution of different jobs to be carried out using different machines in order to achieve the optimisation criteria. In this paper, the formulations of multi-objective flower pollination algorithm obtained by the combination of weighted objectives or secondary storage for managing possible solutions along with their hybrids with genetic algorithm have been developed and applied to the problem of scheduling jobs on machines running in parallel in order to optimise bi-criteria, namely, maximum tardiness and weighted flow time. It has been empirically verified that multi-objective flower pollination algorithm using secondary storage and hybridised with genetic algorithm leads to better results as compared to the existing algorithms. The results obtained have been verified by numerical illustrations and statistical tests.

Scheduling comparison between multi-objective mathematical models and genetic algorithms approach in the textile industry

This paper discusses mixed integer mathematical models and genetic algorithms (GAs) approach for finding an optimal schedule of the bottleneck machine for a company in the textile industry. Single-objective and multi-objective mathematical models and GA are used to obtain an optimal solution to minimise the maximum tardiness (Tmax). The comparison is made between mathematical models and GA according to the primary and secondary performance measures. Primary performance measure is Tmax, while secondary performance measure is number of tardy jobs (nt) and total tardiness (TT) values. The experimentation is performed for small and large size problems. All jobs have five different instances except for 150-job and 200-job problems. Due to memory and time limitations, only one sample could be solved for 150-job and 200-job problem. The experimental results indicated that, most of the time GA finds an optimal solution and proposes alternative schedules for both single-objective and multi-objective mathematical models.

A Batch Scheduling Problem with Two Agents

In this paper, we consider a two-agent batch scheduling problem on a single machine such that the processing times of agent 1 and the due date of agent 2 in the same batch are identical. The objective is to minimize the total completion time of agent 1 with a constraint on the maximum tardiness of agent 2. First, we propose the optimality conditions. Then, we show that the problem is strongly NP-hard. Finally, we prove the problem remains NP-hard even for the case with one batch of agent 2, and develop a pseudo-polynomial algorithm and an approximation algorithm for this case.

Machine scheduling with deteriorating and resource-dependent maintenance activity

In this paper we investigate scheduling problems with a deteriorating and resource-dependent maintenance activity on a single machine. The duration of the maintenance is assumed to be dependent both on its starting time and on the resource allocated to it. The objective is determining the job sequence, the position to perform a maintenance activity and the amount of additional resource allocated to it such that the total cost of related measure and resource is minimized. The considered measures are the makespan, flowtime, maximum tardiness and combination of earliness, tardiness and due-date. Analysis results show that all the considered problems are polynomially solvable.

Two-agent two-machine flowshop scheduling with learning effects to minimize the total completion time

We study a two-agent scheduling problem in a two-machine permutation flowshop with learning effects. The objective is to minimize the total completion time of the jobs from one agent, given that the maximum tardiness of the jobs from the other agent cannot exceed a bound. We provide a branch-and-bound algorithm for the problem. In addition, we present several genetic algorithms to obtain near-optimal solutions. Computational results indicate that the algorithms perform well in either solving the problem or efficiently generating near-optimal solutions.

Improving schedule stability in single-machine rescheduling for new operation insertion

The problem studied here entails inserting a new operation into an existing predictive schedule (preschedule) on a (non-preemptive) single machine by rescheduling its operations, so that the resultant schedule is the most stable one among schedules with minimal maximum tardiness. Stability is measured by the sum of absolute deviations of post-rescheduling start times from the pre-rescheduling start times. In addition to several simple heuristics, this study investigates a hybrid branch-and-bound/local-search algorithm. A large set of instances that include cases with inserted idle times allows for tests of the performance of the heuristics for preschedules with varying degrees of robustness. The results show that algorithms can be developed that significantly improve the stability of schedules with no degradation in Tmax. In addition, new insights emerge into the robustness characteristics of a preschedule. Specifically, the number of gaps in the schedule, equal distribution of total slack among these gaps, and the slack introduced beyond the amount enforced by release times all have effects on schedule robustness and stability.

Efficient non-population-based algorithms for the permutation flowshop scheduling problem with makespan minimisation subject to a maximum tardiness

This paper focuses on the problem of scheduling jobs in a permutation flowshop with the objective of makespan minimisation subject to a maximum allowed tardiness for the jobs, a problem that combines two desirable manufacturing objectives related to machine utilisation and to customer satisfaction. Although several approximate algorithms have been proposed for this NP-hard problem, none of them can use the excellent speed-up method by Taillard (1990) [22] for makespan minimisation due to the special structure of the problem under consideration. In this paper, several properties of the problem are defined in order to be able to partly apply Taillard׳s acceleration. This mechanism, together with a novel feasible tabu local search method, allows us to further exploit the structure of solutions of the problem, and are incorporated in two proposed algorithms: a bounded-insertion-based constructive heuristic and an advanced non-population-based algorithm. These algorithms are compared with state-of-the-art algorithms under the same computer conditions. The results show that both algorithms improve existing ones and therefore, constitute the new state-of-art approximate solution procedures for the problem.

Minimizing maximum tardiness and delivery costs with batch delivery and job release times

Due to high delivery costs, manufacturers are usually required to dispatch their jobs as batches. However, this approach causes several crucial problems in scheduling-related objective functions such as minimizing the maximum tardiness. In this study, we address the scheduling of a set of jobs with specific release times, which need to be processed by a single machine and dispatched to a customer or another machine in a batch delivery condition. Each batch has a particular delivery cost. The aim is to minimize the costs of maximum tardiness plus delivery. First, a mixed integer programming (MIP) model is developed and solved by the CPLEX solver within the GAMS modeling environment. Next, a branch and bound algorithm is developed based on the LP relaxation of the MIP model. Using heuristics, appropriate values for the upper and lower bounds are predicted. The heuristics and pruning rules can obtain the solutions of large problems in logical run times. The problem can be deduced as being NP-hard, so the MIP model is not expected to be solved for extremely large sizes within a reasonable (i.e., polynomially-bounded) CPU time. Hence, by exploiting the features of the problem, two metaheuristic algorithms are developed, i.e., a fast discrete particle swarm optimization and a genetic algorithm. Finally, we present computational results to analyze and verify the solutions obtained.