Introduction to Scheduling

Learning Objectives

After completing this chapter, you should be able to:

• List the six criteria for scheduling and discuss the trade-offs involved with each.

• Provide an overview of the scheduling process including data requirements, order information, sequencing, and dispatching.

• Describe how scheduling for services differs from manufacturing.

• Discuss issues of concern that can occur when scheduling an assembly line.

• Use dispatching rules to schedule jobs and discuss each rule.

• Discuss how priorities are determined in MRP systems.

• Understand forward and backward scheduling with finite and infinite capacity.

• Schedule employees for service operations.

12 © Greg Dale/National Geographic Society/Corbis

Scheduling

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CHAPTER 12Section 12.1 Introduction to Scheduling

12.1 Introduction to Scheduling

Scheduling is coordinating work tasks, people, materials, facilities, and equipment needed to create goods and services at a specific point in time. Scheduling is required for making goods and for providing services successfully. There are many different approaches to scheduling; some of the most common are discussed in this chapter.

Scheduling is the last step in the process that begins with strategic planning and proceeds through increasingly detailed stages. Each successive stage of the planning process builds on its preceding stage. Proper planning in the earlier stages increases the likelihood that a schedule can be created that will meet customer demand at a reasonable cost and without delays.

Scheduling can be one of the most challenging areas of operations management. As many companies have found, scheduling presents many day-to-day problems because there may be changes in customer orders, equipment breakdowns, late deliveries from suppli- ers, and a myriad of other disruptions. Techniques are very sophisticated mathematically because scheduling problems are often very detailed, have lots of information to consider, and have many possible solutions. This chapter focuses on scheduling rules that can lead to good solutions as well as some relatively simple application techniques.

To begin the discussion of scheduling, the master schedule in Figure 12.1 calls for the pro- duction of two different products during a particular time period. Using material require- ments planning (MRP), it has been determined that certain parts for each of those finished products must be started in the production process during week 20, as shown by the circled figures in Figure 12.1.The routings for these two parts are shown in Figure 12.2. Capacity requirements planning (CRP) has been used to determine that insufficient capac- ity will exist in week 20 on the lathe, which is the “gateway,” or first work center, for both parts. Management investigated both short-run and long-run solutions to this capacity problem, but has decided that it will follow a short-run strategy and schedule overtime to alleviate the capacity problem in the lathe department.

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CHAPTER 12Section 12.1 Introduction to Scheduling

Figure 12.1: Production plan for two products

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CHAPTER 12Section 12.1 Introduction to Scheduling

Figure 12.2: Routing for two parts

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CHAPTER 12Section 12.1 Introduction to Scheduling

In this example, there are two scheduling problems. One involves scheduling employees, and the other with scheduling the two parts. It is necessary to schedule employees to work during the overtime used in the lathe department. The second scheduling problem, scheduling the parts, occurs because both parts will be released to the lathe department at the same time. This second scheduling problem is one of sequencing—determining which part to produce first.

Scheduling is a complex process that involves many different steps. This section summa- rizes those steps before describing scheduling techniques.

Data Collection Collecting the data needed for scheduling begins with orders from the customer. These orders identify which product the customer wants, special features, and the product due date, among other things. When data from order entry is combined with process data, the following information about the jobs, activities, employees, equipment, and facilities are available to prepare a schedule.

Jobs Due dates, routings, material requirements, flexibility of due dates

Activities Expected duration, required activities that precede this activity, desired time of completion

Employees Availability, capability, efficiency, wage rates

Equipment Machine or work center capacities and capabilities, cost of operation, availability

Facilities Capacities, possible uses, cost of use, availability

Order Entry Order entry drives the scheduling process. Orders may originate with the customer, but they may also be generated by internal or company orders that are given to create inven- tory. For a make-to-order company, one that produces only to customer orders or that provides services, this occurs when a customer places an order. Given existing produc- tion schedules, capacity available, and the customer’s desired due date, the order can be scheduled. This order scheduling will be an estimate based on capacity requirements to produce the customer’s order. Producing the order will require further scheduling of the individual parts and components for a product or the employees and facilities for a service.

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CHAPTER 12Section 12.1 Introduction to Scheduling

In a make-to-stock company, one that produces for inven- tory and meets customer orders from inventory, production orders are entered by the com- pany based on the inventory level of each item in stock, and the expected future demand of that item. In general, a make- to-stock company has a some- what easier job of scheduling because it has some control over which products will be made. However, unlike a make-to- order company, which must produce whatever is demanded by the customers, the make-to- stock company will have excess inventory if it produces some- thing that customers do not want. This increases costs and may lead to discounting to increase sales of an item.

In an MRP environment, the MRP system will generate planned order releases based on the master schedule. This is another form of order entry—in this case, for individual parts or subassemblies.

Orders Released for Production The planning process involves a continual movement from strategic plans for the distant future toward more detailed plans for the less-distant future. As time frames diminish, plans become more precise and detailed until each order is released for production. At that point, the schedule is implemented.

Scheduling addresses the very near future because it is the last step in production plan- ning. Plans are made to schedule a particular job, activity, or employee, but those plans are not converted into a detailed schedule until the last possible moment. The earlier plan- ning stages determine what level of resources is needed to meet the production plan. Scheduling allocates those resources.

When working with such minute details, such as individual machines, parts, or employ- ees, it is always possible that changes will occur. An employee may become ill or quit, a machine may break down, or the raw materials for a part may not arrive on time. Because of these possibilities, scheduling must usually wait until the existing conditions are known with relative certainty. Even then, last minute changes must often be made, which is what makes scheduling so challenging.

.Thinkstock

Many car manufacturers use a make-to-stock inventory system. If a make-to-stock company produces something that customers do not want, it will have excess inventory of that item, which is one downside to this type of system.

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CHAPTER 12Section 12.1 Introduction to Scheduling

As time passes and the scheduled starting time for a job or order is reached, that job or order is released for production. That step starts the job on its way through the process- ing operations. The final scheduling steps are the sequencing of activities, jobs, or parts in the order they should flow through processing, and then the dispatching of those jobs. Dispatching is the assignment of priorities and the selection of jobs for processing at a work center or facility. For example, a customer order for a made-to-order product must be sequenced with other orders. When the time comes for work to begin on that order, it will be dispatched at the first work center according to its priority at that time.

Managerial Considerations Scheduling is an attempt to allocate scarce resources efficiently. Machine time may be a scarce resource that is allocated to different jobs, employee time is allocated to different activities, and facilities are scheduled for a given activity at a particular time period. In all of these scheduling tasks, different criteria may be used when deciding which of several schedules will work best. Those criteria may relate to the amount of time equipment may sit idle, the importance of a certain order or a certain customer, or the level at which a resource is utilized.

The task of scheduling can be quite complex; what appears to be an optimal schedule from one viewpoint may be far from optimal from another. For example, a certain schedule may utilize one machine very efficiently, but may mean idle time for machines farther along in the processing operations. Another schedule might mean that an important cus- tomer’s order will not be delivered on time. These six criteria may be used when evaluat- ing possible schedules:

• Provides the good or service when the customer wants it • Length of time it takes to produce that good or service (flow time), which

includes both processing and waiting time • Level of work-in-process (WIP) inventories • Amount of time that equipment is idle • Amount of time that employees are idle • Overall costs

The relative importance of each factor depends on the product or service being produced, a company’s particular industry, and, especially, the organization’s competitive strategy. Different production processes will also incur different problems, and certain criteria will, therefore, be more important. It may be impossible to satisfy all of the six criteria listed above at one time. Instead, management must choose among the various trade-offs (see Table 12.1).

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CHAPTER 12Section 12.1 Introduction to Scheduling

Highlight: Tim Horton’s

Tim Horton’s sells coffee, pastries, breakfast, sandwiches, and other items. It responds to customer demands quickly using a combination of make-to-order and make-to-stock. Their coffee is pre-made, that is, made-to-stock, but it has a time limit. If not used within a certain time, it must be thrown out. The donuts and bagels are make-to-stock, but sandwiches are make-to-order with components including bread, meat, and cheese, and prepared for further processing and assembly. Tim Horton’s relies on fast delivery, low cost, and good quality. The store managers must anticipate demand each day, even for each portion of the day, in order to schedule the right people at the right time and without idle employees, which increases costs. They must consider the wait time at the drive up window. Cross training is important so that if there is slack at the front counter, employees can be shifted to other jobs where demand exceeds the restaurant’s ability to serve its customers. Manag- ers must order the materials, such as coffee, pastries, and sliced meat, so the shop has neither too little (so customers cannot get what they want), nor too much (so there is waste). Long term, man- agers should measure equipment use and identify bottlenecks to determine if the number of coffee machines, warming ovens, and other items are sufficient for demand. Should these be increased or possibly reduced? A manager would examine the facility to see how it might be altered to better serve customers. Scheduling is critical to Tim Horton’s success.

Table 12.1: Factors and trade-offs

Factor Trade-off

Providing the good or service when the customer wants it

Requires flexibility. Can lead to large inventories and excess capacity during periods of low demand.

Minimizing flow time Requires flexibility, short set-up times, and fast production rates. Can require having excess capacity available.

Minimizing WIP inventories May require excess capacity or the use of a pull system. Can lead to high machine or employee idle time.

Minimizing machine idle time Often means keeping capacity low, producing product for inventory, or accepting any customer orders whether the order is profitable or not. Can result in high inventories, high costs, the overloading of equipment, and late orders.

Minimizing employee idle time Often means keeping workforce size low, producing product for inventory, or accepting any orders. Can result in employee discontent, late orders, and high inventories.

Minimizing costs Often requires compromises on the preceding criteria. All relevant costs must be properly defined and measured. Can result in poor customer service—a cost that is difficult to measure.

When determining which criteria to use, a company must carefully consider its corporate objectives, competitive strategy, and capabilities. The company’s scheduling decisions will have a great impact on facility design, the type of equipment used, and the workforce requirements. Each of these will, in turn, influence its competitiveness in terms of cost, speed, and delivery reliability.

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CHAPTER 12Section 12.2 Techniques for Successful Scheduling

12.2 Techniques for Successful Scheduling

When scheduling, two key questions are:1. When should a given job, order, or product be processed? 2. How many units should be processed at one time?

The answers to these questions impact the way a processing operation is run. For instance, a company that makes ice cream must decide which flavors should be made and when. If chocolate is made before vanilla, there may be extensive time spent cleaning the equipment before switching to vanilla. Conversely, producing vanilla before vanilla-fudge marble may mean no cleanup between runs. In addition, the company must decide how many gallons of one flavor to make before it starts making another. The com- pany does not want to produce so much of a given flavor that the ice cream deteriorates before it is sold. At the same time, pro- ducing small quantities at one time will mean excessive time spent cleaning and refilling the equipment between batches.

Different scheduling techniques are appropriate for different operation processes. Line flow, batch, and flexible manufacturing process have similarities, and are discussed together in the next section. The job shop process, which is quite different, is discussed in a later section in this chapter.

Continuous Flow Processes A continuous flow process is one in which materials flow in a continuous, or nearly con- tinuous, stream from beginning to end. A good example of a continuous flow process is an oil refinery. Such production processes are generally characterized by a few different finished products, only a few possible routings, and low work-in-process inventories.

Under such conditions, the relevant scheduling criteria become somewhat limited. For example, flow time is determined by the production process, rather than by a schedule because a continuous flow system operates with a defined sequence and that is difficult to interrupt. Generally, it is neither economical nor technically desirable to perform step one in the refining process, then place the output in inventory for a long period of time. Work-in-process inventory is also not a major problem because it is generally quite low

.altrendo images/Thinkstock

An ice cream company must decide which flavors it should make, in what order, and how many gallons should be produced to optimize profit and efficiency while reducing waste.

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CHAPTER 12Section 12.2 Techniques for Successful Scheduling

for continuous flow processes. Thus, the scheduling problem in a continuous flow process requires determining when to change from making one product to making another. The relevant criterion is usually minimizing cost, although minimizing the time the facility is idle during changeover could also be important. When refining oil, a continuous flow process makes adjustments to make more heating oil in the fall for the coming winter, and adjusting again to make gasoline in the late spring for the summer driving season.

Balancing an Assembly Line An assembly-line process is similar to continuous flow, but instead of the products flow- ing continuously, such as a stream of gasoline or a roll of paper, the products are discrete, individual items, such as automobiles.

One of the best examples of an assembly-line process is the automobile assembly line. In this example, the product follows a fixed path. Like the continuous flow process, an assembly-line process usually produces a limited number of products, and the routings are the same. Work-in-process inventory is also typically small. Thus, the same basic tech- niques used for scheduling in continuous flow can also be used for assembly-line process scheduling. There are, however, two particular problems unique to assembly-line sched- uling that are described next.

It is critical to assign the same amount of work to each station because assembly lines are usually a series of workstations with one worker assigned to each station. If the line is unbalanced, meaning that one station has more work than the others, then one worker will be rushed and unable to complete the work while the others will have idle time, thereby generating waste. Successful assembly line balancing depends on having the opti- mal number of appropriate workstations so that idle time is zero or close to zero. The right number of workstations is also important because it helps to determine the cycle time. The cycle time is the amount of work assigned to the station with the most work and time.

Cycle time controls the flow of product along the line, and therefore determines the capac- ity of the assembly. Mathemati- cally, the cycle time for the assembly in minutes per unit of product is the inverse of the pro- duction rate, which determines capacity. Assembly-line balanc- ing provides the framework for scheduling. Assigning tasks to workstations allows the mate- rial flow and job assignments to be specified by the line balance.

Assembly-line balancing is not a perfect science because people with different abilities will be assigned to the worksta- tions. The result may be that a perfect balance was achieved

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Assembly lines are comprised of a series of workstations with one or more workers assigned to each station. Successful assembly lines depend on balancing the line so that idle time is minimized.

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CHAPTER 12Section 12.2 Techniques for Successful Scheduling

theoretically, but it will not be perfect in practice. Some employees will complete their tasks in less than the average time. Others will take longer. The end result is that a theo- retically balanced line may be unbalanced in practice.

Scheduling is one approach to overcoming this problem. A skillful supervisor will know which employees can work faster and will assign those to the stations with more work. Tasks may also be shifted from one workstation to another as trouble spots appear. Thus, assigning employees to workstations or tasks to employees is an integral part of fine- tuning the balance of a line through scheduling.

The details of assembly-line balancing involve complex mathematical problems that are beyond the scope of this book.

Sequencing Sequencing an assembly is determining the order for making different products. In some cases, the differences are small, such as painting a car red versus silver, or mounting 16-inch steel wheels versus 17-inch aluminum wheels. But, in other cases, the differences are very different, such as making a convertible versus a hardtop, or making different car models on a different platform within the same production line. In these cases, sequenc- ing is very important. Assembling a convertible, for example, requires more time at some workstations, so it is better not to put those stations back-to-back. This gives the work- force time to catch up before the next convertible arrives.

Scheduling Batch Processes In batch processes, the number of possible products is greater than can be produced in line-flow processes. As a result, each product is made in a group or batch. The process is stopped; the equipment is changed over, and the next product is made. The production volume of each product is usually less than when made by a line-flow process. As a result, the same resources are used to produce at least several different products, producing a batch of each product at one time. Because of this, determining the number of units to produce in one batch and the sequence of batches becomes important. The criterion of cost minimization is usually used to determine production quantity. Because each product is produced only intermittently, it must be produced often enough to avoid running out of inventory.

Note that many batch operations use continuous flow or assembly-line processing. The difference is that a batch has a defined starting and ending time with a setup or changeover between different batches. From a cost perspective, it would be lower cost (lower set-up costs, less inventory, and higher equipment utilization) to avoid batching by making the same or very similar product without an abrupt change. The problem with this approach is that customer demand requires a greater variety than the production system can deliver without the abrupt change. The ideal, over time, is to find a technology that can eliminate or greatly reduce the changeover so the operations can make smaller batches and eventu- ally run continuously.

The ice cream example described earlier is one example of a continuous flow process that has many options and relatively small batches. There are hundreds of ice cream fla- vors available, and more are being developed every year. Determining the sequence and

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CHAPTER 12Section 12.2 Techniques for Successful Scheduling

batch size for ice cream production is critical to effectively and efficiently schedule pro- duction. Other examples of continuous flow process that are run in batches include paint, pharmaceuticals, and breakfast cereals. Assembly lines can also operate in a batch mode. Appliance assembly lines that make air conditioners and refrigerators are often batched to increase efficiency. Once demand is large enough for a particular model, or the change- over time declines because of technology, the batch size can be greatly reduced or elimi- nated and the assembly lines can flow smoothly.

Run-Out Time The question of batch size only addresses how much to produce; it does not indicate which product should be produced next. One method that can be used to determine which prod- uct should be produced next is called run-out time. This is simply a calculation of how long it will take for the company to run out of each product at current usage rates. Run-out time is determined as follows:

Run-out time 5 current inventory

usage rate

Table 12.2 indicates current inventory and demand rates for five different products made by a process. Run-out time calculations are shown for each of the five different products. Based on those calculations, product E should be produced next because it will run out first—in two weeks.

Table 12.2: Run-out time calculations

Product Current Inventory Demand Rate (Units per Week) Run-Out Time (Weeks)

A 1,000 200 1,000/200 5 5

B 500 150 500/150 5 3.3

C 2,000 500 2,000/500 5 4

D 2,500 500 2,500/500 5 5

E 600 300 600/300 5 2

Flexible Manufacturing Systems Chapter 10 discussed the trade-off between product changeover costs (or set-up costs) and inventory carrying costs. When the cost of changeover becomes extremely small, the question of how many products to produce at one time is less important. Flexible manu- facturing systems (FMS) have been able to reduce changeover costs so much that it is economical to produce just one product or part at one time. The challenge then becomes one of sequencing to keep the changeover time—and consequently the cost—low enough.

Group technology is an important aspect of any FMS. By grouping similar products into families, a group technology cell within a FMS only makes products that have similar characteristics, which tends to reduce sequencing challenges. Because computerized

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CHAPTER 12Section 12.3 Job Shop Scheduling

control is an important part of a FMS, the computer can be used to evaluate different pos- sible sequences and determine the best one for each cell.

12.3 Job Shop Scheduling

There are few satisfactory scheduling techniques for job shop processing. Unlike con-tinuous flow, assembly line, or batch processes, a job shop has many different and intersecting routings. A job shop is fundamentally different from these continuous flow processes because it is arranged with similar machines in one location or work center. The part being produced or the patient in a hospital, moves to the various work centers as needed. Each part or patient may have a different path through the factory or hospital. This is called a process layout. Continuous flow and assembly lines are organized around a common sequence of steps, so that the path through the facility is the same. This is called a product layout.

What makes job shop scheduling more challenging is that different jobs are vying for time on the same machines. Deciding which job to process first on a given machine or work center can have a major impact on what happens at other machines or work centers—pos- sibly overloading some, while leaving others idle. The flow of product and the demands on the work centers in a job shop are different and uneven, which makes scheduling a challenge.

Dispatching Rules One of the earliest approaches to job shop scheduling focused on the criteria for sequenc- ing the jobs that are competing for time at the work center. Those criteria could be used to generate dispatching rules to be used at a machine or work center. A rule such as “first- come, first-served” is commonly used in retail operations because it is perceived as fair. A rule like first-come, first-served with priority for patients with severe problems is used in emergency rooms. This is called triage, where a medical professional makes an initial screening to see if a patient’s injuries are life threatening.

An important advantage of these rules is that they are easy to use. The information is readily available, and it is not necessary to know what is happening at other work centers. As with many things that are simple, the rules can sometimes lead to poor performance. Five of the most common dispatching rules are described below.

Earliest Due Date

The earliest-due-date rule focuses on the criterion of providing the product when a cus- tomer wants it. The rationale is that whichever job is due first should be started first. The advantage of this approach is that some jobs may meet their due dates. This rule is popu- lar with companies that are sensitive to due date changes. However, finishing one job on time may make many others late. This method also does not consider how long it will take to process a job.

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CHAPTER 12Section 12.3 Job Shop Scheduling

Shortest Processing Time

With the shortest-processing-time rule, the rationale is to get the most work done as quickly as possible in order to minimize the level of WIP inventory. Unfortunately, jobs with long processing times may be made quite late as they wait for shorter jobs to be fin- ished. Otherwise, this rule often works best on most measures. One way this rule has been modified is to make an adjustment for long-running jobs that have been waiting for a long time by moving them to the front of the line.

Having determined that there are advantages to using the shortest-processing-time rule, it is still necessary to use good judgment before applying any rule. For example, the shortest-processing-time, including adjustment for long waiting jobs, works poorly in an emergency room. A patient with a severe problem that requires a long time at a work cen- ter will be delayed while other patients needing less care are serviced first. For example, using this rule, patients with minor fractures would move ahead of a patient with a severe compound fracture.

Longest Processing Time

The longest-processing-time rule uses a different strategy—to get the jobs that will take longest done first, leaving time at the end to do the short-processing-time jobs. The ratio- nale behind this rule is that jobs with long processing times may be more likely to miss their due dates than jobs with short processing times are. The great disadvantage of this approach is that many short jobs may also miss their due dates because of one long job. This rule also tends to result in an increase in WIP inventory. It may be used when a criti- cal job has a long lead-time.

First-Come, First-Served

This rule is often used in ser- vice facilities because custom- ers usually see this as the fair- est method. However, it ignores due date, processing time, or the importance of one job over the other; therefore, it does not perform well on such measures. The emergency room example is only one place where this rule performs poorly. In manufac- turing, machining a part that is needed to repair a city’s water supply system should have a greater priority than making a part so that an amateur stock car racer can repair her car. A few years ago (despite that seats were pre-assigned) air- planes were loaded first-come, first-served for fairness; or from

.Creatas/Thinkstock

Airline carriers have different boarding procedures; however, most board passengers based on some measure of customer importance, such as groups or priority status.

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CHAPTER 12Section 12.3 Job Shop Scheduling

Highlight: Airlines Use Dispatching Rules to Load Passengers

Several years ago, most airlines boarded their airplanes by row. After the first-class passengers and those needing extra time were boarded, the last few rows would be allowed to board. Next, the rows just prior to the last few rows were loaded. This boarding pattern was repeated from back to front of the airplane. This was done for efficiency, increasing the ability to rapidly load the airplane; if passengers in the front of the airplane load first, they would tend to block the aisles, slowing down boarding. Loading the airplane from back to front reduces this congestion. This approach worked well. Today, airlines often board based on status. If passengers fly the airline often, they earn gold, silver, or other status, which allows them to board early. Remaining passengers use a “zone” board- ing process, which is unrelated to the area of the airplane, and instead based on the passengers’ frequent flier miles. This is important to passengers who want to carry on luggage for convenience, or to avoid checked baggage fees.

Problem

The Hillside Machine Corporation has four jobs waiting to be run on its lathe. Figure 12.3 shows the days until due date and the processing time remaining for each job. Hillside wants to see which sequences will be generated by using each of the five dispatching rules. Figure 12.3 shows these sequences. It is interesting to note that in this example, the longest-processing-time and critical-ratio rules produce the same sequence of jobs—although that result will not always occur.

back-to-front for loading efficiency so that the planes could be loaded faster. Now, most airlines board their passengers based on some measure of customer importance. Airlines use priority status and zones to let passengers know when they can board.

Critical Ratio

The critical-ratio rule is an attempt to combine aspects of the preceding rules into one that considers both due date and processing time. It is based on calculating the critical ratio (CR), which is

CR 5 time until due date

processing time remaining

This rule is implemented by first scheduling those jobs that have the lowest critical ratio. Values of CR below one mean the job will be past due. A negative value means it is already past due. Thus, an advantage is that those jobs scheduled first are the ones that have the lowest chance of missing their due dates.

It should be noted that the critical-ratio rule differs from the other dispatching rules in that it is dynamic. That is, a job’s critical ratio will change over time as the number of days until the due date changes and the processing time remaining changes. Thus, the critical ratio must be updated constantly.

(continued)

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CHAPTER 12Section 12.3 Job Shop Scheduling

Problem (continued)

Figure 12.3: Comparison of dispatching rules

5 days 3 days 10 days 2 days

10 20 15 40

Job (Order Arrived)

Days Until Due Date

Processing Time Remaining

A B C D

CR 10/5 = 2 20/3 = 6.67 15/10 = 1.5 40/2 = 20

Earliest due date: A-C-B-D Shortest processing time: D-B-A-C Longest processing time: C-A-B-D First-come, First-served: A-B-C-D

Job A B C D

Critical ratio: C-A-B-D

C-A-B-D

Sequencing Jobs on One Machine

Flow time is the amount of time it takes to produce a product. If the product spends a large amount of time waiting to be processed, then its flow time will be long. Average flow time will be minimized by processing as many jobs as possible during a given period of time. The way to achieve this result is by using the shortest-processing-time rule, which has been proven to always minimize average flow time.

Problem

Refer to the Hillside Machine Corporation data in the previous example. Suppose the company tracks the number of days each job requires until completion, using the critical-ratio and shortest-process- ing-time rules. As the results in Figure 12.4 indicate, all four jobs are finished within 20 days, regard- less of which rule is used. However, with the critical-ratio rule, the average time each job spends before completion is 15.75 days. With the shortest-processing-time rule, the average time is only 9.25 days.

(continued)

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CHAPTER 12Section 12.3 Job Shop Scheduling

Problem (continued)

Figure 12.4: Comparison of average flow times for two sequencing rules

Critical-Ratio Rule

Job Start End

Shortest-Processing-Time Rule

C A B D

0 10 15 18

Total

10 15 18 20 63

Average flow time = 63/4 = 15.75 days

Job Start End

D B A C

0 2 5

10 Total

2 5

10 20 37

Average flow time = 37/4 = 9.25 days

Johnson’s Rule When there are two successive machines or work centers through which a group of jobs must all be sequenced, Johnson’s Rule can be used to minimize total processing time for the group of jobs, which is called the makespan time. The method utilizes the following steps:

1. List the jobs and the time each job requires at each work center. 2. From the list, select the job with the shortest time at either work center (if two or

more jobs in the list have the same time, one is selected at random). If the time is for the first work center, proceed to step 2a. If it is for the second work center, proceed to step 2b. a. Place the job as close to the beginning of the sequence as possible without

replacing other jobs. Go to step 3. b. Place the job as close to the end of the sequence as possible without replacing

other jobs. Go to step 3. 3. Eliminate the job just scheduled from your list. Return to step 2.

Note that this rule requires all jobs to follow the same sequence through both work cen- ters. The sequence cannot change at the second work center.

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CHAPTER 12Section 12.3 Job Shop Scheduling

Problem

University Data Services has five computer payroll jobs waiting to be processed before Friday after- noon. Each job requires computing and then printing, in that order. Based on past experience, the company estimates each job will take the following time:

Processing Time (Hours)

Job Computing Printing

A 1.5 1.0

B 1.0 0.75

C 0.5 1.25

D 2.0 1.5

E 0.75 0.5

Using Johnson’s Rule, proceed as follows.

Two jobs, C and E, have the shortest processing times, 0.5 hours. Job C is selected arbitrarily. Because its shortest time is for the first operation, Job C is scheduled at the beginning of the sequence.

C 1

2

3

4

5

Job C is eliminated from further consideration, and the process returns to step 2. Now Job E has the shortest processing time. Because that time is for the second operation (printing), Job E is scheduled at the end of the sequence.

C 1

2

3

4

E 5

Job E is now eliminated from the list. Therefore, Job B has the shortest processing time, which is for the second operation. Job B is scheduled as close to the end of the sequence as possible.

C 1

2

3

B 4

E 5

After eliminating Job B, of the remaining two jobs, A has the shortest processing time. Because that time is for the second process, job A is scheduled as close to the end as possible, which, in this example, is the third position.

C 1

2

A 3

B 4

E 5

The last remaining job, job D, is placed in the remaining slot in the schedule, producing the following sequence:

C 1

D 2

A 3

B 4

E 5

This sequence of jobs produces the processing sequence for each operation shown in Figure 12.5. This method completes all jobs within 6.25 hours and leaves only 0.5 hour of idle time for the printer at the beginning of the sequence and 0.75 hour between Jobs C and D.

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CHAPTER 12Section 12.4 Dispatching in MRP

12.4 Dispatching in MRP

The rules mentioned above are limited because they only consider the conditions that exist for a given point in time and a given work center. By and large, they ignore that a given part may be part of a subassembly that must be complete before the final product can be assembled.

MRP takes into account lead times. As long as the planning lead times used in MRP are valid, then the priority of each item should be based on the MRP lead times. Therefore, in an MRP system, priorities are determined by referring to the planned order releases and lead times. Thus, the dispatching rules are irrelevant to MRP systems. Instead, MRP works from the order due dates, scheduling order releases far enough ahead of time that the due dates should be met. Unfortunately, there still may be conflicts at machines and work centers that need to be addressed.

Machine Loading The dispatching rules previously described attempt to determine a schedule based on the attributes, such as due date or processing time, of each job. However, the time it takes for a job to be processed consists of the following five components:

1. Wait time 2. Move time 3. Queue time 4. Set-up time 5. Run time

Problem (continued)

Figure 12.5: Processing of computer jobs based on sequencing by Johnson’s Rule P

ro ce

ss

EC D A B

EC D A B

Computing

Printing

0 1 2 3 4 5 6 7 8

Time (hours)

Job Being Processed

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CHAPTER 12Section 12.4 Dispatching in MRP

Wait time is the time a job spends waiting before it is moved to the next work center. Move time is the material-handling time between work centers. Queue time is the time a job spends waiting to be processed at a work center. Set-up time is the time to prepare a machine to process that job, and run time is actual processing time.

In general, all of these components—except queue time—will be nearly fixed. Queue time really depends to a large extent on the workload that has been scheduled for each work center. If a machine’s capacity is being used extensively, then it is more likely that many jobs will be waiting for processing at that machine. When the capacity of a work center is exceeded, lines of work (queues) will build up in front of that work center.

Loading is an approach to scheduling that attempts to take capacity utilization into account. There are several different approaches to loading, but loading begins with scheduling.

Forward Scheduling Suppose scheduling begins immediately so that each job starts at the earliest possible moment. This is called forward scheduling. As jobs progress through a production facil- ity, each work center will have a certain workload placed on it from the jobs assigned to that work center. Figure 12.6 illustrates the schedule that could be generated by forward scheduling four jobs (A, B, C, and D) through three work centers (lathe, mill, and drill). This schedule assumes six hours for wait and move time between machines. Note that the jobs use the same three work centers, but use them in different orders, so Operation l for Job A uses the lathe, but Operation l for Job D uses is the drill. Also note that Job B and Job D do not use the lathe and the mill, respectively.

Figure 12.6: Forward schedule for four jobs with finite loading

Job A

Job B

Job C

Job D

Time (hours)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Start from time 0 and work forward

Wait/move

Wait/move

Wait/move

Wait/move

Queue for lathe

Queue for drill

Wait/move

Wait/moveDrill

Drill

Drill

Drill

Mill

Mill

Mill

Lathe

Lathe

Lathe

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CHAPTER 12Section 12.4 Dispatching in MRP

Work Center Sequence and Processing Time

(Number Is Sum of Set-up and Run Times in Hours)

Job Operation I Operation II Operation III

A Lathe 3 Drill 2 Mill 4

B Mill 4 Drill 3

C Lathe 2 Mill 3 Drill 4

D Drill 5 Lathe 4

In a forward schedule shown in Figure 12.6, each job begins as close to time zero as pos- sible, and each job is scheduled similarly through the successive operation, allowing six hours for wait and move time between machines. Some jobs have been delayed (queue time) at certain work centers because another job had already started at that work cen- ter. For example, Job C had to wait three hours before it could start on the lathe because Job A was still being processed on that machine. This approach of making one job wait if another has been scheduled on the same machine is called finite loading because it takes into consideration the limited capacity on each machine. Another approach uses infinite loading, which does not take capacity considerations into account. Infinite load- ing assumes that there is unlimited or infinite capacity.

Backward Scheduling Backward scheduling starts from a desired due date and works backward. The informa- tion for the four jobs and three work centers previously presented is used again, but the following due dates are added:

Job Due Date

A Hour 24

B Hour 16

C Hour 24

D Hour 16

In this case, infinite loading will be used, eliminating the problem of more than one job at the same work center at the same time. The resulting schedule is shown in Figure 12.7. Backward scheduling begins by scheduling the last operation for each job so that it would end at the time due, and then works backward through each operation. As a result of infi- nite loading, some work centers have been scheduled to do more than one job at one time. This may not be a problem if more than one machine is available. Actually, either finite or infinite loading can be used with either forward or backward scheduling.

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CHAPTER 12Section 12.4 Dispatching in MRP

Figure 12.7: Backward schedule for four jobs with infinite loading

Job A

Job B

Job C

Job D

Time (hours)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Start from due date and work backward

Lathe

Lathe

Lathe

Wait/move

Wait/move

Wait/move

Wait/move

Wait/move

Drill

Drill

Drill

Drill

Wait/move Mill

Mill

Mill

Possible conflict Possible conflict

Either of the preceding schedules can also be used to generate a load profile for each work center. A load profile indicates the workload being placed on that work center. Figure 12.8 shows the load profiles for the backward schedule of Figure 12.7 at an hourly rate. These load profiles were obtained by adding up the number of jobs scheduled during each hour for each machine. Notice that any hour in which more than one hour of machine time is scheduled could present a problem if only one of each machine is available.

Figure 12.8: Load profiles for backward schedule

Lathe Hours

of load

Hours of

load

Hours of

load

Mill

Drill

Time (hours)

0

2

1

0

2

1

0

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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CHAPTER 12Section 12.4 Dispatching in MRP

Forward and backward scheduling are both widely used—and many companies use both. Forward scheduling is useful for jobs that need to start immediately. Backward schedul- ing works well when a desired due date is specified. Both finite and infinite loading can be used with forward and backward scheduling. Finite loading requires much more effort for companies to keep track of which jobs are scheduled for which machines and at what time. Unforeseen problems, variations in processing time, and other factors can combine to make this a wasted effort. Therefore, most companies use infinite loading and then address over-loaded work centers after examining the load profile.

This approach to scheduling helps to point out the importance of capacity requirements planning and its tie-in with both the medium-range production plan and the master schedule. While capacity requirements planning is only a rough estimation, it still helps to ensure that sufficient capacity will be available. If the master schedule indicates a realistic capacity, then infinite loading does not often produce too many problems.

Sequencing When using a forward schedule with finite loading, two jobs are not allowed to be in the same work center at the same time. Thus, if Job 1 had been started at work center A, Job 3 had to wait. But, would it have been better to start Job 3 on work center A first and make Job 1 wait? To answer that question, it is possible to use a tool to schedule each work cen- ter—the Gantt load chart.

Each work center can be indicated by one bar on the Gantt load chart. The job being processed at each work center and its processing time can also be indicated. Figure 12.9 shows the Gantt load chart that corresponds to the forward finite load schedule of Figure 12.6. The primary difference between the forward schedule shown in Figure 12.6 and the Gantt load chart in Figure 12.9 is that the former is organized by job and time, and the latter is organized by operation and time. The Gantt load chart is very useful for finite scheduling because it allows only one job to be run on each machine or work center at one time. Any conflicts will immediately become apparent.

Figure 12.9: Gantt load chart for forward schedule

Lathe

Mill

Drill

Time (hours)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Job A

Job B

Job D Idle Job A Job B Idle Job C

Idle Job C Idle Job A Idle

Job C Idle Job D Idle

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CHAPTER 12Section 12.4 Dispatching in MRP

Input/Output Control Input/output control is a simple method for managing work flow and queue lengths. If work is put into a work center faster than it comes out, a queue will build up. If work is put in at a slower rate than it comes out, the work center may run out of work.

Figure 12.10 shows the input/output report for a work center. The cumulative deviation of actual input from planned input, and cumulative deviation of actual output from planned output are recorded each week. Further, the cumulative change in backlog is determined each week by comparing actual input to actual output. For example, in week 43, actual output exceeds actual input by 30 hours. Therefore, the cumulative backlog decreases by that amount. In week 45, actual input exceeds actual output by 20 hours, therefore, back- log increases by 20 hours.

Figure 12.10: Input/output report in standard hours

Planned input

Actual input

Cumulative deviation

400 380 410 370

350 400

-50 -40 -50

390 370

-50

Week

43 44 45 46

375

47

360

48

365 380

-60 -40

Planned output

Actual output

Cumulative deviation

410 400 400 370

380 380

-30 -30 -50

400 400

-20

Week

43 44 45 46

380

47

390

48

380 370

-20 -40

Backlog hours 80 50 40 60 30 15 25

Simulation in Developing Schedules Scheduling and sequencing can be rather difficult in some situations. This is especially true in job shops where many different end products require different operations. Unfor- tunately, manually developing schedules in such situations can be extremely time con- suming and difficult because there are too many combinations to consider.

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CHAPTER 12Section 12.5 Special Problems in Scheduling Services

Computers help to address this difficulty. Using simulation techniques, it is possible to develop a trial schedule on the computer and then test that schedule without actually processing the jobs. Through this simulation, potential problems can be identified and an improved schedule can be developed. Today, more companies are developing computer simulation programs to help solve their scheduling problems.

12.5 Special Problems in Scheduling Services

One major difference between scheduling the production of goods and scheduling the production of services is that a service cannot be inventoried. For example, a company that manufactures air conditioners can build up its inventory during the winter months in preparation for peak summer demand. But a hospital cannot build up an inventory of emergency room services in advance. Unlike goods, services can be produced only at the time of demand, which means that the strategies for meeting that demand are more limited than for goods. When scheduling some services, such as phone service or public transportation, there is less concern with sequencing and more concern with capacity and service delays or waiting time. Because most service operations cannot store finished goods, they try to resolve excess demand problems with extra capacity or by rationing capacity. These firms provide incentives for people to use services in off-peak times, such as traveling to Hawaii in the summer or offering discounts to seniors for shop- ping at non-peak times. These efforts to shift demand are tools that service industries use to manage capacity.

Sequencing rules are usually applied to situations in which parts or products are waiting to be processed. In the service industry it may be customers who are waiting. In general, companies often apply the first-come, first-served rule in such situations. Of course, that can be frustrating for those of us who, for example, simply want to just cash a check at the bank and must wait for someone with a time-consuming transaction. Banks have adjusted by creating a single waiting line to serve multiple tellers rather than a line for each teller; one person with a very long transaction does not impact everyone waiting in line because that person is free to go to any of the other available tellers. ATMs are widely available so that a simple transaction can be handled many places outside of the bank branch. Some banks have found ways to assuage those callers who must wait to speak with an employee. For example, frequent messages alert waiting customers that their calls will be answered shortly.

Services offer some unique challenges for scheduling. The following sections discuss some of the more common approaches to scheduling for services.

Schedule for Peak Demand One possible approach to scheduling for services is to schedule for peak demand. That means that sufficient capacity will be available at any time to meet the peak expected demand. The advantage of this approach is that it allows for demand to be met at all times under normal conditions. Its greatest disadvantage is that a large portion of capacity may be idle a large percentage of the time.

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CHAPTER 12Section 12.5 Special Problems in Scheduling Services

Utility companies like electricity providers face this problem because they are required by government regulation to meet the demand of its consumers. Electrical power generation systems are very expensive, so idle equipment becomes very expensive. In response, some utilities have offered homeowners a free programmable thermostat with the caveat that the utility can turn up the thermostat by a couple of degrees on days when demand for air conditioning is high in order to reduce usage during a power peak. The utility companies offer discounts to manufacturing companies who use power during low-demand times, like at night. Electric utilities can also buy power from another utility that is nearby when extra power is needed.

Chase Demand There are two methods that companies can use to adjust production rates to match demand—varying the workforce and using overtime. Either of these strategies can be very useful for service companies if they can estimate expected demand with reasonable accuracy. For example, Burger King fast-food restaurants maintain extensive records of historical demand during various days of the week and hours of the day. Each restaurant uses this information to determine how many employees it will need to schedule during each hour.

This approach works best if the employees are willing to work on a part-time basis. Fast food is one industry that is able to schedule its employees in this way. The primary advan- tage of this approach is that it costs less than scheduling for peak demand, while it enables the organization to meet its anticipated demand. The disadvantages are that it requires an extremely flexible workforce, and demand forecasts must be accurate.

Other Approaches Other methods for coping with uneven demand include scheduling appointments or reservations for service, increasing consumer self-service, cre- ating adjustable capacity, sharing capacity, and cross-training employees.

The reservation strategy is commonly used by restaurants, hotels, and airlines. Reservations allow an organization to determine the advance demand for its service while also limiting access to that service. Airlines, in particular, have used reservations to control access to their lowest fares. Those travelers who are willing to book their flights far in advance and satisfy certain length-of- stay criteria receive the best fares; those who book only hours before the flight, when space may be limited, must pay the highest fares. Conversely, when demand for a particular flight is light, late booking may pay dividends with a low-cost fare.

.Tetra Images/Getty Images

Reservations allow an organization to determine the advance demand for its service, while also limiting access to that service.

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CHAPTER 12Chapter Summary

Fast-food restaurants have successfully used consumer participation, such as allowing customers to serve themselves from the salad bar or pour their own drinks, as a way to reduce staffing requirements. This strategy considerably reduces workforce scheduling problems because fewer people are needed. Self-service gas stations also use this tech- nique. The single employee who takes the customers’ money can usually handle any level of demand because the most labor-intensive part—pumping the gas—is done by the customers.

Adjustable capacity involves the ability to use only part of the facilities or available employ- ees at any given time. For example, restaurants can close off sections when demand is low. The wait staff who serve those sections can fill saltshakers and perform other activities to prepare for peak demand. As demand increases, those waiters and waitresses can be moved to wait on tables as sections are opened.

Cross-training employees also provides similar advantages. If employees are trained to perform more than one activity, then they can be shifted from one to another as demand changes, as when employees in a supermarket stock shelves when not working as check- ers or baggers. Sharing capacity is a way that different organizations, or different parts of the same organization, with different demand patterns can use the same facilities, and, possibly, the same employees. For example, many churches have found that their Sunday school facilities, which are idle during the week, can be put to good use as day-care cen- ters. On the weekend, when day care is not in session, the church will use those facilities for other activities. Airlines share gates, check-in facilities, and even ground crews.

Chapter Summary

• There are a wide variety of criteria considered for scheduling, including due date, flow time, WIP inventory, equipment idle time, employee idle time, and costs. Performing well on some criteria can mean performing poorly on others.

• Scheduling involves obtaining the right data about orders (jobs), activities, employees, equipment, and facilities.

• Scheduling a continuous flow process and an assembly line are based on know- ing how that facility is organized and what work is assigned to each workstation or department.

• Scheduling a batch process, where different products with similar processing requirements share the same equipment, involves determining the load on the equipment and the sequence that provides the best outcome.

• Some of the most commonly used dispatching rules for scheduling job shops and some service operations are the earliest due date; shortest processing time; longest processing time; first-come, first-served; and critical ratio.

• Johnson’s rule is a way to schedule a set of jobs across two departments. This provides an optimal result based on flow through time.

• Forward and backward scheduling allows organizations to assign tasks to machines to finish as early as possible to give maximum assurance that due dates will be met (forward scheduling), or as late as possible to avoid holding extra inventory (backward scheduling). These can be done with finite loading, which assumes limited capacity, or infinite loading, which assumes unlimited capacity.

• Priorities are set in an MRP system by considering the due dates and lead times of jobs.

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CHAPTER 12Case Study

Case Study

Central Electronics Company The Central Electronics Company makes electronic chassis that are used to hold the com- ponents of electronics such as televisions and microcomputers. Central has just received an order from a large microcomputer manufacturer with whom Central would like to develop a long-term relationship. If this order can be completed by the due date, such a relationship is almost assured. However, the chances of meeting that due date do not look good.

Each chassis in this order consists of four parts. Each part has the routing and the run times given below. In addition, there is a one-hour set-up time on each machine when- ever it is changed from making one part to another, or from performing one operation to another on the same part. The following table shows the run time in minutes per unit for each part.

Rail Bracket A

Press—2 mins. Shear—1 min.

Drill—1 min. Press—1 min.

Press—2 mins. Press—3 mins.

Shear—1 min. Drill—5 mins.

Bracket B Shield

Shear—1 min. Shear—6 mins.

Press—2 mins. Press—1 min.

Drill—1 min. Drill—1 min.

Shear—2 mins.

Drill—4 mins.

Central has only one press, one drill, and one shear, and each is available only eight hours per day. The order for 150 units must be completed within five days. Each machine must be set up at the start of processing, and again each time a different operation or part is processed on it. There is no assembly time, as the individual parts are shipped to the cus- tomer, which assembles them. However, 150 units of each part must be completed within five days for the order to be filled.

1. If the parts are made in batches of 150, will it be possible to meet the deadline? (Hint: Develop a Gantt load chart for each machine.)

2. Can you identify one machine that has the heaviest load (the bottleneck machine)?

3. What should your strategies be for scheduling production on that bottleneck machine?

4. How can you schedule other machines to be sure that the bottleneck is not idle?

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CHAPTER 12Problems

Discussion Questions

1. Discuss the ways in which flexible manufacturing systems may alter the activi- ties of production scheduling.

2. List the six criteria that can be used for scheduling. 3. Which scheduling criterion do you think is most relevant for a fast-food restau-

rant? For a physician’s office? For a hospital emergency room? 4. Which of the dispatching rules do you use to decide which homework assign-

ment to do first? 5. Explain why scheduling a continuous flow production process involves different

methods than those used for scheduling a job shop process. 6. Which service operations may use the scheduling methods traditionally used for

job shops? 7. For each of the dispatching rules, indicate which scheduling criteria will be satis-

fied, as well as the advantages and disadvantages of that rule. 8. List the data needed for scheduling, and indicate the usual sources. 9. How does dispatching differ from sequencing? 10. How are priorities set for jobs in an MRP system 11. Explain the purpose of using input/output control. 12. How can computer simulation be used for scheduling? 13. Discuss different scheduling procedures that might be used for various types of

service operations, such as a restaurant, a hospital, or an airline.

Problems

1. A company produces four types of paper in batches. Based on the following information, which product should be produced next according to the run-out time criterion?

Product Demand Rate (1,000 ft. per Month)

Current Inventory (1,000 ft.)

Kraft paper 30,000 80,000

Duplicator bond 20,000 40,000

Regular bond 60,000 150,000

Carbon tissue 10,000 40,000

2. The David-Harleyston Bicycle Company produces its two models of bicycles, the Avenger and the Hawk, in batches. Based on the following information, which model should be produced next?

Model EOQ Current Inventory

Monthly Sales

Avenger 2,000 10,000 30,000

Hawk 5,000 6,000 20,000

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CHAPTER 12Problems

3. A consultant must complete four reports. She estimates that report A will take four hours, report B will take three hours, report C will take six hours, and report D will take two hours. In what sequence should she complete the reports, using the shortest-processing-time rule?

4. A job shop has four jobs waiting to be processed on its computer numerically controlled (CNC) lathe. Determine the sequence of these jobs by using each of the five dispatching rules. Assume today is day 107, jobs arrived for processing in the order listed, and the following information is given:

Job Due (Day) Process Time on CNC Lathe (Hours)

Total Processing Time Remaining (Days)

A 120 4 12

B 113 8 5

C 125 2 7

D 115 10 10

5. Late Wednesday afternoon, Data Processing Associates had four jobs waiting to be processed the next day. Each of these jobs requires keying in the data and then processing it on the company’s computer. The DPNs data entry clerks, who work from 8:00 a.m. to 5:00 p.m., with an hour for lunch at noon, complete the data entry. The computer will be available continuously beginning at 9:00 a.m. on Thursday. Jobs may be processed immediately after being entered, or held for processing later.

Job Data Entry Time (Hours)

Processing Times (Hours)

Time Due

A 1 1 3:00 p.m.

B 1 2 12:00 noon

C 2 0.5 2:00 p.m.

D 2 2 5:00 p.m.

a. Develop schedules using the shortest-processing-time, longest-processing- time, and earliest-due-date rules, and draw Gantt load charts for data entry and processing, based on each rule.

b. Evaluate each of the schedules in part a to accommodate for customer service by calculating average past due hours per job for each scheduling rule.

6. Bill Berry, the heat treating department’s second shift foreman at Ace Machine Tool Company, wants to become foreman on the first shift. To look good, Bill wants to keep queues in his department to a minimum, so he has been using the shortest-processing-time rule to schedule work. The assembly department, which

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CHAPTER 12Problems

usually receives jobs after they have been processed in Berry’s department, is complaining they often do not get jobs early enough to meet the due dates.

The following jobs are currently in queue at the heat treating department and must all be processed through the heat treating department and then through the assembly department. Develop a schedule based on the shortest-processing-time rule, and draw a Gantt chart for each department.

Processing Time (Days)

Job Heat Treating Assembly Days Until Due

317 3 1 12

318 1 3 4

324 2 3 10

326 4 2 8

a. Determine whether there is a schedule that can meet all the due dates. b. Comment on the implications of allowing each machine or work center to

schedule its own work.

7. Dr. Houseworth, an orthopedic surgeon, likes to be kept busy during his office hours. All patients scheduled must first have X-rays before they see the doctor. On a certain Monday morning, Dr. Houseworth arrives at his office, and the following three patients are waiting to be X-rayed before seeing him. Determine the sequence in which the patients should be X-rayed to minimize the time Dr. Houseworth is idle.

Patient Time to X-Ray (Min.) Time with Doctor (Min.)

Mrs. Green 5 10

Mr. White 15 20

Ms. Gray 10 20

8. The following jobs are waiting to be processed on one machine. Determine the sequence that will minimize average flow time.

Job Processing Time (Days)

A 4

B 2

C 6

D 3

E 5

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CHAPTER 12Problems

9. The following jobs are waiting to be processed through two work centers. a. Use Johnson’s Rule to determine a sequence. b. Draw a Gantt load chart for each work center.

Processing Time (Hours)

Job Work Center 1 Work Center 2

A 3.0 2.0

B 2.4 3.2

C 1.8 4.0

D 2.2 3.5

10. A printer has six printing jobs. Each job requires typesetting and printing. a. Use Johnson’s Rule to sequence the jobs based on the following expected pro-

cessing times. b. Draw Gantt load charts for printing and typesetting.

Processing Time (Hours)

Job Typesetting Printing

1 2.00 3.00

2 3.00 4.00

3 2.50 1.75

4 1.25 2.00

5 3.50 2.50

6 2.25 3.00

11. A city government requires that all new construction projects be reviewed by an architect, a city planner, and an environmental engineer (in that order). Four different construction projects are waiting to be reviewed, and the review time of each has been estimated as shown in the following.

Project Architect City Planner

Environmental Engineer

A 3 hrs. 2 hrs. 4 hrs.

B 2 hrs. 3 hrs. 2 hrs.

C 4 hrs. 1 hr. 3 hrs.

D 2 hrs. 1 hr. 3 hrs.

If the four projects must be processed in the order A, B, C, D by each person, use forward scheduling with finite loading to develop a Gantt load chart for each person.

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CHAPTER 12Key Terms

backward scheduling An approach to scheduling that starts from a desired due date and works backward.

critical-ratio rule A measure of the ratio between time until an order is due and the processing time remaining.

dispatching Assigning priorities and selection of jobs for processing at a work center.

dispatching rules Rules used for assign- ing processing priorities to jobs for scheduling.

finite loading An approach to machine loading that considers available capacity.

forward scheduling An approach to scheduling that starts from the present time and schedules each job to start at the earliest possible moment.

Gantt load chart A graphic device for indicating the schedule of jobs on equip- ment or facilities.

infinite loading An approach to machine loading that does not take capacity consid- erations into account.

input/output control A method for man- aging work flow and queue lengths by comparing input to a machine with output from it.

load profile A diagram that indicates the work load being placed on each work center.

loading An approach to scheduling that tries to take capacity utilization into account.

makespan time The total time required to complete a set of jobs.

12. Five parts must be processed through the following operations, and each has the due date shown. The following table shows the time required for each processing operation:

Part A Part B Part C Part D Part E

Lathe (2 days) Lathe (1 day) Mill (1 day) Mill (3 days) Drill (1 day)

Mill (3 days) Grind (1 day) Drill (1 day) Grind (1 day) Mill (3 days)

Drill (1 day) Mill (2 days) Lathe (2 days) Grind (1 day)

Due at end of day 8

Due at end of day 6

Due at end of day 5

Drill (1 day) Drill (1 day)

Due at end of day 10

Due at end of day 6

Use backward scheduling with infinite loading to develop a schedule for each part.

13. Develop a load profile for the city planner in Problem 11.

14. Develop a load profile for the milling operation in Problem 12.

Key Terms

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CHAPTER 12Key Terms

make-to-order company A company that produces only to customer orders.

make-to-stock company A company that produces for inventory and meets cus- tomer orders from inventory.

move time The material handling time between work centers.

peak demand The highest level of demand that can be expected during a specific time period.

queue time The time a job spends waiting to be processed at a work center.

run-out time The period of time before a company will run out of a particular product.

run time The actual processing time for a job.

scheduling A final, detailed determina- tion of the times employees will work, the sequence in which goods or services will be provided, and the operating times for machines.

sequencing A step in the scheduling pro- cess in which the ordering of jobs or work is determined.

wait time The time a job spends wait- ing before being moved to the next work center.

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