Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective

This paper presents several search heuristics and their performance in batch scheduling of parallel, unrelated machines. Identical or similar jobs are typically processed in batches in order to decrease setup times and/or processing times. The problem accounts for allotting batched work parts into unrelated parallel machines, where each batch consists of a fixed number of jobs. Some batches may contain different jobs but all jobs within each batch should have an identical processing time and a common due date. Processing time of each job of a batch is determined according to the machine group as well as the batch group to which the job belongs. Major or minor setup times are required between two subsequent batches depending on batch sequence but are independent of machines. The objective of our study is to minimize the total weighted tardiness for the unrelated parallel machine scheduling. Four search heuristics are proposed to address the problem, namely (1) the earliest weighted due date, (2) the shortest weighted processing time, (3) the two-level batch scheduling heuristic, and (4) the simulated annealing method. These proposed local search heuristics are tested through computational experiments with data from dicing operations of a compound semiconductor manufacturing facility.     

A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.     

Optimal schedules for single facility with two job classes

A single facility scheduling problem with jobs divided into two mutually exclusive classes is considered when the setup time depends on the class of jobs immediately preceding the job being currently processed. The jobs in a given class need not be processed together. Based on a combinatorial analysis of the problem, an algorithm is developed to obtain an optimal schedule when the objective is to minimize mean flow time. The proposed algorithm is polynomially bounded in terms of the computational effort needed to solve the problem.     

Scheduling in a manufacturing shop with sequence-dependent setups

In this paper, the problem of scheduling multiple jobs in a flexible manufacturing cell with multiple machine stations is addressed. Due to the large capital investments that usually characterize flexible manufacturing systems (FMS), an area of control of great interest to system users is that of maximizing the system performance through the minimization of machine idle and setup times. The magnitude of total time spent on machine setups and idle times is influenced by the availability of jobs, job mix, similarities of jobs and job scheduling procedure used. Similar jobs on the same machine require less setup times. Similarly, the use of an adequate scheduling method also reduces total idle and setup times. Such reduction improves the flow times of jobs. In this paper, a heuristic algoritm for scheduling jobs with sequence dependent setup times in a FMS is presented. The measure of performance for evaluating schedule adequacy is the production makespan.     

Block models for scheduling jobs on two parallel machines with a single server

We consider the problem of scheduling a set of non-preemptable jobs on two identical parallel machines such that the makespan is minimized. Before processing, each job must be loaded on a machine, which takes a given setup time. All these setups have to be done by a single server which can handle at most one job at a time. For this problem, we propose a mixed integer linear programming formulation based on the idea of decomposing a schedule into a set of blocks. We compare the results obtained by the model suggested with known heuristics from the literature.     

Group scheduling and job-dependent due window assignment based on a common flow allowance

We study a single-machine group scheduling and job-dependent due window assignment problem in which each job is assigned an individual due window based on a common flow allowance. In the group technology environment, the jobs are divided into groups in advance according to their processing similarities and all the jobs of the same group are processed consecutively in order to improve production efficiency. A sequence-independent machine setup time precedes the processing of the first job of each group. A job completed earlier (later) than its due window will incur an earliness (tardiness) penalty. Our goal is to find the optimal sequence for both the groups and jobs, together with the optimal due window assignment, to minimize the total cost that comprises the earliness and tardiness penalties, and the due window starting time and due window size costs. We give an O(n log n)time algorithm to solve this problem.     

Single-machine group scheduling with both learning effects and deteriorating jobs

In the paper two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered. By learning effects, deteriorating jobs and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.     

The use of turnover rate as a passive surveillance indicator for potential low back disorders

Passive surveillance techniques which rely only on injury reporting to locate ergonomic problems within a facility may not be sensitive enough to identify all jobs that place a worker at risk of low back disorder. The current study examines whether turnover rate data provide useful input to a passive surveillance approach. It is hypothesized that the turnover of employees through individual jobs, when not attributable to differential pay scales within a facility, is likely to indicate the presence of ergonomic hazards associated with low back cumulative trauma disorders. This study used the database and multiple logistic regression model developed by Marras et al. (1993) to evaluate this hypothesis. Two data sets were evaluated with the model to determine whether jobs with turnover resemble those with a high historical risk of LB-CTD. The first data set contained trunk motion and workplace data from jobs in which there had been turnover but there were no incidents of LB-CTD. When comparing these data to truly low risk jobs (no LB-CTD incidents or turnover), the model yielded an odds ratio of 5·2. This moderate odds ratio indicates that many of the jobs with turnover have characteristics similar to those found in high LB-CTD risk jobs. The second data set included jobs with turnover and moderate LB-CTD incident rates. The model's resulting odds ratio of 11·0 indicates that jobs with moderate incident rates and turnover are very similar to jobs with a high LB-CTD risk. These results suggest that passive surveillance programs would be more sensitive if turnover rates were determined for each job within a facility and were used to supplement incident rate data.     

A non-delayed relax-and-cut algorithm for scheduling problems with parallel machines,due dates and sequence-dependent setup times

Consider the problem of scheduling a set of jobs to be processed exactly once, on any machine of a set of unrelated parallel machines, without preemption. Each job has a due date, weight, and, for each machine, an associated processing time and sequence-dependent setup time. The objective function considered is to minimize the total weighted tardiness of the jobs.This work proposes a non-delayed relax-and-cut algorithm, based on a Lagrangean relaxation of a time indexed formulation of the problem. A Lagrangean heuristic is also developed to obtain approximate solutions.Using the proposed methods, it is possible to obtain optimal solutions within reasonable time for some instances with up to 180 jobs and six machines. For the solutions for which it is not possible to prove optimality, interesting gaps are obtained.     

Optimal due date assignment and resource allocation in a group technology scheduling environment

We study a single machine scheduling problem in which the scheduler determines due dates for different jobs in a group technology environment. In group technology (GT) environment, a partition of the jobs into groups (families) is given and jobs of the same family are required to be processed consecutively. The partition of the jobs into families is done in order to achieve efficiency of high-volume production by exploiting similarities of different products and activities in their production. Since customers of similar jobs may expect that all jobs within the same group will be assigned with the same due date, we suggest an original due date assignment method in which all jobs within a family are restricted to be assigned the same due date, while each family can be assigned a due date without any restriction. The proposed method provides an extension of two earlier methods that appear in the literature, one which includes a single family and the other in which the number of families is identical to the number of jobs. Our objective is to find the job schedule and the due date for each group that minimizes an objective function which includes earliness, tardiness and due date assignment penalties. We also extend the analysis to address the case in which the job processing times are resource dependent. For this case we include the total weighted resource consumption and the makespan penalties to the objective function.     

A heuristic approach for single-machine scheduling with due dates and class setups

The single-machine sequence-independent class setup scheduling problem is examined in this paper. It is assumed that jobs are classified into classes and a setup is required between jobs of different classes, but not of the same class. Furthermore, this setup time is fixed and depends only on the current job. Since the problem is NP-hard, a heuristic algorithm is proposed to find an approximate schedule that minimizes the maximum lateness on a set of jobs. The algorithm can easily be modified to solve the maximum tardiness problems as well. The accuracy of the heuristic algorithm in generating near optimal solutions is empirically evaluated.Scope and purposeFor batch manufacturing, it maybe desirable to produce many items of the same type, or class, at the same run in order to save the setup cost. However, committing facilities to long production runs for one product may inevitably make others tardy. Small batch size may conform urgent jobs to their delivery date, but one of the consequences would be the loss of productive efficiency due to numerous setups. Therefore, scheduling is basically a trade-off between the inherently conflicting efficiency measure and due-date compliance. This paper considers a single-machine scheduling problem in which jobs are classified into classes and a setup is required between jobs of different classes. The setup time is fixed and depends only on the current job. This problem is called a sequence-independent class setup problem and is NP-complete.     

Scheduling injection molding operations with multiple resource constraints and sequence dependent setup times and costs

This paper addresses a production scheduling problem in an injection molding facility. It appears to be the first attempt to schedule parallel machines for multiple items in presence of multiple capacitated resource constraints with sequence-dependent setup costs and times. The objective is to meet customer demands while minimizing the total inventory holding costs, backlogging costs and setup costs. We present a mathematical formulation of the problem. The computational complexity associated with the formulation makes it difficult for standard solvers address industrial-dimensioned problems in reasonable solution time. To overcome this, a two-phase workcenter-based decomposition scheme has been developed in this paper. The computational results for different problem sizes demonstrate that this scheme is able to solve industrial-dimensioned problems within reasonable time and accuracy.     

A tabu search heuristic for a sequence-dependent and time-dependent scheduling problem on a single machine

This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.     

Scheduling problems with deteriorating jobs and learning effects including proportional setup times

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered setup times. We introduce a new scheduling model in which job deterioration and learning, and setup times are considered simultaneously. In the proposed model, the actual processing time of a job is defined as a function of the setup and processing times of the jobs already processed and the job’s own scheduled position in a sequence. In addition, the setup times are assumed to be proportional to the actual processing times of the already scheduled jobs. We derive polynomial-time optimal solutions for some single-machine problems with or without the presence of certain conditions.     

On-line scheduling of two parallel machines with a single server

In this paper, we consider the on-line scheduling of two parallel identical machines sharing a single server with the objective of minimizing the latest completion time of all jobs. Each job has to be setup by the server before being processed on one of the machines. Three special cases: equal length jobs, equal processing times and regular equal setup times are considered and the asymptotic competitive ratios of list scheduling are determined. Also, a lower bound for the equal length job case is given, and two heuristics with tight asymptotic competitive ratios for the other two cases are proposed.     

One-machine scheduling problems with deteriorating jobs and position-dependent learning effects under group technology considerations

In this paper, we introduce a group scheduling model with general deteriorating jobs and learning effects in which deteriorating jobs and learning effects are both considered simultaneously. This means that the actual processing time of a job depends not only on the processing time of the jobs already processed, but also on its scheduled position. In our model, the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent learning effects and time-dependent deterioration. The objective of scheduling problems is to minimise the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.     

Modeling realistic hybrid flexible flowshop scheduling problems

This paper aims to contribute to the recent research efforts to bridge the gap between the theory and the practice of scheduling by modelizing a realistic manufacturing environment and analyzing the effect of the inclusion of several characteristics in the problem formulation. There are several constraints and characteristics that affect the scheduling operations at companies. While these constraints are many times tackled in the literature, they are seldom considered together inside the same problem formulation. We propose a formulation along with a mixed integer modelization and some heuristics for the problem of scheduling n jobs on m stages where at each stage we have a known number of unrelated machines. The jobs might skip stages and, therefore, we have what we call a hybrid flexible flowshop problem. We also consider per machine sequence-dependent setup times which can be anticipatory and non-anticipatory along with machine lags, release dates for machines, machine eligibility and precedence relationships among jobs. Manufacturing environments like this appear in sectors like food processing, ceramic tile manufacturing and several others. The optimization criterion considered is the minimization of the makespan. The MIP model and the heuristics proposed are tested against a comprehensive benchmark and the results evaluated by advanced statistical tools that make use of decision trees and experimental designs. The results allow us to identify the constraints that increase the difficulty.     

Capacitated facility location problem with general setup cost

This paper presents an extension of the capacitated facility location problem (CFLP), in which the general setup cost functions and multiple facilities in one site are considered. The setup costs consist of a fixed term (site setup cost) plus a second term (facility setup costs). The facility setup cost functions are generally non-linear functions of the size of the facility in the same site. Two equivalent mixed integer linear programming (MIP) models are formulated for the problem and solved by general MIP solver. A Lagrangian heuristic algorithm (LHA) is also developed to find approximate solutions for this NP-hard problem. Extensive computational experiments are taken on randomly generated data and also well-known existing data (with some necessary modifications). The detailed results are provided and the heuristic algorithm is shown to be efficient.     

Tool-feeder partitions for module assignment in PCB assembly

The assembly of electronic components on printed circuit boards is performed in a line of automated placement machines, each equipped with a feeder unit that contains the component reels required for a product type. Assembling multiple product types by a single machine requires the replacement of certain components in the feeder unit. Increasingly, assembly machines are equipped with modular feeder units, enabling the replacement of a larger group of component reels. To minimize the machine setup time, component reel modules can be preassigned with the necessary component types, thus requiring only the loading of a suitable module set for each product. This work introduces and analyzes the problem of constructing the minimum number of component reel modules, with the objective that a set of jobs can be manufactured without individual component reel changes. We show that the problem is NP-hard and provide an integer programming formulation for it. We also introduce two heuristics based on job grouping, and analyze the results.     

Scheduling non-similar groups on a flow line: multiple group setups

This research addresses lead-time reduction and makespan minimization for cut and sew operations of upholstered furniture manufacturing through efficient scheduling. Jobs are grouped based on different characteristics at each operation of this two stage flow line. There are identical parallel machines at each stage and jobs proceed individually from the 1st stage to the 2nd. A heuristic for the case of multiple setups per group at the 2nd stage is developed, compared to a single setup per group at each stage, and integrated into a genetic algorithm. Results demonstrate that the heuristic effectively adds minimal setups to a single setup schedule while significantly improving schedule makespan.