Improving Urgency-based Backlog Sequencing of Jobs: An Assessment by Simulation

When order release is applied, jobs are withheld in a backlog from where they are released to meet certain performance targets. The decision that selects jobs for release is typically preceded by a sequencing decision. It was traditionally assumed that backlog sequencing is only responsible for releasing jobs on time, whereas more recent literature has argued that it can also support load balancing. Although the new load-based rules outperform time-based rules, they can be criticized for requiring workload information from the shop floor and for delaying large jobs. While some jobs will inevitably be delayed during periods of high load, we argue that this delaying decision should be under control of management. A simulation study of a wafer fab environment shows that a time-based rule matches the performance of more complex load-based backlog sequencing rules that have recently emerged. The new rule realizes the lowest percentage of tardy jobs if the lower bound that distinguishes between early and urgent jobs is set appropriately. It provides a simpler means of improving release performance, allowing managers to delay jobs that have adjustable due dates.


Introduction
Protecting throughput from variance is the key to achieving lean (Hopp & Spearman, 2004). If order release is applied, jobs (or orders) are not immediately released onto the shop floor upon arrival at the production system, but release is controlled to meet certain performance targets, which creates a so-called backlog or pre-shop pool that effectively buffers the shop floor. Wellknown approaches to order release include Constant Work-in-Process (ConWIP; e.g. Spearman et al., 1990;Hopp & Spearman, 2004;Jaegler et al., 2018), Drum-Buffer-Rope (DBR, e.g. Goldratt & Cox, 1984;Simons & Simpson, 1997;Watson et al., 2007), and Workload Control (e.g. Cigolini, & Portioli-Staudacher, 2002;Portioli-Staudacher & Tantardini, 2011;Thürer et al., 2012;Haeussler & Netzer, 2020), among others. Meanwhile, a similar logic is also implemented in more recent manufacturing paradigms, such as cloud manufacturing (e.g., Delaramet et al., 2022, Wu et al., 2021, Liu et al., 2017, Soualhia et al., 2017and Xu et al., 2014. The decision concerning which jobs to release is typically subdivided into a backlog sequencing decision, which determines the sequence in which jobs are considered for release, and a selection decision, which decides for each job, in sequence, whether it should be released given certain release criteria, e.g., applying a limit to the workload released to a station. Most studies on order release have focused on the selection decision, implicitly assuming that the sequencing decision should use some measure of urgency. Only recently it has been shown that incorporating load considerations in the sequencing decision can improve performance in the context of Workload Control (e.g., Thürer et al., 2015), ConWIP (e.g., Thürer et al., 2017) and DBR (e.g., Thürer et al., 2018). However, including load considerations requires feedback from the shop floor and significantly increases the complexity of the backlog sequencing decision. The challenge is whether simple time-based rules can be developed that mimic the behavior of load-based rules but without requiring regular information being fed-back from the shop floor.
Taking a closer look at load-based backlog sequencing rules reveals that they gain an advantage by delaying large jobs during periods of high load. In other words, during periods when the incoming workload largely exceeds the available capacity, load-based rules focus on producing as many small jobs on time as possible to the detriment of some large jobs. It has long since been shown that this improves overall performance (Land et al., 2010). In this study, we mimic this behavior by proposing a new urgency-based rule that creates three classes of jobs: early (non-urgent), urgent, and very urgent. Using a simulation model of a re-entrant flow shop (Graves et al., 1983) we conjecture that prioritizing urgent over very urgent jobs leads to similar results to those obtained for load-based sequencing, but in a simpler way.
Re-entrant flow shops are of high practical relevance. They can be found, for example, in semiconductor wafer fab environments (see e.g., Muhammad et al., 2015) and in flexible manufacturing systems (see e.g., Rifai et al., 2016). Moreover, the advent of lean management and industry 4.0 fostered a product-based view instead of a resource-based view (Fullerton et al. 2014).
This enables companies to streamline their production systems, so products can be manufactured using a fixed sequence of flexible resources (Kundu et al., 2020). But re-entrant flow shops are also very challenging environments for order release methods (Neuner & Haeussler, 2021) since jobs repeatedly pass through the same station (or stations) at different stages of processing. Our new rule not only provides a simpler means of improving order release performance in such contexts, but by using dedicated classes of jobs based on urgency it also facilitates the selection of those jobs that should be delayed in practice. The new rule mainly differs from load-based rules by not requiring feedback information from the shop floor.
The remainder of this paper is structured as follows. The literature is next reviewed in Section 2 to identify the order release method and the alternative backlog sequencing rules to be considered in our study. Section 3 then outlines the simulation model used to evaluate performance before the results are presented and discussed in Section 4. Finally, Section 5 puts forward a conclusion and outlines the managerial implications and limitations of the study.

Literature Review
This section identifies the order release method, and the backlog sequencing rules to be included in our study in Section 2.1 and Section 2.2, respectively. A discussion of the literature is then presented in Section 2.3.

Order Release
Given its importance, several Workload Control release methods have been proposed in the literature, see e.g., the reviews by Wisner (1995), Fredendall et al. (2010), Bagni et al. (2021) and Gomez Paredes et al. (2022). In this paper, we use a continuous version of Workload Control order release given its good performance in previous studies (see e.g., Fernandes & Carmo-Silva, 2011).
Workload Control restricts the load released to stations on the shop floor by load norms or load limits. Whenever a new job (or order) arrives to the production system, or whenever an operation is complete on the shop floor, the following steps are executed to decide on the release of jobs: (1) Jobs waiting for release in the backlog are sorted according to a sequencing rule, and the job with the highest priority is considered for release first.
(2) If the load that results from releasing the job does not exceed the load norms for all stations in its routing, then the job is selected for release and released. Otherwise, the job remains in the backlog and the job with the next highest priority is considered for release.
(3) The release procedure stops when all jobs in the backlog have been considered for release or when there are no more jobs in the backlog to be released.
The load contribution to a station is calculated by dividing the processing time of the operation at a station by the station's position in a job's routing (Oosterman et al., 2000). That is, : = + ∀ ∈ , where is the workload released to station s, i is the station position in the routing of the job, is the processing time of job j at the i th operation in its routing, and the set of jobs awaiting release in the backlog.

Backlog Sequencing Rules
Many backlog sequencing rules have been applied in the literature. Most of this literature has assumed that backlog sequencing is only responsible for ensuring that orders are released on time.
Consequently, most studies have applied a time-oriented backlog sequencing rule. For example, MODCS considers two classes of jobs, urgent and non-urgent, depending on whether jobs have a planned release date (refer to Equation (1)) that has already been passed or not. Urgent jobs have priority over non-urgent jobs. Urgent jobs are sequenced according to the Capacity Slack CORrected (CSCOR) rule. Non-urgent jobs are sequenced according to PRD rule. CSCOR is a load-oriented rule that sequences jobs according to a capacity slack ratio, as given by Equation (2).
The capacity slack ratio integrates three elements into one priority measure: the workload contribution of a job to a station, ; the load gap, at the station that process the i th operation of a job, and the number of operations in the routing of the job, i.e., the routing length nj. The latter is used to average the ratio between workload contribution to stations and load gap at stations across the routing of the job. The lower the capacity slack ratio, , the higher the priority of job j. This capacity slack rule was originally proposed by Philipoom et al. (1993) and later used, e.g., by Fredendall et al. (2010).

Discussion
Studies comparing the performance of different sequencing rules (e.g., Fredendall et al., 2010;Thürer et al. 2015) showed that load-based rules (i.e., CS and MODCS) outperform time-based rules. However, there are two major issues. First, the CSCOR rule is rather complex and requires detailed information from the shop floor. Second, the CSCOR rule gains advantage by delaying larger jobs. This behavior is maintained also within MODCS during periods of high load when many jobs tend to become urgent. In this study we seek to address both issues by asking:

Can a new backlog sequencing rule be designed that matches the high performing MODCS rule whilst only considering job information and enabling a more controlled decision to be taken on which jobs to delay?
In response, we propose a new time-oriented rule. This rule creates three classes of jobs based on urgency given by the PRD of the job, as illustrated in Figure 1: early (non-urgent), urgent, and very urgent. We then conjecture that prioritizing urgent over very urgent jobs provides similar results to those obtained for MODCS, despite the relative simplicity of the new rule. The new rule differs from load-based rules as it does not require feedback information from the shop floor. It only requires a PRD to be determined for each job to create three classes of urgency that then are used to prioritize jobs. By using dedicated classes, the new rule also facilitates the selection of jobs that should be delayed in practice. In general, it should be noted that, as per the definition, some jobs will almost inevitably be delivered tardy during periods of high load . The simulation model used to test our conjecture and the experimental design will be outlined next in Section 3.

Simulation
A simulation model of a re-entrant flow shop has been implemented using ARENA ® software. In the model job inter-arrival times, processing times and due dates are stochastic variables. The reentrant flow shop considered here is balanced and consists of three stations, each with two machines preceded by a single input buffer. Job routings are based on the six-step Mini-Fab model of Kempf (1994), as depicted in Figure 2. That is, the production of each job is completed following a sequence of six processing steps. In this study it is assumed that all materials for job processing are available and all the required information regarding job routings, job processing times, etc. is known at order arrival. This is in line with previous simulation studies on order release control (e.g., Fredendall et al., 2010;Thürer et al., 2012, 2019, Fernandes et al., 2018. Processing times at machines follow a lognormal distribution with a mean of one time unit. Processing time variability of jobs is considered an experimental factor. We consider three levels for the coefficient of variation (cv) of the processing times, namely: 0.1, 0.2 and 0.4. We further assume that set-up times are sequence independent and considered to be part of the operation processing times. To avoid moving away from the focus of the research question and to avoid confounding factors, batch processing and unreliable machines have not been considered. The inter-arrival time of jobs to the shop follows an exponential distribution. The mean of this distribution was defined to result in a system steady-state utilisation rate of 90%. Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Station 1 Machines A, B

Order Release and Backlog Sequencing
Six setting of the load norms are considered, namely 4, 5, 6, 7, 8 and 9 time units. As a baseline a setting of immediate release (IMR) of jobs to the shop floor is also considered, i.e., without controlled order release. Since EDD and PRD backlog sequencing are equivalent in shops with a single routing for all jobs, only PRD will be considered. We consequently consider three backlog

Dispatching
Jobs waiting in the input buffer of a station are prioritized according to operation due dates. The operation due date for the last operation in the routing of a job is equal to the due date of the job, as given by formula (1), while the operation due date of each preceding operation is determined by successively subtracting the estimated station waiting time and processing time from the operation due date of the next operation. In this study, estimated station waiting times are given by the cumulative moving average, i.e., the average of all station waiting times realized until the current simulation time.

Experimental Design and Performance Measures
Our study considers three experimental factors tested at different levels: ( The key performance measures considered are the total throughput time, the percentage of tardy jobs and the mean tardiness. The total throughput time refers to the time that elapses between job entry to the system and job completion. The percentage of tardy jobs refers to the percentage of jobs completed after their due date. Tardiness is defined to be zero if the job is on time or early and it is equal to the completion date minus the due date if the job is late. In addition, we also measure the average shop floor throughput time, which is used as an instrumental performance variable. While the total throughput time includes the time that jobs wait before being released, i.e., the backlog waiting time, the shop floor throughput time refers to the time that elapses between job release to the shop floor and job completion.

Results and Discussion
An initial statistical analysis of simulation results was conducted using an ANOVA (Analysis of Variance). ANOVA results are presented in Table 2. All main effects and most of the two-way interactions were found to be statistically significant. There were no significant three-way interactions. This can also be observed from the results for the Scheffé multiple comparison procedure, which was applied to obtain a first indication of the direction and size of the performance differences. Table 3 gives the 95% confidence interval. When this interval includes zero, performance differences are not considered to be statistically significant. We can observe significant performance differences for all pairs for at least one performance measure except for between FCFS and PRD, which perform statistically equivalent. This will be explored further in Section 4.1 and Section 4.2 where detailed performance results will be presented and their robustness evaluated.

Performance Assessment
Results for a coefficient of variation (cv) of the processing times of 0.1 together with the 95% confidence intervals are given in Table 4. Results for different levels of the CVs will be presented as part of our robustness analysis in Section 4.2.  only occurs at tighter norms, it was found not to be statistically significant in our ANOVA.
Most importantly, our new backlog sequencing rule has the potential to outperform existing backlog sequencing rules if the lower bound that distinguishes between early and urgent jobs is set appropriately. The results further highlight that there is no best rule for all performance measures.
NEW(-5) allows the lowest percentage of tardy jobs to be obtained, while NEW(-1) approaches the tardiness values of MODCS and PRD. Meanwhile, if the lower bound is set too large/loose (i.e., PRD minus 10 time units), then we increase the set of urgent jobs to include some jobs that are still early. As a result, the number of very urgent jobs is likely to increase, resulting in worse performance. This can be observed from Table 5, which provides more detailed information on the tardiness of jobs for a workload norm level of 4 time units. The results in Table 5 highlight that: (i) both MODCS and our new rule improve overall performance by delaying some jobs and (ii) it is important for our new rule to capture only the jobs that are at risk of becoming tardy and still have a chance of being delivered on time as part of the urgent class of jobs that are released first.

Robustness Analysis
The relative performance of the different backlog sequencing rules is also not affected by the cv of the processing times. This can be observed from Table 6 and Table 7, which give the results for a cv of 0.2 and 0.4, respectively. The main effect of the CV is on the best-performing norm level.
The best-performing norm level in terms of the mean tardiness remains at five time units, but for the percentage tardy the best-performing norm level increases with the coefficient of variation.
Since we also observe less of an impact on the total throughput time and percentage tardy with an increase to the CV. A higher variability in processing times increases the load balancing opportunities for the release method, which in turn provides 'less room' for the sequencing rules.

Conclusions
Load-based backlog sequencing rules were recently highlighted as an important means to improve order release performance. However, they rely on feedback information from the shop floor and they delay jobs with long processing times during periods of high loads. In answer to our research question -Can a new backlog sequencing rule be designed that matches high performing MODCS rule whilst only considering job information and enabling a more controlled decision to be taken on which job to delay?we have shown that similar performance can be achieved in our simulations by simply subdividing orders in the backlog into early, urgent, and very urgent orders, and then releasing urgent before very urgent orders.
Our new, purely time-oriented rule not only provides a simpler means of improving order release performance, using dedicated classes, but it also facilitates the selection of jobs that is desirable to delay. This allows managers in practice to delay specific jobs for which customer due dates can be adjusted. It puts the control of which jobs to delay in the hand of managers. In fact, it may be an alternative explanation for the Workload Control paradox which recognizes that order release methods often perform better in practice than expected given their simulation results (Bertrand & van Ooijen, 2002). Managers in practice are likely to show exactly this behavioragreeing on new due date allowances for jobs that are otherwise 'hopelessly' delayed.
A main limitation of our study is that we have only focused on one order release method.
Although this is justified by Workload Control arguably being the best order release method for high-variety contexts, future research could assess the impact of our new rule on the performance of alternative release methods, such as ConWIP and DBR. Another limitation is that the study only considered the specific case of a re-entrant flow shop. Future research could consider other shop configurations, e.g., flow shops and job shops. Meanwhile, a main advantage of our new method is that it uses dedicated job classes to determine which jobs should be delayed. This allows for delaying jobs with flexible customer due dates as part of the due date negotiation process.