Scheduling is a process where data from specific jobs and workloads are arranged, controlled and optimized in a production or manufacturing process. A few of the tasks that scheduling has are to allocate plant and machinery resources, the planification of human resources, organization of production processes, and material purchasing. Every time we get to work on processes for certain services or in manufacturing, we can make use of scheduling techniques. It is believed that most service business are under the process called front-office process because of their levels in customer contact, specific workflows, customization, and a broad scheduling environment. On the other hand, we have back-office process, which has low levels in customer involvement, make use of line work flows, and have available standardized services. When calculating single machine models, a few of the parameters that it should include are processing time, release date, due date, weight, and completion time. For this reason, scheduling has specific dispatching rules for a single machine. The dispatching rule that we will be explaining is SPT, shortest processing time, but we can also find other rules such as ERD (earliest release date), EDD (earliest due date), CR (critical ratio), and WSPT (weighted shortest processing time).
SPT, or shortest processing time, is utilized to schedule the jobs from shortest processing time to the largest. With the help of this rule, we can reduce the flow time and/or the average flow time of the system. The system is considered to be optimal if all the jobs have the same release date. The importance behind scheduling is to facilitate the assignation of jobs to either employees or workstations under specific time periods. Also, when putting process under appropriate scheduling, we obtain effective scheduling to aid managers or upper level supervisors achieve a full potential of available resources for their supply chains. When scheduling under shortest processing time, should keep in mind a set of performance measures to keep control of the data. These parameters include makespan, flow time, late jobs. Makespan is the total amount of time that is required to complete a group of jobs. When we minimize a makespan it is with the goal to prioritize lower costs in a fast manner. Flow time is referred to the time that a job spends on a specific manufacturing or service system. Past due or a late job refers to the total amount of time that a job has missed its due date.
In most cases, more than one job must be processed at one or more workstations, but one job can be completed at one specific workstation because of the many tasks that one station can perform. This is where effective scheduling occurs. If schedules are not carefully planned, we might be running into tardiness in jobs and even waiting times to get jobs completed. For example, when a customer puts in an order for the specific manufacturing of a part, the raw materials must be collected in order to move that order to the first workstation. When deciding to move each job to the next workstation, these decisions face the rate of job arrivals and the processing rate for each job done at each workstation. These decisions lead to develop a schedule to organize the procedures of each job at each stations at appropriate time periods. For this reason, we call this sequencing the jobs to see how to better organize the jobs in order to complete them all in a timely manner.
Sequencing can be introduced into two different types: job shop sequencing and flow shop sequencing. Job shop sequencing focuses on low-to-medium-volume production and uses processes that include jobs or groups of jobs. Just like any other process, job shop generates schedules by priority sequence rules allowing a specific work under a certain time period, in some cases provided by a customer. In order words, the schedule for job shop make it easier to see which workstation will become available for the continuation of the job. This sequence process allows for last-minute information in an order and can be included in the schedule for further time calculations and corrections. Also, job shop sequencing includes specifically SPT and critical ratio (CR). On the other hand, flow shop sequencing is the operations of jobs with line flows and focuses on medium-to-high-volume production using line or continuous flow processes [12].
Throughout the years, we can see that new discrepancies rise when scheduling jobs based on workstations available and processing time. In this article, we learned of the study regarding scheduling an amount of jobs depending on unrelated parallel machines keeping into consideration certain key points. These key points include the number of jobs and the processing time for each independent job. The purpose of this research and experimentation was to optimize the system and to minimize the total cost based on completion time of the jobs on all machines used. As evidence, the authors of this article, found a few surveys that stated that the job processing times can be fixed and constant values. However, because of unexpected happening such as deterioration or uncontrollable processing times, the total completion times are always subject to change because of issues that rise that weren’t expected. A set of algorithm test were done to show that scheduling jobs is in most cases necessary to have an idea of how much a job will take to be completed. Although some set back can occur and we may not have an exact amount of time for the processing time of a job, scheduling makes it easier to plan a job time period lasting [13].
Often times, customer who put in orders for a certain job, expect the job to be completed under a specific time and give a due date. Besides the due date, these orders also go along constraints, maintenance activities, and a list of scenarios of changing processing times. Based on this article, we learn that due dates on a job go hand in hand with scheduling problems in the production planning because management face issues with the due dates for a specific number of jobs. We earlier learned that scheduling aides with the optimization sequencing of jobs. However, all jobs, including technological, assembly, classical deterministic models all have different processing times. Some may have constraints for the completion of that job, but other may have a constant number as the processing time because it may be a repetitive job. This article provides us with real-life scenarios to show the different types of scheduling errors that may come up in a job. In some cases, some assignments schedule has a controllable processing time and the scheduler can speed up a job [14].
With so many issues with scheduling happening, the authors of this article created a new technique to somewhat end with these problems. This new technique improves the running times of the jobs by illustrating the technique with two different problems. One of those problems was scheduling on unrelated parallel machines with costs and the job shop scheduling problem. As stated by the authors of this article, the main goal is to emphasize a fair general idea to obtain approximation schemes for makespan minimization problems. The results of this technique will be applied to speed up and significantly simplify all previously mentioned schemes for scheduling issues. The main idea of this technique is to reduce the number of jobs to a constant and apply enumeration or dynamic programming towards the end by performing the following steps: rounding and profiling, grouping, and enumerating.
As mentioned before, shortest processing time (SPT) is a priority sequencing rule that specifies that the job requiring the shortest processing time is the next job to be processed. When sequencing jobs, we can both do it for jobs with one workstation but also with multiple workstations. Jobs with a single workstation are divided into two dimension rules. The first dimension is single, which determine a priority of a single aspect job based on the arrival time, due date, or the processing time. The second dimension rule is multiple, which apply to more than one aspect of the job, previously mentioned in the single-dimension rule. To schedule jobs for multiple workstations, we must determine when a workstation become idle, and from the waiting in line jobs, we choose the job with the highest priority to complete. To help us have a better understanding on SPT, the example we will see in the following pages will explain this topic into detail regarding sequencing work at single workstations, multiple workstations, flow time, and past due or tardy jobs.
Background
Scheduling first became known before the 1990s, this happened due to the systemized manufacturing that started taking place in venetian arsenals, mills and american armouries. Although not called scheduling, the process that these manufacturers used contained high volumes of products which were manufactured, yet they had not created a term for their manufacturing logic. It wasn’t until the 1830’s that concepts such as quality and production became important enough for manufacturers to worry about their manufacturing logic.
Due to the expansion of manufacturing in the 1850’s, manufacturers started looking for ways to optimize their production processes. It wasn’t until 1896, when a man called Lewis discussed manufacturing management, which included the importance of the layout of manufacturing plants, cost accounting, and shipping. Slowly more people started studying the general states of manufacturing which included control and organization, which later proved to be a challenge for manufacturers.
During the 1900’s to 1930’s systemization of manufacturing processes became popular. Many publications from authors such as Ford, Diemer and Taylor, included different ranges of topics that had to do with processes in manufacturing such as process arrangements, mass production, chain management, hand to mouth inventory and many more. Although oftentimes many manufacturing activities required little work and supervision, exclusions such as just in time inventory existed. Although these tools such as just in time existed, it is known that companies rarely used these manufacturing techniques, tools and concepts. Companies did not take advantage of the advances in manufacturing knowledge and managed their efforts with simple tracking and basic controls.
Manufacturers advanced in topics such as economic order quantity and forecasting, but for topics such as planning and scheduling there was very little advancement in mathematical analysis. During the 1960’s, manufacturers found it quite difficult to plan and schedule tasks within their facilities. These problems led to the slow evolution of the first ever computer meant for businesses and scheduling, making it one of the major developments for manufacturers at the time. Although the computer was a major advancement, many companies did not use it and continued using the statistical order quantity. By the year 1970, many manufacturers were struggling to keep up with production and scheduling by hand due to the many options available to the consumer. It became more difficult for companies to have duplicated equipment for each one of their products due to the wide range of products available, this led to the adoption of a functional factory style. With this, they found that their approach did not help them oversee their inventory, therefore the use of the Material Requirements Planning (MRP) approach became a more acceptable idea [1]. MRP is a computer based system which can develop plans for production and scheduling. Some of the outputs of this system include, planned order schedule, and changes to planned orders. MRP lots include, fixed order quantity, periodic order quantity, and lot for lot.
The MRP processes still contained several difficulties that needed to be solved before it the approach could be successful. One of the main problems was that the lead time was used independently of the plant status, it contains high reliability, inventory, the process is stable, and products were not able to go in or out the line. Movements and products are constantly changing in the assembly line and inventories oftentimes change depending on the demand. MRP has a difficulty if the process is not stable and cannot determine whether more product needs to be stored in inventory, therefore it became difficult for manufacturers to use this approach. Although this approach comes with some difficulties, some manufacturing situations were able to work well with it, which successfully led to the development of a broader and similar approach which was called Manufacturing Resource Planning II. This new plan provided a closed loop manufacturing management system that allowed for the integration of normal material database with more functions including, finance, planning, accounting and logistics.
Within this MRP II system, operations scheduling existed. Operations scheduling allowed for the sequencing and scheduling of manufactured goods. These scheduling processes included Shortest processing time (SPT), which allows for the maximization of workstation usage and minimizes the average job flow time [2]. There are now several scheduling techniques available to use for production operations, but for this paper we will be focusing in SPT and how it is used.
Results
Most sequencing rules usually base a job’s priority assignment according to the jobs waiting for processing at the individual workstation. These are single-dimension rules because they determine priority based on a single characteristic of the job [9]. This can be shown with the example below:
Example 1
The Taylor Machine Shop rebores engine blocks. As of now, five engine blocks are waiting to be processed. An engine expert on duty has diagnosed the processing times for the jobs. Completion times have been agreed upon with the shop’s customers. Taylor Machine Shop is open from 8:00 A.M. until 5:00 P.M. each weekday, plus weekend hours as needed, the customer pickup times are measured in business hours from the current time. Determine the schedule for the engine expert by using the SPT rule. Calculate the average flow time, average hours early, and average hours past due. Compare EDD and SPT rules, if average past due is most important, which rule should be chosen?
Under the SPT rule, the sequence starts with the engine block with the shortest processing time, the Econoline 150. The sequence ends with the Bronco. The engine block sequence, the processing, finishing and flow times, along with the pickups, is contained in the following table.
The performance measures are:
Average Flow Time = 6+19+29+29+45 = 25.6 hrs
5
Average Hours Early = 15+3+0+0+0 = 3.6 hrs
5
Average Hours Past Due = 0+0+7+7+24 = 7.6 hrs
5
The EDD results, which are:
Average Flow Time = 28.2 hrs, Average Hours Early = 0.6 hrs, Average Hours Past Due = 7. 2 hrs.
Decision: The EDD results are better than the SPT rule with respect to the past due dates, but worse with respect to flow times in this example. The company’s choice should depend on which performance indicator is valued the most.
In Example 1 it is seen that, the EDD schedule gave better customer service, as measured by the average hours past due, and a lower maximum hours past due (22 versus 24). On the other hand, the SPT schedule gives a lower average flow time. The SPT rule will push help jobs move faster through completion. This can help—but only if jobs can be delivered sooner than the due date and revenue collected earlier. If they cannot, the completed job must stay in the finished inventory. Because of this, the priority rule chosen can help or harm the firm in meeting its competitive priorities.
The SPT rule helps to minimize the mean flow time (assuming time since arrival is 0 for all jobs) and the percentage of jobs past due. It also helps to maximize shop utilization. For the single-workstation case, the SPT rule always give the lowest mean finish time. But SPT could increase total inventory because it pushes all work to the finished state. It also produces a large variance in past due hours, this is because the larger jobs might have to wait a longer time to be processed. Also, it gives no opportunity to change schedules when due dates change. The advantage of this rule over others becomes smaller as the load on the shop increases [9].
Other rules, such as CR (Critical Ratio) and S/RO (Slack per Remaining Operations), contain information about the workstations at which the job is to be processed, in addition the processing time at the present workstation or the due date considered by single-dimension rules. We call these rules multiple-dimension rules because they apply to more than one side of the job. Example 2 shows the use for CR and S/RO.
Example 2
The table below, shows information about a set of four jobs that just arrived (end of hour 0 or beginning of hour 1) at an engine lathe. They are waiting to be processed. Several operations, including the one at the engine lathe, remain to be done on each job. Determine the schedule by using (a) the CR rule and (b) the S/RO rule. Compare these schedules to those generated by FCFS, SPT, and EDD.
a. Using CR to schedule the machine, we divide the time remaining until the due date by the shop time remaining to get the priority index for each job. For job 1,
CR = 15 = 2.46
6.1
By arranging the jobs in sequence with the lowest critical ratio first, it is seen that the sequence of jobs to be processed by the engine lathe is 4, 2, 3, and then 1, assuming that no other jobs arrive in the meantime.
b. Using S/RO, the difference is divided between the time remaining until the due date and the shop time remaining by the number of remaining operations. For job 1,
S/RO = 15 – 6.1 = 0.89
10
Arranging the jobs by starting with the lowest S/RO yields a 4, 3, 1, 2 sequence of jobs.
Decision: The two different schedules were obtained from the application of the priority rule. The SPT sequence, based on processing times (measured in hours) at the engine lathe only, is 1, 3, 2, and 4. No preference is given to job 4 in the SPT schedule, even though it may not be finished by its due date. The EDD sequence is 4, 2, 1, and 3. We have assumed that the FCFS sequence is 1, 2, 3, and 4. All four jobs arrived at the workstation at the end of hour 0, so the finish times and flow times are identical for all five rules.
The S/RO rule is better than the EDD rule and the CR rule, but it is much worse than the SPT rule and the FCFS rule for this example. However, EDD, CR, and S/RO all have the advantage of allowing schedule changes when due dates change. These results cannot be generalized to other situations because only four jobs are being processed.
Research studies depict that S/RO is better than EDD when talking about the percentage of jobs past due but worse than SPT and EDD with respect to average flow times. It is also known that CR results in longer flow times than SPT, but CR also gives less variance in the distribution of past due hours. The use of the multiple-dimension rules requires more information and there is no clear choice on which one is the best one. Each rule is intended to be tested in its own environment [9].
Discussion
Shortest Processing Time or SPT is one of the main processes and type of optimization work process within the concept of scheduling. SPT arranges the data from smallest to largest based on the processing time of such. The main purpose of arranging and obtaining data with the shortest processing time technique is to minimize the flow time. Flow time meaning the amount of time a unit spends in the process from beginning to end. From the examples above it is evident that SPT’s priority is to minimize the amount of flow time while others factors such as due dates and tardiness are not of preference. Therefore in some instances, other techniques such as critical ratio, give better results for those factors that SPT gives less priority to. The business wanting to implement scheduling into their business plan has to identify and prioritize their main objectives. When that is done, the business can then evaluate if Shortest Processing Time is the best optimal scheduling technique for their use.