Single-machine Total Weighted Tardiness Problem Research Articles

The proportionate flow shop total tardiness problem

We consider the proportionate flow shop total tardiness problem and show how to implement Lawler's (1977) pseudo-polynomial dynamic programming (DP) algorithm for the single-machine total tardiness problem to the multi-machine environment of proportionate flow shop. We also present solvable special cases including one with small/big jobs that has not been considered for the corresponding single-machine problem. We then convert the DP algorithm for the proportionate flow shop to a fully polynomial time approximation scheme (FPTAS). Finally, we show by a counterexample that Pinedo's (2002, p. 140) statement that “the elimination criteria for the single-machine total weighted tardiness problem also apply to the proportionate flow shop total weighted tardiness problem” does not always hold and present an appropriately revised statement.

An Effective Solution for Large Scale Single Machine Total Weighted Tardiness Problem using Lunar Cycle Inspired Artificial Bee Colony Algorithm.

Single machine total weighted tardiness problem (SMTWTP) is one of the fundamental combinatorial optimization problems. The problem consists of a set of independent jobs with distinct processing times, weights, and due dates to be scheduled on a single machine. The goal of the problem is to minimize the total weighted tardiness. Several swarm intelligence (SI) motivated techniques have been proposed to solve SMTWTP. Still, the solution for large scale SMTWTP instances within a reasonable amount of time is a challenging task. Artificial bee colony (ABC) algorithm is one of the efficient SI based techniques to solve real world optimization problems. This article presents an effective amended ABC based strategy to solve SMTWTP. A local search (LS) approach, influenced from the lunar cycle is proposed and hybridized with ABC to escalate the exploitation capacity of the algorithm. The proposed LS approach is titled as the lunar inspired LS (LLS) approach and the proposed hybridized strategy is known as lunar inspired ABC (LuABC) algorithm. The proposed LuABC algorithm has been applied on 25 large SMTWTP instances of job size 1000. The obtained outcomes prove that the proposed algorithm obtains the optimum solutions for all the considered instances within a reasonable amount of time.

A hybrid evolutionary approach for the single-machine total weighted tardiness problem

This paper presents a hybrid evolutionary algorithm (HEA) for solving the single-machine total weighted tardiness problem, which incorporates several distinctive features such as a fast neighbourhood search and a buffer technique. HEA solves all the standard benchmark problem instances with 40, 50, and 100 jobs from the literature within 0.04s. For larger instances with 150, 200, 250, and 300 jobs, HEA obtains the optimal solutions for all of them within four minutes. To the best of our knowledge, HEA is the only metaheuristic algorithm that can obtain the optimal solutions for all the 25 instances with 1000 jobs within an average time of 3.97h, demonstrating the efficacy of HEA in terms of both solution quality and computational efficiency. Furthermore, some key features of HEA are analyzed to identify its critical success factors.

Multiple-variable neighbourhood search for the single-machine total weighted tardiness problem

ABSTRACTThe single-machine total weighted tardiness (SMTWT) problem is a typical discrete combinatorial optimization problem in the scheduling literature. This problem has been proved to be NP hard and thus provides a challenging area for metaheuristics, especially the variable neighbourhood search algorithm. In this article, a multiple variable neighbourhood search (m-VNS) algorithm with multiple neighbourhood structures is proposed to solve the problem. Special mechanisms named matching and strengthening operations are employed in the algorithm, which has an auto-revising local search procedure to explore the solution space beyond local optimality. Two aspects, searching direction and searching depth, are considered, and neighbourhood structures are systematically exchanged. Experimental results show that the proposed m-VNS algorithm outperforms all the compared algorithms in solving the SMTWT problem.

Breakout dynasearch for the single-machine total weighted tardiness problem

We present a breakout dynasearch algorithm (BDS) for solving the single-machine total weighted tardiness problem, in which a set of independent jobs with distinct processing times, weights, and due dates are to be scheduled on a single machine to minimize the sum of the weighted tardiness of all the jobs. BDS explores the search space by combining the dynasearch procedure and the adaptive perturbation strategy. Experimental results show that BDS virtually solves all the standard benchmark problem instances with 40, 50, and 100 jobs from the literature within 0.1s. For 500 larger instances with 150, 200, 250, and 300 jobs, BDS obtains all the upper bounds with the same objective function of the optimal solutions within an average of 252s, demonstrating the efficacy of BDS in terms of both solution quality and computational efficiency. We also analyze some key features of BDS to identify its success factors.

Scheduling step-deteriorating jobs to minimise the total weighted tardiness on a single machine

ABSTRACTThis paper addresses the scheduling problem of minimising the total weighted tardiness on a single machine with step-deteriorating jobs. With the assumption of deterioration, the job processing times are modelled by step functions of job starting times and pre-specified job deteriorating dates. The introduction of step-deteriorating jobs makes the single-machine total weighted tardiness problem more intractable. Until now, the computational complexity of this problem under consideration was not determined. In this study, it is proved to be strongly NP-hard. Then, a linear ordering mixed-integer programming model is derived for solving the problem instances optimally. In order to tackle large-sized problems, seven dispatching heuristic procedures are developed for near-optimal solutions. Meanwhile, the solutions delivered by the proposed heuristics are further improved by a pairwise swap movement. Computational results are presented to reveal the performance of all proposed approaches.

Biogeography-based Optimization (BBO) Algorithm for Single Machine Total Weighted Tardiness Problem (SMTWTP)

Scheduling problem is one of popular combinatorial cases. One of the basic scheduling problem is Single Machine Total Weighted Tardiness Problem (SMTWTP). This problem falls in NP-hard problem which is not easy to solve using an exact method as the scale getting larger. Nowadays, the number of research which develop and apply metaheuristics methods in solving combinatorial problems are quite high. One of new metaheuristics method which adopt biogeography phenomenon is Biogeography-based Optimization (BBO). BBO algorithm is known to have a quite good performance to solve continuous problems. In this research, BBO is developed to solve a discrete problem such as SMTWTP. Based on experimental results, BBO is able to solve 57 out of 75 instances. BBO has a better performance compared to Particle Swarm Optimization (PSO) with solving 19 out of 75. But, compared to modified Genetic Algorithm which can solve 67 instances, BBO is not better.

Application of Viral Systems for Single-Machine Total Weighted Tardiness Problem

In this paper, a relatively new algorithm inspired by the viral replication system called Viral Systems is used to solve the Single-Machine Total Weighted Tardiness (SMTWTP). SMTWTP is a job scheduling problem which is one of classical combinatorial problems known as np-hard problems. This algorithm makes the process of finding solutions through neighborhood and mutation mechanism. The experiment was conducted to evaluate its performance. There are seven parameters which are required to tune in to find best solution. The experiment was implemented on data sets of 40 jobs, 50 jobs, and 100 jobs. The results show that the algorithm can solve 235 optimally out of 275 problems.

An iterated greedy algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times

This article presents an enhanced iterated greedy (EIG) algorithm that searches both insert and swap neighbourhoods for the single-machine total weighted tardiness problem with sequence-dependent setup times. Novel elimination rules and speed-ups are proposed for the swap move to make the employment of swap neighbourhood worthwhile due to its reduced computational expense. Moreover, a perturbation operator is newly designed as a substitute for the existing destruction and construction procedures to prevent the search from being attracted to local optima. To validate the proposed algorithm, computational experiments are conducted on a benchmark set from the literature. The results show that the EIG outperforms the existing state-of-the-art algorithms for the considered problem.

An exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times

This study proposes an exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times. The algorithm is an extension of the authors' previous algorithm for the single-machine scheduling problem without setup times, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. In the first stage of the algorithm, the conjugate subgradient algorithm or the column generation algorithm is applied to a Lagrangian relaxation of the original problem to adjust multipliers. Then, in the second stage, constraints are successively added to the relaxation until the gap between lower and upper bounds becomes zero. The relaxation is solved by dynamic programming and unnecessary dynamic programming states are eliminated to suppress the increase of computation time and memory space. In this study a branching scheme is integrated into the algorithm to manage to solve hard instances. The proposed algorithm is applied to benchmark instances in the literature and almost all of them are optimally solved.

A Novel Ant Colony Algorithm for the Single-Machine Total Weighted Tardiness Problem with Sequence Dependent Setup Times

A Novel Ant Colony Algorithm for the Single-Machine Total Weighted Tardiness Problem with Sequence Dependent Setup Times

A Novel Ant Colony Algorithm for the Single-Machine Total Weighted Tardiness Problem with Sequence Dependent Setup Times

This paper deals with the NP-hard single-machine total weighted tardiness problem with sequence dependent setup times. Incorporating fuzzy sets and genetic operators, a novel ant colony optimization algorithm is developed for the problem. In the proposed algorithm, artificial ants construct solutions as orders of jobs based on the heuristic information as well as pheromone trails. To calculate the heuristic information, three well-known priority rules are adopted as fuzzy sets and then aggregated. When all artificial ants have terminated their constructions, genetic operators such as crossover and mutation are applied to generate new regions of the solution space. A local search is then performed to improve the performance quality of some of the solutions found. Moreover, at run-time the pheromone trails are locally as well as globally updated, and limited between lower and upper bounds. The proposed algorithm is experimented on a set of benchmark problems from the literature and compared with other metah...

New constructive heuristics for the total weighted tardiness problem

This note considers the single-machine total weighted tardiness problem. Three new heuristic algorithms are suggested and compared with other competing heuristics from the literature, such as Apparent Tardiness Cost, Weighted Covert and Weighted Modified Due Date. The experimental tests show that the suggested heuristic algorithms outperform the existing heuristics.

２機械順列フローショップ問題に対するｄｙｎａｓｅａｒｃｈの拡張

The purpose of this study is to construct a solution algorithm for the two-machine permutation flowshop problem based on the dynasearch. The dynasearch is an efficient local search algorithm that employs a special neighborhood structure called dynasearch swap neighborhood. Its primary advantage is that the neighborhood of a solution can be explored in polynomial time although it is composed of an exponential number of solutions. The dynasearch for machine scheduling was originally developed for the single-machine total weighted tardiness problem. Then, it was extended to the problem with idle time and setup times. This study further extends the dynasearch to the two-machine permutation flowshop problem and its effectiveness is examined by numerical experiments for both total weighted tardiness and total weighted earliness-tardiness objectives.

Hybrid heuristic algorithms for single machine total weighted tardiness scheduling problems

This paper addresses on solving a well known Non Polynomial (NP) hard type problem, namely the single machine total weighted-tardiness problem. The performances of three hybrid heuristic algorithms to solve the single machine scheduling problems with the objective of minimising the total weighted tardiness are presented and compared. In the first hybrid algorithm, a dynamic dispatching rule, namely Modified Due Date (MDD), is hybridised with local search mechanism. In the second hybrid algorithm, a greedy heuristic, namely backward phase, is proposed and hybridised with local search mechanisms. The third hybrid algorithm hybridises the backward phase heuristics with an iterated local search (ILS) having an evolutionary perturbation tool. The algorithms are tested by solving all the 125 benchmark problem instances available in the OR-Library for different sizes and compared with the best known values. It is observed that the hybrid algorithm with evolutionary perturbation tool is performing better than the others.

A branch-and-bound parallel algorithm for single-machine total weighted tardiness problem

This paper presents the branch-and-bound algorithm for the single-machine total weighted tardiness problem. Among exact solution approaches, the branch-and-bound algorithm from Potts and Van Wassenhove solves problems of up to 40 jobs and the algorithm from Babu et al. for 50 jobs (not for all instances). We have taken advantage of the properties of permutation broken into blocks. These properties are much stronger than elimination criteria (Potts CN, Van Wassenhove LN, 1991. IIE Trans 23:346–354; Rinnoy Kan AGH, Lageweg BJ, Lenstra JK 1975 Minimizing total cost one-machine scheduling. Oper Res 26:908–972) applied so far and they allow us to eliminate many branches of the solution tree. Parallel implementation of the algorithm enables us to reduce computational time significantly and to solve larger problems. We have tested the algorithms on randomly generated instances (of up to 80 jobs) and benchmark instances taken from the OR-Library [4]. The solutions obtained have been compared with the results yielded by the best algorithms discussed in the literature. The results show that the proposed algorithm solves the problem instances with high accuracy in a very short time.

A fast ant-colony algorithm for single-machine scheduling to minimize the sum of weighted tardiness of jobs

The problem of scheduling on a single machine is considered in this paper with the objective of minimizing the sum of weighted tardiness of jobs. A new ant-colony optimization (ACO) algorithm, called fast ACO (FACO), is proposed and analysed for solving the single-machine scheduling problem. By considering the benchmark problems available in the literature for analysing the performance of algorithms for scheduling on a single machine with the consideration of weighted tardiness of jobs, we validate the appropriateness of the proposed local-search schemes and parameter settings used in the FACO. We also present a comparison of the requirements of CPU time for solving the single-machine total-weighted tardiness problem by the FACO and the existing algorithms.