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LEARNING GOALS After reading this supplement, you should be able to:

Define new performance measures (beyond and past due) for evaluating flow time a schedule. Describe the decision rules (beyond FCFS EDD) to sequence and jobs. Determine schedules for single and multiple workstations.

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his supplement focuses on operations scheduling, which involves assigning jobs to workstations or employees to jobs for specified time periods. Effective scheduling helps managers achieve the full potential of their supply Chapter 14, Operations Planning chains. and Scheduling, covers the basics of scheduling Gantt workforce scheduling, two rules (FCFS charts, and EDD) for sequencing work at a single workstation, commonly used performance and two measures and past due). Here we deepen (flow time your understanding with additional performance mea- and priority sequencing rules, a discussion of sures scheduling multiple workstations, and a discussion of scheduling a two-station flow shop.

T

myom lab and the Companion Website at www.pearsonglobaleditions.com/krajewski designed supplement. for this contain many resources tools, activities, and

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operations scheduling scheduling in which jobs A type of are assigned to workstations or employees are assigned to jobs for specified time periods.

Scheduling Processes Manufacturing

Service

and

The scheduling techniques we discuss in this supplement cut across the various process types found in services and manufacturing. Many service firms are characterized by aront-office process f with high customer contact, divergent work flows, customization, and, consequently, a complex scheduling environment. Often customer demands are difficult to predict, which puts a high premium on scheduling employees to handle the varied needs of customers. At the other extreme in the service industry, back-office a process has low customer involvement, uses more line work flows, and provides standardized services. Inanimate objects are processed; these processes take on the appearance of manufacturing processes. Manufacturing processes also benefit from operations scheduling techniques. Our discussion of the operations scheduling techniques in this supplement has application for job, batch, and line processes in services as well as in manufacturing. Schedules for continuous processes can be developed linear programming (see Supplement E, with Linear Programming). Although the scheduling techniques in this chapter provide some structure to the selection of good schedules, many alternatives typically need to be evaluated. We begin by looking at the performance measures managers use to selectschedules. good

Performance MeasuresWe already covered two important performance measures in Chapter 14, Operations Planning and Flow time is the time a job spends in the service or Scheduling. ing system, and past due (tardiness) is manufactur- of time by which a job missed its the amount date. In this regard, a job isdue object receiving service or being manufactured. For the example, a job may be a customer waiting for service at a state licensing bureau or it may be a batch of pistons waiting for a manufacturing process. These two performance measures can be insufficient, depending on the competitive priorities of a process. Additional performance measures follow: makespan The total amount of time required to complete agroupof jobs. Makespan. The total amount of time required to complete a group of jobs is called makespa . Minimizing makespan supports the competitive priorities of cost n inventory) (lower time (delivery and speed). Makespan = Time of completion of last job - Starting time of the first job Total Inventory. This performance measure is used to measure the effectivness of schedules for manufacturing processes. The sum scheduled receipts and on-hand of inventories is the total . inventory Total inventory = Scheduled receipts for all items + On-hand inventories of all items Minimizing total inventory supports the competitive priority of cost (inventory holding costs). Utilization. The degree to which equipment, space, or the workforce is currently being used, measured as the ratio of the average output rate to maximum capacity. Maximizing the utilization of a process supports the competitive priority of cost (slack capacity) . These performance measures often are interrelated. For example, minimizing the average flow time tends to increase utilization. Minimizing the makespan for a group tends to increase utilization. Understanding how flow time, makespan, past due, of jobs and utilization interact can make the selection of good schedules easier.

total inventoryof scheduled receipts and onThe sum hand inventories.

Sequencing Operations schedules are short-term plans designed to implement the sales and operaJobs

tions plan. Often, several jobs must be processed at one or more workstations. Typically, of tasks can be performed at each workstation. If schedules are not a variety carefully to avoid bottlenecks, waiting lines may develop. For example, Figure J.1 planned depicts

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the complexity of scheduling a manufacturing process. When a job order is received for a part, the raw materials are collected and the batch is moved to its first operation. The colored arrows show that jobs follow different routes through the manufacturing process, depending on the product being made. At each workstation, the next job to process is a decision because the arrival rate of jobs at a workstation often differs from the processing rate of the jobs at a workstation, thereby creating a waiting line. In addition, new jobs can enter the process at any time, thereby creating a dynamic environment. Such complexity puts pressure on managers to develop scheduling procedures handle the workload that will efficiently. section, we focus on scheduling approaches used in two environments: (1) In this divergent flow processes and (2) line flow processes. A manufacturer's operation with divergent flows is often called a job , which specializes in low- to medium-volume shop production front office would be the equivalent for a service and job or batch processes. The utilizes Jobs in divergent flow processes are difficult to schedule because of the variability provider. in job routings and the continual introduction of new jobs to be processed. Figure J.1 depicts a manufacturers job shop. A manufacturer's operation with line flows is often called flow a sho , which specializes in medium- to high-volume production and line or p utilizes continuous flow processes. The back office would be the equivalent for a service provider. Tasks are easier to schedule because the jobs have a common flow pattern through the sys- Nonetheless, scheduling mistakes can be costly in either tem. situation.

job shop A manufacturer's operation that specializes medium-volume production in low- to and utilizes job or batch processes. flow shop A manufacturer's operation that specializes in medium- to highvolume production and utilizes line or continuous flow processes.

Job Shop SequencingJust as many schedules are feasible for a specific group of jobs at a particular set of workstations, numerous methods can be used to generate schedules. They range from straightforward such as manipulating Gantt charts, to sophisticated computer models manual methods, for developing optimal schedules. One way to generate schedules in job shops is by using sequencing rules priority , which allows the schedule for a workstation to evolve over a period of time. The decision about which job to process next is made with simple priority rules whenever the workstation becomes available for further processing. One advantage of this method is that last-minute information on operating conditions can be incorporated into schedule as it the evolves. already covered two important sequencing rules in Chapter 14, Operations We and Planning Scheduling. first-come, first-served (FCFS) rule gives the job arriving at the The the highest priority. first earliest due date (EDD) workstationthe job with the earliest due date rule gives The on assigned due dates the highest priority. Such rules can be applied by a worker or based

FIGURE Diagram of a Manufacturing Job J.1Shop Process

Legend: Batch of parts Workstation

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incorporated into a computerized scheduling system that generates a dispatch list of jobs and priorities for each workstation. Additional priority sequencing rules follow: critical ratio (CR) Critical Ratio. The critical ratio is calculated by dividing the time remaining (CR) shop time remaining for the job, which is defined as the until a jobs due date by the total A ratio that is calculated by dividing setup, processing, move, and expected waiting times of all remaining operations, the remaining until a jobs due date by time including the operation being scheduled. The formula the shop time remaining for the job, total is which is defined as the setup, processing, move, CR = Due date - Todays date and expected waiting times of all Total shop time remaining including the operation being operations, remaining The difference between the due date and todays date must be in the same time units scheduled as total shop time remaining. A ratio less than 1.0 implies that the job is behind the . sched- a ratio greater than 1.0 implies that the job is ahead of schedule. The job with ule, and the lowest CR is scheduled next. Shortest Processing Time. The job requiring the shortest processing time at the shortest processing time (SPT) (SPT) workstation is processed A priority sequencing rule that specifies next. that job requiring the shortest the Slack per Remaining Operations . Slack is the difference between the time processing next job to be processed. time is the until a jobs due date and the totalremaining remaining, including that of the shop time operation being scheduled. A jobs priority is determined by dividing the slack by the number of operations that remain, including the one being scheduled, to arrive at slack per slack per the remaining (S/RO) remaining operations . operations (S/RO) A priority sequencing rule S/RO = (Due date - Todays date) - Total shop time remaining that determines priority by dividing the Number of operations slack number of operations that remain, remaining by the The job with the lowest S/RO is scheduled next. Ties are broken in a variety of ways including the one being if or more jobs have the same priority. One way is to arbitrarily choose one of the two scheduled. tied for processing next. jobs Although the priority sequencing rules seem simple, the actual task of scheduling dredshunof jobs through hundreds of workstations requires intensive data gathering and manipulation. The scheduler needs information on each jobs processing requirements: the jobs due date; its routing; the standard setup, processing, and expected waiting times at each operation; whether alternative workstations could be used at each operation; and the inputsinternal or external suppliers at each operation. In addition, the scheduler needs from to know the jobs current status: its location (waiting in line for a workstation or being processed at a workstation), how much of the operation has been completed, the actual arrival and departure times at each operation or waiting line, and the actual processing and setup times. The scheduler or software uses the priority sequencing rules to determine the processingof jobs at a workstation and the remaining information for estimating job sequence arrival at the next workstation, as well as determining whether an alternative times workstationused when the primary one is busy. Because this information may change should be through- day, computers are needed to track the data and to maintain valid out the priorities.

Sequencing Jobs for One WorkstationAny priority sequencing rule can be used to schedule any number of workstations. For purpose of illustrating the rules, however, we focus on scheduling several jobs at a the single workstation. We divide the rules into two categories: (1) single-dimension rules (2) multiple-dimension and rules. Single-Dimension Some priority sequencing rules (e.g., FCFS, EDD, and SPT) Rules jobs priority assignment only on information about the jobs waiting for processing at base a the individual workstation. We call these single-dimension because they deterrules priority based on a single aspect of the job, such as arrival time at the workstation, the rules mine due date, or the processing time. We begin with an example of single-dimension rules.

single-dimension rules of rules that bases the priority of a A set job on a single aspect of the job, such as arrival time at the workstation, the due or the processing time. date,

EXAMPLE J.1

Comparing the EDD and SPT RulesThe Taylor Machine Shop rebores engine blocks. Currently, five engine blocks are waiting for processing. At any the company has only one engine expert on duty who can do this type of work. The engine problems time, have diagnosed, and the processing times for the jobs have been estimated. Expected completion times been have agreed upon with the shops customers. The accompanying table shows the current situation. Because been the

Tutor J.1 in myomlab provides a new example to practice EDD and SPT rules.

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Taylor Machine Shop is open fromM . untilP .M . each weekday, plus weekend hours as needed, the A. 8:00 5:00 customer pickup times are measured in business hours from the current time. Determine the schedule for the engine expert by using (a) the EDD rule and (b) the SPT rule. For each rule, calculate the average flow time, Model J.1 in myomlab provides Active average hours early, and average hours past due. If average past due is most important, which rule should additional insight on the use of singlebe dimension rules. chosen? Business Hours Until Date (customer time)

Business Hours Engine Since Block Arrived Ranger 12 8 10 Explorer 10 6 12 Bronco 1 15 20 Econoline 150 3 3 18 Thunderbird 0 12 22

Processing Time, Order Including (hours)

Setup

Due pickup

SOLUTIO Na. The EDD rule states that the first engine block in the sequence is the one with the closest due date. Consequently, the Ranger engine block is processed first. The Thunderbird engine block, with its due furthest in the future, is processed last. The sequence is shown in the following table, along with date the flow times, the hours early, and the hours past due.

Hour s Since Order Begi n Arrive Work d Ranger 12 0 + 8 = 8 20 10 10 2 Engine Block Sequence Explorer 10 8 + 6 = 14 24 12 14 2 Econoline 150 3 14 + 3 = 17 20 18 18 1 Bronco 1 17 + 15 = 32 33 20 32 12 Thunderbird 0 32 + 12 = 44 44 22 44 22

Processin gTime (hr)

Finis h Time (hr)

Flow Time (hr )

Schedule d Custome r Pickup Time

Actua l Custome r Pickup Time

Hour sEarly

Hour sPas t Due

1 The flow time for each job is its finish time, plus the time since the For example, the Explorer job arrived.blocks finish time will be 14 hours from now (8 hours waiting time before the engine expert engine started on it plus 6 hours processing). Adding the 10 hours since the order arrived at this to work workstationprocessing of this group of orders began) results in a flow time of 24 hours. You might think of (before the the sum of flow times as the totaljob hoursspent by the engine blocks since their orders arrived at the workstation until they were processed. The performance measures for the EDD schedule for the five engine blocks are

Average flow time = 20 + 24 + 20 + 33 + 44 5 = 28.2 hrs Average hours early = 2 + 0 + 1 + 0 + 0 5 = 0.6 hrs Average hours past due = 0 + 2 + 0 + 12 + 22 5 = 7.2 hrsFlow time, as a performance measure in its traditional use, does not count the time a job spends outside the system under our control. Our system in this supplement is the single workstation (or two workstations in the case of Johnsons rule in the next section). Arrival time here relates to when the job was first available for processing at the workstation. Adding the time since the order arrived at the work- to the jobs finish time departs from conventions used in early research on static problems, station which assumed that no jobs arrive during the time span covered by the resulting schedule. With tradi- assumptions, a jobs finish time and flow time are identical and SPT will always have the best tional flow performance. With our definition of flow time, the SPT rules do not necessarily produce the time best time performance, such as when the job with the shortest processing time arrived at the workstation flow well before the other jobs.

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