A common due-date assignment problem on parallel identical machines

Minmax earliness–tardiness costs with unit processing time jobs

We solve a due-window assignment problem on parallel identical machines. In addition to the standard objective of finding the optimal job schedule, in due-window assignment problems one has to assign a time interval during which goods are delivered to customers with no cost. Jobs scheduled prior to or after the due-window are penalized according to their earliness/tardiness value. We assume that jobs have identical processing times, but may have job-dependent earliness and tardiness costs (eg, due to possible different destinations). We show that the problem can be reduced to a non-standard asymmetric assignment problem, and introduce an efficient (O(n4)) solution procedure.

Due-Date assignment with acceptable lead-times on parallel machines

We study the bicriteria scheduling of equal length jobs on uniform parallel machines. By introducing a new scheduling model, called single-machine scheduling with generated completion times (shortly, GCT-scheduling), we show that the scheduling of equal length jobs on uniform parallel machines can be polynomially transformed into the single-machine GCT-scheduling with a special setting of generated completion times. In the GCT-scheduling, a sequence of completion times is given in advance and the job scheduled at the i-th position will be assigned the i-th completion time. We present a comprehensive study on the complexities of the bicriteria single-machine GCT-scheduling problems with respect to various regular criteria. We then turn these complexity results into the forms of bicriteria scheduling of equal length jobs on uniform (or identical) parallel machines. Our research generalizes the existing results on bicriteria scheduling of equal length jobs in the literature. Particularly, one of our results solves the open problem posed by Sarin and Prakash (J Comb Optim 8:227–240, 2004), which asks for minimizing the total weighted completion time subject to the optimality of minimizing the total number of tardy jobs on identical parallel machines, and we show that this problem is solvable in polynomial time.

We study the scheduling problem with a common due date on two parallel identical machines and the total early work criterion. The problem is known to be NP-hard. We prove a few dominance properties of optimal solutions of this problem. Their proposal was inspired by the results of some auxiliary computational experiments. Test were performed with the dynamic programming algorithm and list algorithms. Then, we propose the polynomial time approximation scheme, based on structuring problem input. Moreover, we discuss the relationship between the early work criterion and the related late work criterion. We compare the computational complexity and approximability of scheduling problems with both mentioned objective functions.

MILP models to minimise makespan in additive manufacturing machine scheduling problems

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent and asymmetric earliness and tardiness unit costs. The scheduler may process only a subset of the jobs, i.e. the option of job-rejection is allowed. The objective function consists of three cost components: the total earliness-tardiness cost of all scheduled jobs, the cost of the common due-date, and total rejection cost. For a given number of rejected jobs and a given due-date, the problem is reduced to a non-standard linear assignment problem. Consequently, the optimal solution is shown to be obtained in polynomial time in the number of jobs. The case of a given (possibly restrictive) due-date, the extension to a setting of more than two machines, and a number of special cases, are also discussed.

Two extensions of the classical scheduling model with two parallel identical machines and a partially ordered set of unit execution time tasks are considered. It is well known that the Coffman—Graham algorithm constructs for this model a so-called ideal schedule: that is, a schedule which is optimal for both makespan and total completion time criteria simultaneously. The question of the existence of such a schedule for the extension of this model, where each task has a release time, has remained open over several decades. The paper gives a positive answer to this question and presents the corresponding polynomial-time algorithm. Another straightforward generalization of the considered classical model is obtained by the introduction of multiprocessor tasks. It is shown that, despite the fact that a slightly modified Coffman-Graham algorithm solves the makespan problem with multiprocessor tasks for arbitrary precedence constraints, generally an ideal schedule does not exist and the problem with the criterion of total completion time turns out to be NP-hard in the strong sense even for in-trees.

In this paper, we propose an innovation strategy in the industry (case of the scheduling problem on two parallel identical machines), with the objective of minimizing the weighted sum of the end dates of jobs, this problem is NP-hard. In this frame, we suggested a novel heuristics: (H1), (H2), (H3), with two types of neighborhood (neighborhood by SWAP and neighborhood by INSERT). Next, we analyze the incorporation of three diversification times (T1), (T2), and (T3) with the aim of exploring unvisited regions of the solution space. It must be noted that job movement can be within one zone or between different zones. Computational tests are performed on 6 problems with up to 2 machines and 500 jobs.

In this paper, we investigate online scheduling problems on two parallel identical machines under a grade of service provision with makespan as the objective function. The jobs arrive over time and each job can be scheduled only when it has already been arrived. We consider three different versions: (i) the two machines cannot be idle at the same time until all arrived jobs have been processed; (ii) further to the first problem, jobs are processed on a first-come, first-serviced basis; (iii) each job must be assigned to one of the two machines as soon as it arrives. Respectively for three online scheduling problems, optimal online algorithms are proposed with competitive ratio $$ (\sqrt 5 + 1)/2 $$ , $$ (\sqrt 5 + 1)/2 $$ and $$ 5/3 $$ .

This paper addresses the problem of scheduling n jobs on a single machine and on m identical parallel machines to minimize the completion time variance of jobs. This problem of scheduling jobs on parallel machines is motivated by a case study in an automobile ancillary unit. First, a heuristic to solve the single-machine scheduling problem is proposed. The parallel-machine scheduling problem is solved in two phases: job-allocation phase and job-sequencing phase. Two heuristics are proposed in the job-allocation phase, whereas in the job-scheduling phase, the single-machine scheduling approach is used. In this paper, both versions of parallel-machine scheduling problem (restricted and unrestricted) are considered. A good upper bound is obtained using a genetic algorithm, to evaluate the performance of the proposed heuristics for the parallel-machine scheduling problem. An extensive computation evaluation of the proposed heuristics is presented for both single-machine scheduling problem and the parallel-machine scheduling problem (especially considering the case study), along with the comparison of performances with the existing heuristics in the literature.

In this paper, we discuss a scheduling problem for jobs on identical parallel machines. Ready times of the jobs, precedence constraints, and sequence-dependent setup times are considered. We are interested in minimizing the performance measure total weighted tardiness. Scheduling problems of this type are quite important in semiconductor manufacturing. We suggest a variable neighborhood search (VNS) scheme for this problem. Based on computational experiments with stochastically generated test instances we are able to show that the VNS approach clearly outperforms heuristics based on the apparent tardiness cost with setups and ready times (ATCSR) dispatching rule in many situations.

Consider a flexible flow shop with s stages in series and at each stage a number of identical machines in parallel. There are n jobs to be processed and each job has to go through the stages following the same route. Job j has release date rj, due date dj, weight wj and a processing time pjl at stage l, l=1,…,s. The objective is to minimize the total weighted tardiness of the n jobs. In this paper we describe and analyse three heuristics. The first one is a decomposition algorithm that solves the problem by decomposing the flexible flow shop problem into a series of single-stage scheduling subproblems. The second one is an algorithm based on local search. The third heuristic is a hybrid algorithm that combines the first two. We conclude with a comparative study of the three heuristics. Copyright © 2000 John Wiley & Sons, Ltd.

Scheduling batches on parallel machines with major and minor set-ups