Total Completion Time Criterion Research Articles

Minimizing total completion time and makespan for a multi-scenario bi-criteria parallel machine scheduling problem

Multi-criteria scheduling problems under uncertainty remain a relatively unexplored topic in theoretical computer science despite substantial practical interests. This work studies a bi-objective identical parallel machine scheduling problem under uncertainty, in which the first objective is to minimize the total completion time, and the second is to minimize the makespan. Especially a job’s processing time is assumed to be represented by a polynomial function with respect to scenario u∈U, where U⊂R+ is an interval containing an infinite number of scenarios.In this work, we are looking for a compact and complete description of the set of possibly optimal solutions, along with their objective function values, over the set of scenarios or an approximation with a performance guarantee. First, to better understand the characteristics of the studied problem, we consider two single-objective problems: parallel machine scheduling problem under uncertainty with the total completion time and makespan criterion, respectively. For the problem with the total completion time criterion, we demonstrate that the set of possibly optimal schedules can be found in polynomial time. In contrast, for the problem with the makespan criterion, we provide a (1+ϵ)-approximation algorithm. For the bi-objective problem, we provide a 2-approximation algorithm for any number of parallel machines and a (1+ϵ)-approximation algorithm where a fixed number of parallel machines is considered.

Total Completion Time Minimization for Scheduling with Incompatibility Cliques

This paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph equivalent to a collection of disjoint cliques. No two jobs in a clique are allowed to be assigned to the same machine. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the case of disjoint cliques has received increasing attention in recent years. While the research up to this point has been focused on the makespan objective, we broaden the scope and study the classical total completion time criterion. In the setting without incompatibilities, this objective is well-known to admit polynomial time algorithms even for unrelated machines via matching techniques. We show that the introduction of incompatibility cliques results in a richer, more interesting picture. We prove that scheduling on identical machines remains solvable in polynomial time, while scheduling on unrelated machines becomes APX-hard. Next, we study the problem under the paradigm of fixed-parameter tractable algorithms (FPT). In particular, we consider a problem variant with assignment restrictions for the cliques rather than the jobs. We prove that, despite still being APX-hard, it can be solved in FPT time with respect to the number of cliques. Moreover, we show that the problem on unrelated machines can be solved in FPT time for reasonable parameters, in particular, the parameter combination: maximum processing time, number of job kinds, and number of machines or maximum processing time, number of job kinds, and number of cliques. The latter results are extensions of known results for the case without incompatibilities, and can even be further extended to the case of total weighted completion time. All of the FPT results make use of n-fold Integer Programs that recently received great attention by proving their usefulness for scheduling problems.

An improved lower bound for the blocking permutation flow shop with total completion time criterion

The block in-process permutation flow shop with total completion time criterion is known to be NP-hard for m⩾2. Since the literature is scarce in this theme, this article aims to fill this gap. It presents an improvement of the branch and bound algorithm to solve this problem through the development of a new machine-based lower bound which exploits the machine idleness and the occurrence of blocking. The computational experiments point out that the algorithm can handle n⩽20 test problems in less than 2 min. Therefore, this work can support the scheduling of many applications in manufacturing systems with limited buffers.

Metaheuristics for Order Scheduling Problem with Unequal Ready Times

In recent years, various customer order scheduling (OS) models can be found in numerous manufacturing and service systems in which several designers, who have developed modules independently for several different products, convene as a product development team, and that team completes a product design only after all the modules have been designed. In real-life situations, a customer order can have some requirements including due dates, weights of jobs, and unequal ready times. Once encountering different ready times, waiting for future order or job arrivals to raise the completeness of a batch is an efficient policy. Meanwhile, the literature releases that few studies have taken unequal ready times into consideration for order scheduling problem. Motivated by this limitation, this study addresses an OS scheduling model with unequal order ready times. The objective function is to find a schedule to optimize the total completion time criterion. To solve this problem for exact solutions, two lower bounds and some properties are first derived to raise the searching power of a branch-and-bound method. For approximate solution, four simulated annealing approaches and four heuristic genetic algorithms are then proposed. At last, several experimental tests and their corresponding statistical outcomes are also reported to examine the performance of all the proposed methods.

Memetic social spider optimization algorithm for scheduling two-stage assembly flowshop in a distributed environment

Abstract This paper studies the distributed two-stage assembly flowshop problem with separate setup times, which is a generalisation for the regular two-stage assembly flowshop problem in the distributed manufacturing environment. The optimization objective is to find a suitable job schedule such that the criterion of total completion time is minimized. To deal with such a problem, we propose a novel memetic algorithm (MA) based on a recently developed social spider optimization (SSO). To the best of our knowledge, it is the first effort to explore the SSO-based MA (MSSO) and to apply SSO in the field of combinational optimization. In the proposed MSSO algorithm, we first modify the original version of SSO to adapt to the distributed problems, and then integrate two improvement techniques, problem-special local search and self-adaptive restart strategy, within MA framework. In the numerical experiment, the parameters used in MSSO are calibrated and suitable parameter values are suggested based on the Taguchi method. Experimental results and comparisons with the existing algorithms validate the effectiveness and efficiency of the proposed MSSO for addressing the considered problem. In addition, the effect of problem scale parameters on MSSO and the effectiveness of the proposed improvement techniques are also investigated and demonstrated.

Complexity of interval minmax regret scheduling on parallel identical machines with total completion time criterion

We consider the problem of scheduling jobs on parallel identical machines, where only interval bounds of processing times of jobs are known. The optimality criterion of a schedule is the total completion time. In order to cope with the uncertainty, we consider the maximum regret objective and seek a schedule that performs well under all possible instantiations of processing times. We show how to compute the maximum regret, and prove that its minimization is strongly NP-hard.

Optimizing blocking flow shop scheduling problem with total completion time criterion

The blocking flow shop scheduling problem has found many applications in manufacturing systems. There are a few exact methods for solving this problem with different criteria. In this paper, efforts will be made to optimize the total completion time criterion for this problem. We present two mixed binary integer programming models, one of which is based on the departure times of jobs from machines, and the other is based on the idle and blocking times of jobs. An initial upper bound generator and some lower bounds and dominance rules are also developed to be used in a branch and bound algorithm. The algorithm solves 17 instances of the Taillard's benchmark problem set in less than 20min.

A Generalized Algorithm for Solving Multicriteria Scheduling Problems

In this paper, the scheduling problem involving optimization of multiple criteria (or objectives) is explored. There are many variants of the problem. The particular variant, in which the objectives are aggregated into a scalar function (with each criterion having weight which denotes its relative importance), is considered. An algorithm which can be used to solve very large classes of the multicriteria scheduling problem is proposed. The proposed algorithm and two solution methods selected from the literature were evaluated on a total of 900 randomly generated multicriteria scheduling problems (ranging from 10 to 500 jobs). Two variants of the release dates (0 – 24 and 0 – 49) are utilized. Results show that the proposed algorithm performed better than the selected solution methods when the total completion time criterion is much more important than the other criteria. However, when the total completion time criterion is much less important than the other criteria, the selected solution methods outperformed the proposed algorithm. The results are consistent under the two variants of the release dates.

A FPTAS for minimizing total completion time in a single machine time-dependent scheduling problem

In this paper a single machine time-dependent scheduling problem with total completion time criterion is considered. There are given n jobs J 1 , … , J n and the processing time p i of the ith job is given by p i = a + b i s i , where s i is the starting time of the ith job ( i = 1 , … , n ) , b i is its deterioration rate and a is the common base processing time. If all jobs have deterioration rates different and not smaller than a certain constant u > 0 , then for each ϵ > 0 a solution with the value of the goal function that is at most 1 + ϵ times greater than the optimal one can be found. We give a FPTAS that finds such a solution in O n 1 + 6 log 1 + u 2 1 ϵ 2 log 1 + u 2 time. Consequently, the problem cannot be NP-hard in the strong sense.

Computational complexity of some scheduling problems with multiprocessor tasks

The paper is concerned with scheduling problems with multiprocessor tasks and presents conditions under which such problems can be solved in polynomial time. The application of these conditions is illustrated by two quite general scheduling problems. These results are complemented by a proof of NP-hardness of the problem with a UET task system, two parallel processors, the criterion of total completion time, and precedence constraints in the form of out-trees.

A PSO and a Tabu search heuristics for the assembly scheduling problem of the two-stage distributed database application

The assembly flowshop scheduling problem has been addressed recently in the literature. There are many problems that can be modeled as assembly flowshop scheduling problems including queries scheduling on distributed database systems and computer manufacturing. The problem has been addressed with respect to either makespan or total completion time criterion in the literature. In this paper, we address the problem with respect to a due date-based performance measure, i.e., maximum lateness. We formulate the problem and obtain a dominance relation. Moreover, we propose three heuristics for the problem: particle swarm optimization (PSO), Tabu search, and EDD. PSO has been used in the areas of function optimization, artificial neural network training, and fuzzy system control in the literature. In this paper, we show how it can be used for scheduling problems. We have conducted extensive computational experiments to compare the three heuristics along with a random solution. The computational analysis indicates that Tabu outperforms the others for the case when the due dates range is relatively wide. It also indicates that the PSO significantly outperforms the others for difficult problems, i.e., tight due dates. Moreover, for difficult problems, the developed dominance relation helps reduce error by 65%.

Comparison of Heuristics for Solving a Flowshop Problem

We propose an experimental and theoretical analysis of heuristics solving the n-job two-machine flowshop problem with the total completion time criterion. We developed a heuristic and a lower bound and compare them with two well known heuristics from the literature and two classical lower bounds. Computational experiments and an analysis are given afterwards.

Note: On the two-machine no-idle flowshop problem

In this short note we study a two-machine flowshop scheduling problem with the additional no-idle feasibility constraint and the total completion time criterion function. We show that one of the few papers which deal with this special problem contains incorrect claims and suggest a way how these claims can be rectified. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:353–358, 2000

No‐wait and separate setup three‐machine flowshop with total completion time criterion

AbstractThis paper considers the three‐machine no‐wait flowshop problem with the objective of minimizing total completion time where setup times are considered as separate from processing times and sequence independent. We present optimal solutions for certain cases, and a dominance relation for the general case. We also develop and evaluate five heuristic algorithms for small and large number of jobs. Computational experience for up to 100 jobs shows that the proposed heuristics are quite effective and their performance do not depend on the number of jobs. The computational experience has been conducted for the uniform processing time distributions of U(1, 10) and U(1, 100). The best heuristic gives an overall average error of 0.47% for U(1, 10) and it gives an overall average error of 1.23% for U(1, 100).

No-wait and separate setup three-machine flowshop with total completion time criterion

This paper considers the three-machine no-wait flowshop problem with the objective of minimizing total completion time where setup times are considered as separate from processing times and sequence independent. We present optimal solutions for certain cases, and a dominance relation for the general case. We also develop and evaluate five heuristic algorithms for small and large number of jobs. Computational experience for up to 100 jobs shows that the proposed heuristics are quite effective and their performance do not depend on the number of jobs. The computational experience has been conducted for the uniform processing time distributions of U(1, 10) and U(1, 100). The best heuristic gives an overall average error of 0.47% for U(1, 10) and it gives an overall average error of 1.23% for U(1, 100).

On job assignment for a parallel system of processor sharing queues

Two of the optimality criteria most commonly considered to compare job assignment policies, namely, the stochastic order and the average total completion time criterion, are discussed. It is shown that the latter, while being weaker than the former, still provides a useful criterion when policies are to be evaluated in terms of average performance measures such as the system average response time. Some of the most relevant results available in the literature on job assignment to parallel first come, first served (FCFS) servers are summarized. The assignment problem is discussed for a parallel system of processor sharing (PS) queues with exponential interarrival times and exponential and identical service requirements. The optimality of the join-the-shortcut-queue (JSQ) assignment policy for this case is proven. Feasible policies for general service time distribution are discussed. An approach allowing a meaningful comparison of servers in the perspective of job assignment is proposed. A comparison of the assignment problem for FCFS and PS parallel systems is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>