Dispatching rules for scheduling in assembly jobshops - Part 1

Research on jobshop scheduling has tended to concentrate on the development of dispatching rules for jobs that are independent, i.e. single-component jobs. However, in real-life situations, many jobs involve assembly operations that require scheduling of multiple components through the jobshop where both serial and parallel operations take place. In this two-part paper, we consider the problem of scheduling in assembly jobshops, i.e. jobshops that manufacture multi-level assembly jobs. The development of new and efficient dispatching rules with a view to address various measures of performance related to flowtime and staging delay of jobs is first undertaken. A new concept, called 'operation synchronization date' is introduced and made use of in the new dispatching rules. The best existing dispatching rules and the proposed dispatching rules are relatively evaluated by an exhaustive simulation study. The results indicate that the proposed rules emerge to be superior to the existing ones for most measures of performance.     

Scheduling in dynamic assembly job-shops with jobs having different holding and tardiness costs

Most studies on scheduling in dynamic job-shops assume that the holding cost of a job is given by the flowtime of the job and that the tardiness cost of a job is given by the tardiness of the job. In other words, unit holding and unit tardiness costs of a job are assumed. However, in reality, such an assumption need not hold, and it is quite possible that there are different costs for holding and tardiness for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (manufacturing multilevel jobs) with the consideration of different holding and tardiness costs for different jobs. An attempt is made to develop efficient dispatching rules by incorporating the relative costs of holding and tardiness of jobs in the form of scalar weights. The primary objective of scheduling considered here is the minimization of the total scheduling cost consisting of the sum of holding and tardiness costs. The performance of the scheduling rules in minimizing the individual components of total scheduling cost is also observed. The results of an extensive simulation study on the performance of different dispatching rules show that the proposed rules are effective in minimizing the means and maximums of the primary measure, and are quite robust with respect to different job structures and experimental settings.     

A comparative study of priority dispatching rules in a hybrid assembly/job shop

This paper reports on research conducted on the use of priority dispatching rules in a hybrid assembly/job shop which manufactures both single-component and multiple-component products. A simulation model was constructed and a large stale experiment performed. Statistical analysis of the simulation results indicated significant impact of both the priority rules tested, and the product-mix considered on shop performance.

Among the 12 priority rules tested, the SPT (shortest processing time) rule and the ASMF-SPT (assembly jobs first with SPT as tie-breaker) rule performed very well with respect to measures like lateness, flow time, tardiness, staging time, and percent of jobs tardy. These findings lead to further investigation of a combined priority rule, MIXED, which implements the ASMF-SPT rule at all machine centres that process components of assembly jobs, and the SPT rule at the remaining machine centres which process non-component jobs. The additional research results yielded evidence that the MIXED rule can reduce the staging time of the SPT rule, and yielded betrer results than the ASMF-SPT rule with regard to other performance measures.

The most interesting finding, however, was the small variation in flow time distribution resulting from use of the MIXED rule when there were more assembly jobs. In an MRP environment, it is especially desirable to have a priority dispatching rule resulting in minimum variation in individual flow times which allows the replenishment lead times to be estimated with greater accuracy.     

A study on the performance of scheduling rules in buffer-constrained dynamic flowshops

Most studies on scheduling in manufacturing systems using dispatching rules deal with jobshops, while there are only few reports dealing with dynamic flowshops. It is known that the performance of many dispatching rules in dynamic jobshops is different from that in dynamic flowshops. Moreover, many research reports assume that there are no buffer constraints in the shop, and even those reports dealing with buffer-constrained shops present the evaluation of existing dispatching rules for unconstrained shops in the context of buffer constraints with the consideration of a limited number of objectives of scheduling. In this study, we deal with the problem of scheduling in dynamic flowshops with buffer constraints. With respect to different time-based objectives, the best dispatching rules for scheduling in unconstrained shops have been identified from the existing literature. In addition, two new dispatching rules specially designed for flowshops with buffer constraints are proposed. All dispatching rules under consideration are evaluated in dynamic flowshops with buffer constraints on the basis of an extensive simulation study covering different levels of buffer constraints, shop load or utilization, and missing operations in flowshops. The proposed rules are found to perform better than the existing dispatching rules in buffer-constrained flowshops with respect to many measures of performance.     

An extension of modified-operational-due-date priority rule incorporating job waiting times and application to assembly job shop

The well-known priority dispatching rule MOD (Modified Operational Due Date) in job shop scheduling considers job urgency through ODD (Operational Due Date) and also incorporates SPT (Shortest Processing Time)-effect in prioritising operationally late jobs; leading to robust behaviour in Mean Tardiness (MT) with respect to tightness/looseness of due dates. In the present paper, we study an extension of the MOD rule using job-waiting-time based discrimination among operationally late jobs to protect long jobs from excessive delays by incorporating an ‘acceleration property’ into the scheduling rule. Formally, we employ a weighted-SPT dispatching priority index of the form: (Processing time)/(Waiting time)^α for operationally late jobs, while the priority index is ODD for operationally non-late jobs; and the latter class of jobs has a lower priority than the former class. In the context of Assembly Job Shop scheduling, some existing literature includes considerable focus around the concept of ‘Staging Delay’, i.e., waiting of components or sub-assemblies for their counterparts for assembly. Some existing approaches attempt dynamic anticipation of staging delay problems and re-prioritisation of operations along converging branches. In the present paper, rather than depending on such a centralised and largely backward scheduling approach, we consider a partially decentralised approach, endowing jobs with a priority index yielding an ‘acceleration property’ based on a ‘look-back’ in terms of waiting time, rather than ‘look-ahead’. For the particular case, in our proposed rule, whenα is set at zero and when all jobs at a machine are operationally late, our rule agrees with MOD as both exhibit the SPT effect. In simulation tests of our priority scheme for assembly job shops, in comparison with leading heuristics in literature, we found our rule to be particularly effective in: (1) minimising conditional mean tardiness, (2) minimising 99-percentile-point of the tardiness distribution, through proper choice ofα. We also exploit an interesting duality between the scheduling and queueing control versions of the problem. Based on this, some exact and heuristic analysis is given to guide the choice ofα, which is also supported by numerical evidence.     

Learning dispatching rules using random forest in flexible job shop scheduling problems

In this paper, we address the flexible job-shop scheduling problem (FJSP) with release times for minimising the total weighted tardiness by learning dispatching rules from schedules. We propose a random-forest-based approach called Random Forest for Obtaining Rules for Scheduling (RANFORS) in order to extract dispatching rules from the best schedules. RANFORS consists of three phases: schedule generation, rule learning with data transformation, and rule improvement with discretisation. In the schedule generation phase, we present three solution approaches that are widely used to solve FJSPs. Based on the best schedules among them, the rule learning with data transformation phase converts them into training data with constructed attributes and generates a dispatching rule with inductive learning. Finally, the rule improvement with discretisation improves dispatching rules with a genetic algorithm by discretising continuous attributes and changing parameters for random forest with the aim of minimising the average total weighted tardiness. We conducted experiments to verify the performance of the proposed approach and the results showed that it outperforms the existing dispatching rules. Moreover, compared with the other decision-tree-based algorithms, the proposed algorithm is effective in terms of extracting scheduling insights from a set of rules.     

Using dispatching rules for job shop scheduling with due date-based objectives

This paper addresses the job shop-scheduling problem with due date-based objectives including the tardy rate, mean tardiness and maximum tardiness. The focused approach is the dispatching rules. Eighteen dispatching rules are selected from the literature, and their features and design concepts are discussed. Then a dispatching rule is proposed with the goal of achieving a good and balanced performance when more than one objective is concerned at the same time. First, three good design principles are recognized from the existing rules. Second, it introduces a due date extension procedure to solve a problem of negative allowance time. Third, a job candidate reduction mechanism is developed to make the rule computationally efficient. Lastly, a comprehensive simulation study is conducted with the 18 existing rules as the benchmarks. The experimental results verify the superiority of the proposed rule, especially on the tardy rate and mean tardiness.     

New dispatching rules for shop scheduling: A step forward

This paper provides a set of new dispatching rules for the minimization of various performance measures such as mean, maximum and variance of flow time and tardiness in dynamic shops. A static rule which minimizes the number of tardy jobs is also proposed. To evaluate these proposed rules, their relative performance is analysed in open job shops and reported in comparison with the standard benchmark rules such as the SPT (shortest process time) and EDD (earliest due-date), popular rules like ATC (apparent tardiness cost) and MOD (modified operational due-date), and the best performing rules in current literature such as RR, PT + WINQ, PT + WINQ + SL and AT-RPT. Thereafter, a comparative analysis of the relative performance of these rules is carried out in job shops (with no machine revisitation of jobs) and flow shops (with missing operations on jobs) in dynamic environments. Based on the simulation study and analysis of results in different manufacturing environments viz. job shops and flow shops, observations and conclusions are made, highlighting some interesting aspects about the effect of routeing on the individual performance of rules.     

Learning effective dispatching rules for batch processor scheduling

Batch processor scheduling, where machines can process multiple jobs simultaneously, is frequently harder than its unit-capacity counterpart because an effective scheduling procedure must not only decide how to group the individual jobs into batches, but also determine the sequence in which the batches are to be processed. We extend a previously developed genetic learning approach to automatically discover effective dispatching policies for several batch scheduling environments, and show that these rules yield good system performance. Computational results show the competitiveness of the learned rules with existing rules for different performance measures. The autonomous learning approach addresses a growing practical need for rapidly developing effective dispatching rules for these environments by automating the discovery of effective job dispatching procedures.     

Modelling and analysis of wafer fabrication scheduling via generalized stochastic Petri net and simulated annealing

Some of the important characteristics of the semiconductor wafer fabrication factories are re-entrant process flows, a dynamic and uncertain environment, stringent production control requirements, etc. that pose a major challenge to the scheduling decisions in integrated circuit wafer fabrication process. Keeping in view the high capital investment and quick response to the market changes, it is essential for the integrated circuit fabrication process to exercise effective control on its production operations so that production resources can be employed in a flexible and efficient manner. The present research has focussed on the development of a generalized stochastic Petri net model that faithfully captures dynamic behaviours such as re-entrant processing, machine failures, loading and unloading, etc., pertaining to wafer fabrication. A simulated annealing-based scheduling strategy using mean cycle time and tardiness as performance measures was also developed to obtain an efficient and robust schedule for a known hard problem. Analysis of variance was applied to examine the interaction effects of various scheduling rules and to identify the main as well as the interaction effects of dispatching rules, dispatching rules and set-up rules, and set-up rules and batching rules. Paired t-tests were applied to assess the performance of rule combinations for lot and batch scheduling. The proposed simulated annealing-based solution methodology was tested on a well-known data set adopted from the literature and its performance reveals that simulated annealing-based scheduling rules work better than existing rules in terms of the two performance measures mean cycle time and tardiness.     

Dynamic adjustment of dispatching rule parameters in flow shops with sequence-dependent set-up times

Decentralised scheduling with dispatching rules is applied in many fields of production and logistics, especially in highly complex manufacturing systems. Since dispatching rules are restricted to their local information horizon, there is no rule that outperforms other rules across various objectives, scenarios and system conditions. In this paper, we present an approach to dynamically adjust the parameters of a dispatching rule depending on the current system conditions. The influence of different parameter settings of the chosen rule on the system performance is estimated by a machine learning method, whose learning data is generated by preliminary simulation runs. Using a dynamic flow shop scenario with sequence-dependent set-up times, we demonstrate that our approach is capable of significantly reducing the mean tardiness of jobs.     

Correlation among tardiness-based measures for scheduling using priority dispatching rules

One of the most commonly used methods to schedule manufacturing systems is to use priority dispatching rules (pdrs). It is frequently desired to distinguish the behaviour of pdrs with regard to tardiness-based performance measures. However, the relation among these performance measures is generally not obvious even for simple scheduling strategies such as pdrs. In this paper, we first focus on the maximum tardiness, which is a very interesting performance measure for the decision-maker on the shop floor. However, because of its singularity, it is not trivial to assess. We conducted a simulation study on a benchmark model of a dynamic job-shop system to evaluate the relative performance of a set of pdrs chosen either because they are used extensively or because they exhibit very good performance. Based upon the distribution of the maximum tardiness of these benchmark pdrs, we identify two sub-sets of pdrs. From this, we conducted experiments on the root-mean-square tardiness, which is used to distinguish a system with a few very tardy jobs from a system with a lot of less tardy jobs. The experiments show a positive correlation between maximum tardiness and root-mean-square tardiness. Because of the fact that the root-mean-square tardiness is an aggregate measure, it is much easier to assess than the maximum tardiness. This provides an opportunity to predict the relative performance of pdrs with regard to the maximum tardiness as well as the width of the tardiness by evaluating the root-mean-square tardiness only.     

Heuristic dispatching rule to maximize TDD and IDD performance

Although mean flow time and tardiness have been used for a long time as indicators in both manufacturing plants and academic research on dispatching rules, according to Theory of Constraints (TOC), neither indicator properly measures deviation from production plans. TOC claims that using throughput dollar-day (TDD) and inventory dollar-day (IDD) can induce the factory to take appropriate actions for the organization as a whole, and that these can be applied to replace various key performance indices used by most factories. However, no one has studied dispatching rules based on TDD and IDD performance indicators. The study addresses two interesting issues. (1) If TDD and IDD are used as performance indicators, do those dispatching rules that yield a better performance in tardiness and mean flow time still yield satisfactory results in terms of TDD and IDD performance? (2) Does a dispatching rule exist to outperform the current dispatching rules in terms of TDD and IDD performance? First, a TDD/IDD-based heuristic dispatching rule is developed to answer these questions. Second, a computational experiment is performed, involving six simulation examples, to compare the proposed TDD/IDD-based heuristic-dispatching rule with the currently used dispatching rules. Five dispatching rules, shortest processing time, earliest due date, total profit, minimum slack and apparent tardiness cost, are adopted herein. The results demonstrate that the developed TDD/IDD-based heuristic dispatching rule is feasible and outperforms the selected dispatching rules in terms of TDD and IDD.     

Heuristics for minimizing total weighted tardiness in complex job shops

Semi-conductor manufacturing is arguably one of the most complex manufacturing processes in existence today. A semi-conductor wafer fabrication facility is comprised of batching machines, parallel machines, machines with sequence-dependent set-ups, and re-circulating product flow. The individual job release times and due dates combine with the other processing environment characteristics to form a ‘complex’ job shop scheduling problem. We first present a mixed-integer program (MIP) to minimize total weighted tardiness in a complex job shop. Since the problem is NP-hard, we compare a heuristic based on the MIP (MIP heuristic) with both a tuned version of a modified shifting bottleneck heuristic (SB heuristic) and three dispatching rules using random problem instances of a representative model from the literature. While the MIP heuristic typically produces superior schedules for problem instances with a small number of jobs, the SB heuristic consistently outperforms the MIP heuristic for larger problem instances. The SB heuristic's superior performance as compared to additional dispatching rules is also demonstrated for a larger, ‘real world’ dataset from the literature.     

The Sensitivity of the Relative Effectiveness of Job Shop Dispatching Rules with Respect to Various Arrival Distributions

The study investigates the effects which various arrival rate distributions may have on the relative success of implementing various job shop heuristic dispatching rules. Sixteen different arrival rate distributions are tested on ten dispatching rules. General conclusions imply that the distribution with respect to shape and range of the arrival rate for incoming jobs is not a significant variable in evaluating the relative effectiveness of dispatching rules.     

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.     

Evaluation of the Shortest Processing Time Scheduling Rule with Truncation Process

This paper discusses the development of a scheduling rule and summarizes the results of the evaluation of its performance with respect to some tardiness related criteria. Studies done on job shop scheduling indicated that the simple dispatching rules which mostly perform well with respect to a criterion of performance may have undesirable results with respect to other criteria. In this paper, a scheduling rule with truncation process called SPT-T is introduced and studied. Simulation results showed that the shortcomings of simple dispatching rules are remedied by using the SPT-T scheduling rule.     

Performance of an ant colony optimisation algorithm in dynamic job shop scheduling problems

The goal of the current study is to identify appropriate application domains of Ant Colony Optimisation (ACO) in the area of dynamic job shop scheduling problem. The algorithm is tested in a shop floor scenario with three levels of machine utilisations, three different processing time distributions, and three different performance measures for intermediate scheduling problems. The steady-state performances of ACO in terms of mean flow time, mean tardiness, total throughput on different experimental environments are compared with those from dispatching rules including first-in-first-out, shortest processing time, and minimum slack time. Two series of experiments are carried out to identify the best ACO strategy and the best performing dispatching rule. Those two approaches are thereafter compared with different variations of processing times. The experimental results show that ACO outperforms other approaches when the machine utilisation or the variation of processing times is not high.     

An investigation of cooperative dispatching for minimising mean flowtime in a finite-buffer-capacity dynamic flowshop

Scheduling in a dynamic flowshop that receives jobs at random and unforeseen points in time has traditionally been done by using dispatching rules. This study compares the performances of leading dispatching rules with a cooperative dispatching approach, for the objective of minimising mean flowtime in a flowshop, in which the buffers that hold in-process jobs between machines have finite capacities. Cooperative dispatching employs a consultative and consensus-seeking methodology for deciding which job to dispatch next on a machine. Computational experiments using randomly generated test problems for three different utilisation (congestion) levels are carried out for 5- and 10-machine flowshops, under a wide range of buffer capacities. The results highlight the sensitivity of some of the popular dispatching rules to buffer size. In contrast, cooperative dispatching emerges as a robust method that performs consistently well across the range of buffer sizes and machine utilisations tested. The reductions in mean flowtime obtained by cooperative dispatching, in comparison to the other dispatching rules, are particularly large in flowshops that operate with very tight buffer capacities and elevated levels of congestion     

Some dominance properties for single-machine tardiness problems with sequence-dependent setup

Some dominance properties are proposed for the NP-hard problems of scheduling N jobs on a single machine with due dates, and sequence-dependent setup times. The algorithms based on Ragatz's branch and bound scheme with the dominance properties are developed to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.