Common Date Research Articles

Machine scheduling in the presence of sequence-dependent setup times and a rate-modifying activity

Rate modifying activity (RM) is a type of maintenance after which the processing rate of the machine increases. RM is a very new topic in academic studies. However, it is very common in real world situations. In this paper, we study the integrated problem of assigning a common due-date to all jobs, scheduling the jobs and making decisions about the position of RM in a single machine environment in which the setup times are sequence dependent. The objective is minimising the summation of earliness costs, tardiness costs and due date related costs. This problem has never been studied in the literature with any arbitrary criterion. We construct a time-dependent travelling salesman problem (TDTSP) formulation for this problem. The position of the optimal common due date and some dominance properties for the position of RM are presented. A branch and bound (B&B) procedure is developed to solve the problem optimally. Numerical results justify the effectiveness of the B&B method for small problems. For larger problems, two robust metaheuristics are proposed.

Scheduling to a Common Due Date on Unrelated Parallel-Machine with Deteriorating Jobs

This paper explores scheduling to a common due date on unrelated machines with resource allocation and deteriorating jobs. The main purpose is to determine the optimal resource allocation and the optimal job sequence so that the cost function that includes the sum of earliness, tardiness, and resource cost will be minimized. Result showed that the problem is polynomial time solvable when the number of machine is fixed.

Unrelated parallel-machine scheduling simultaneously with rate-modifying activities and earliness and tardiness penalties

In this paper, we consider a scheduling problem simultaneously with rate-modifying activities and earliness and tardiness penalties on an unrelated parallel-machine setting. We assume that each machine has at most one rate-modifying activity to improve its production efficiency during the scheduling horizon and all the jobs have a common due-date. The objective is to determine jointly the optimal positions of rate-modifying activities, the optimal common due-date of all jobs, and the optimal schedule to minimize the sum of earliness and tardiness costs. We show that the problem can be optimally solved in polynomial time.

Common Due-Date Assignment and Scheduling with Sequence-Dependent Setup Times: a Case Study on a Paper Remanufacturing System

In this paper, we report a case study on the common due-date assignment and scheduling problem in a paper remanufacturing system that produces corrugated cardboards using collected waste papers for a given set of orders under the make-to-order (MTO) environment. Since the system produces corrugated cardboards in an integrated process and has sequence-dependent setups, the problem considered here can be regarded as common due-date assignment and sequencing on a single machine with sequence-dependent setup times. The objective is to minimize the sum of the penalties associated with due-date assignment, earliness, and tardiness. In the study, the earliness and tardiness penalties were obtained from inventory holding and backorder costs, respectively. To solve the problem, we adopted two types of algorithms: (a) branch and bound algorithm that gives the optimal solutions; and (b) heuristic algorithms. Computational experiments were done on the data generated from the case and the results show that both types of algorithms work well for the case data. In particular, the branch and bound algorithm gave the optimal solutions quickly. However, it is recommended to use the heuristic algorithms for large-sized instances, especially when the solution time is very critical.

Common Due-Date Assignment and Job Scheduling on Single Machine and Parallel Machines

In this paper we consider a total penalty for the n job, one machine scheduling problem in which all jobs have a common due date. This penalty function is based on the due date value and on the earliness or the lateness of each job in the selected sequence. The main objective is to determine the optimal value of this due date and an optimal sequence to minimize a total penalty function. We prove that the optimal due date result can be generalized to the parallel machine problem. The problem of simultaneously available jobs on several parallel and identical machines. The problem is to find the optimal due date, assuming this to be the same for all jobs and we present a simple heuristic to find an approximate solution. On the basis of a limited experiment, we observe that the heuristic is very effective solution.

Scheduling job classes on uniform machines

We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.

DUE-DATE ASSIGNMENT AND OPTIONAL MAINTENANCE ACTIVITY SCHEDULING PROBLEM WITH LINEAR DETERIORETING JOBS

The focus of this work is to analyze linear deteriorating jobs in a single-machine scheduling problem with due-date assignment and maintenance activity. The linear deteriorating jobs means its processing time is an increasing function of their starting time. The objective is to minimize the total of earliness, tardiness and due-date cost. To solve the scheduling problem addressed in this work, we have to determine the job sequence, the common due-date, and the location of a maintenance activity. We show that the problem can be solved optimally in O(n 2 log n) time.

Single-machine Robust Scheduling with a Common Due Date Considering the Weighted Sum of Earliness and Tardiness(Theory and Methodology)

Single-machine Robust Scheduling with a Common Due Date Considering the Weighted Sum of Earliness and Tardiness(Theory and Methodology)

Single machine scheduling for minimising earliness and tardiness penalties by scatter search approach

This paper proposes a new evolutionary technique named scatter search for scheduling a number of jobs on a single machine against a restrictive common due date. Individual earliness and tardiness penalties for the jobs are under consideration and the objective is to find an optimal schedule, which jointly minimises the sum of the earliness and tardiness costs. In this paper, the results are obtained for numerous benchmark problems generated by Biskup and Feldmann (2001) for common due date (CDD) problems. The best results of each of the benchmark problems of the three meta-heuristic techniques used by Feldmann and Biskup (2003) are selected and they are compared with the results of SS. This methodology provides substantially better results than the benchmark problems. At the same time, this method holds almost the same result as the best results (best-FB) of three meta-heuristic approaches of Feldmann and Biskup (2003).

Single machine multiple common due dates scheduling with learning effects

In this paper, we consider the problem of simultaneous determination of optimal due dates and optimal schedule for the single machine problem with multiple common due dates. The penalty for a job is assumed to be a linear function of the due date and the earliness/tardiness for the job. The objective function is to minimize the total penalty for all jobs. We show that with the introduction of learning to job processing times the problem remains polynomially solvable for a given number of multiple common due dates.

Variable Parameters Lengths Genetic Algorithm for Minimizing Earliness-Tardiness Penalties of Single Machine Scheduling With a Common Due Date

Abstract Modern manufacturing philosophy of just-in-time emphasizes that a job should be completed as close as possible to its due date to avoid inventory cost and loss of customers goodwill. In this paper, the single machine scheduling problem with a common due date, where the objective is to minimize the total earliness and tardiness penalties in the schedule of jobs, is considered. A new genetic algorithm inspired by the philosophy of dynamic programming, where the chromosome and the population lengths are varied from one iteration to another, is proposed.

Single-Machine Scheduling with Due-Date Assignment and Aging Effect under a DeterioratingMaintenance Activity Consideration

This study investigates single-machine due-date assignment and scheduling problems with a job-dependent aging effect under a deteriorating maintenance activity consideration simul-taneously. The maintenance activity can be scheduled immediately after any one of the jobs has been completed. In order to model the problem more realistic, we assume that: (1) once the maintenance activity has been completed, the machine will revert to its initial condition and the aging effect will start anew, and (2) the machine maintenance duration depends on its starting time. The objective is to find the optimal maintenance position as well as the optimal location of the common due-date for minimizing the total of earliness, tardiness and due-date costs. We introduce a polynomial O(n^4) time solution for the problem. We also present two special cases of the problem and show that they can be optimally solved by a lower order algorithm.

Minimizing Arbitrary Earliness/Tardiness Penalties with Common Due Date in Single-Machine Scheduling Problem Using a Tabu-Geno-Simulated Annealing

In this paper, the single machine scheduling problem for a common due date with arbitrary earliness/tardiness penalties is discussed. The objective is to determine the common due date and processing sequence of new jobs together with the re-sequencing of old jobs to minimize the sum of total earliness/tardiness (E/T), completion time, and due date (dd) related penalties. We propose a new approach Tabu-Geno-Simulated Annealing (TGSA) by hybridization of three well-known metaheuristics, which have proven to be effective for this non deterministic polynomial time (NP) hard scheduling problem, namely, genetic algorithms (GA), tabu search, and simulated annealing (SA). Computational results have shown the effectiveness of the proposed approach in comparison with the ad-hoc heuristics on various single-machine scheduling problems. The assessment of the proposed hybridization indicates the efficiency in both the result and the time versus the other methods.

Minimum weighted number of tardy jobs on an m-machine flow-shop with a critical machine

Abstract We study a flow-shop problem, where each of the jobs is limited to no more than two operations. One of these operations is common for all the jobs, and is performed on the same (”critical”) machine. Reflecting many applications, jobs are assumed to be processed in blocks on the critical machine. All the jobs share a common due-date, and the objective is minimum weighted number of tardy jobs. We prove that the problem is NP-hard. Then we formulate the problem as an integer program, and introduce a pseudo-polynomial dynamic programming algorithm, proving that the problem is NP-hard in the ordinary sense. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. Finally, we show that the special case of identical weights is polynomially solvable.

Scheduling with a common due-window: Polynomially solvable cases

The single machine scheduling problem to minimize maximum weighted absolute deviations of job completion times from a common due-date, is known to be NP-hard. However, two special cases have been shown to have polynomial time solutions: the case of unit processing time jobs, and the case of due-date assignment for a given job sequence. We extend both cases to a setting of a common due-window. We show that the unit-job problem includes 12 different sub-cases, depending on the size and location of the (given) due-window. Scheduling and due-window assignment for a given job sequence is solved for a single machine, for parallel identical machines and for flow-shops. For each of the above cases, an appropriate special-structured linear program is presented.

The common due-date early/tardy scheduling problem on a parallelmachine under the effects of time-dependent learning and linear and nonlinear deterioration

This paper considers earliness/tardiness (ET) scheduling problem on a parallel machine environment with common due-date under the effects of time-dependent learning and linear and nonlinear deterioration. In this paper, the effects of learning and deterioration are considered simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. This study shows that optimal solution for ET scheduling problem under effects of learning and deterioration is V-shape schedule under certain agreeable conditions. Furthermore, we present a mathematical model for the problem under study and an algorithm for solving large test problems. The algorithm can solve problems of 1000 jobs and four machines within 3 s on average.

Parallel machine scheduling problem to minimize the earliness/tardiness costs with learning effect and deteriorating jobs

The focus of this work is to analyze parallel machine earliness/tardiness (ET) scheduling problem with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we mean that the processing time of a job is defined by an increasing function of its starting time and a decreasing function of the position in the sequence. We develop a mixed integer programming formulation for the problem and show that the optimal sequence is V-shaped: all jobs scheduled before the shortest jobs and all jobs scheduled after the shortest job are in a non-increasing and non-decreasing order of processing times, respectively. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The illustrative example with 11 jobs for 2 machines and 3 machines shows that the model can easily provide the optimal solution, which is V-shaped, for problem.

A note on due-date assignment and single machine scheduling with a learning/aging effect

This paper considers the learning/aging effect in an n job single machine scheduling problem with common due date. The objective is to determine the optimal common due date and the optimal sequence of jobs that minimizes a cost function in the presence of learning/aging effect. The cost function depends on the individual job earliness and tardiness values; i.e., ∑ j = 1 n { E [ j ] + T [ j ] } . This is a well-known problem when the learning/aging effect is not considered and it is shown in earlier studies that there are more than one optimal sequence and optimal common due dates. It is shown in earlier studies that there are 2 r - 1 optimal sequences to this problem if n is odd, and 2 r optimal sequences if n is even. The value of r is ( n + 1 ) / 2 if n is odd, and the value of r is n / 2 if n is even. In this paper, we derive two bounds B α and B α * for the learning index α . We show that when B α < α < 0 , then the optimal sequence is unique and provide an O ( n log n ) algorithm to obtain this unique optimal sequence and the optimal common due date. We also show that when α < B α * , the optimal sequence is obtained by arranging the longest job in first position and the rest of the jobs in SPT order. Similarly, we derive two bounds A α and A α * for the aging index α . We show that when 0 < α < A α , then the optimal sequence is unique and provide an O ( n log n ) algorithm to obtain this unique optimal sequence and the optimal common due date. We also show that when α > A α * , the optimal sequence is obtained by arranging the jobs in LPT order. We also present a numerical example for ease of understanding.

Parallel machine earliness/tardiness scheduling problem under the effects of position based learning and linear/nonlinear deterioration

This paper considers a parallel machine earliness/tardiness (ET) scheduling problem with different penalties under the effects of position based learning and linear and nonlinear deterioration. The problem has common due-date for all jobs, and effects of learning and deterioration are considered simultaneously. By the effects of learning we mean that the job processing time decreases along the sequence of partly similar jobs, and by the effects of deterioration we mean slowing performance or time increases along the sequence of jobs. This study shows that optimal solution for ET scheduling problem under effects of learning and deterioration is V-shape schedule under certain agreeable conditions. Furthermore, we design a mathematical model for the problem under study and algorithm and lower bound procedure to solve larger test problems. The algorithm can solve problems of 1000 jobs and four machines within 3 s on average. The performance of the algorithm is evaluated using results of the mathematical model.

Minimizing earliness–tardiness penalties for common due date single-machine scheduling problems by a recovering beam search algorithm

This study considers the NP-hard problem of scheduling jobs on a single-machine against common due dates with respect to earliness and tardiness penalties. An effective and efficient recovering beam search (RBS) algorithm is proposed to solve this problem. To validate and verify the developed algorithm, computational experiments are conducted on a well-known benchmark problem set, and the results are compared with nine meta-heuristics from the relevant literature. The experimental comparison results reveal that the proposed RBS algorithm is a state-of-the-art approach to the single-machine scheduling problem with earliness and tardiness penalties. In terms of both solution quality and computational effort, this study successfully develops a near-optimal approach that will hopefully encourage practitioners to apply it to real-world problems.