EXAMPLE: A GEAR MANUFACTURING JOB SHOP

13.5 EXAMPLE: A GEAR MANUFACTURING JOB SHOP

Recall that transportation activities in manufacturing systems employ two modes of transportation: transporters to carry discrete loads (e.g., trucks, forklifts), and conveyors to carry a continuous stream of material or product (e.g., conveyor belts). The Arena facilities for these modes are analogous. Consequently, we focus in this example only on transporters moving among stations (in this case, workstations), thereby sequencing the operations in the requisite order.

Consider a job shop producing three types of gears, G1, G2, and G3, for three different types of cars. The job shop is spread out geographically on the factory floor and its layout consists of the following locations:

An arrival dock

A milling workstations with four milling machines

A drilling workstations with three drilling machines

A paint shop with two spray booths

A polishing area with a single worker

A shop exit The distances among locations are given in Table 13.2.

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Figure 13.46 Simulation results for the improved toll plaza model.

Gear jobs arrive in batches of 10 units and their interarrival times are uniformly distributed between 400 and 600 minutes. Of arriving batches, 50% are of type G1, 30% are of type G2, and 20% are of type G3. A gear job arrives at the arrival dock and from there is dispatched to its specific (type-dependent) sequence of manufacturing oper- ations. A sequence consists of a subset of milling, drilling, painting, and polishing operations. Table 13.3 displays the operations plan showing the sequence of operations and the associated processing times for each gear type. The layout of the job shop and operation sequences of gear types are depicted in Figure 13.47.

Gears are transported among locations by two trucks running at a constant speed of 100 feet/minute. Each truck can carry only one gear at a time. When a job is complete at

a location, the gear is placed into an output buffer, a transport request is made for a truck, and the gear waits for the truck to arrive. Once a gear is transported to the next

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Table 13.2 Distances among job shop locations

From Location

To Location

Distance (feet)

arrival dock

100 arrival dock

milling workstation

100 milling workstation

drilling workstation

300 milling workstation

drilling workstation

400 milling workstation

paint shop

150 paint shop

polishing area

300 drilling workstation

polishing area

150 drilling workstation

paint shop

400 paint shop

polishing area

250 polishing area

arrival dock

250 polishing area

arrival dock

200 shop exit

shop exit

550 shop exit

arrival dock

500 shop exit

drilling workstation

300 shop exit

milling workstation

400 shop exit

paint shop

polishing area

Table 13.3 Operations plan for gears by type

Gear Type

Operations Sequence

Processing Time (minutes)

G1 milling

G2 milling

G3 drilling

location, it is placed in a FIFO input buffer. Finally, when the polishing operation is completed, the finished gear departs from the job shop via the shop exit. Similar models of job shops can be found in Schriber (1990) and Kelton et al. (2004).

To analyze the performance of the job shop, we plan to run a simulation over 1 year of operation. The following statistics are of interest:

Gear flow times (by type) Gear delays at operations locations Machine utilizations

Figure 13.48 depicts an Arena model for the gear shop, consisting of three main segments: gear batch arrivals, gear transportation, and gear processing. A segment-by- segment walkthrough of the model follows next.

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Arrival Shop Dock

Exit

G1 Drilling

Polishing

G2

G3 Workstation

Area

Figure 13.47 Layout of job shop and operation sequences by gear type.

Figure 13.48 Arena model for the gear manufacturing job shop.

13.5.1 G EAR J OB A RRIVALS

Gear entities are created in the Create module, called Create Jobs, whose dialog box is displayed in Figure 13.49. The Entities per Arrival field indicates that gear jobs arrive in batches of 10, and the Time Between Arrivals section specifies batch interarrival times to be uniformly distributed between 400 and 600 minutes. Following arrival, each incoming gear entity proceeds as a separate entity.

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Figure 13.49 Dialog box of the Create module Create Jobs.

Figure 13.50 Dialog box of the Assign module Assign Job Type and Sequence.

An arriving gear entity next enters the Assign module, called Assign Job Type and Sequence, whose dialog box is displayed in Figure 13.50. Here, a gear entity is assigned

a type by sampling it from a discrete distribution, and saving the type code (1, 2, or 3) in its Type attribute. In addition, the ArrTime attribute is assigned the value of the simulation clock, Tnow, for later use in computing the gear entity , s flow time. Finally, the Arena attribute Entity.Sequence is assigned the value of the Type attribute. This attribute acts as an index that associates a gear type with the corresponding operations sequence.

The operations sequences for gear types are specified in the Sequence module from the Advanced Transfer template panel, whose dialog spreadsheet is displayed at the bottom of Figure 13.51. Three sequences (row entries) are defined here, one for each

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Figure 13.51 Dialog spreadsheet of the Sequence module (bottom), the Steps dialog spreadsheet for specifying operations steps of type G1 gears (middle), and the Steps Assignment spreadsheet for specifying milling time assignment of type G1 gears (top).

gear type. Each sequence consists of a sequence name (Name column) and a series of steps (Steps column), listed in the order of processing.

To specify steps, the modeler clicks the button under the Steps column and pops up the Steps dialog spreadsheet. The five steps of type G1 gears processing are displayed in the middle spreadsheet of Figure 13.51. Each step is a row entry specifying the location name and associated values (under the Assignments column). Clicking the correspond- ing button pops up the associated Assignments dialog spreadsheet. The assignment of time for the milling time operation is exemplified in the top spreadsheet of Figure 13.51. Arena , s internal sequencing mechanism is explained in the next section.

13.5.2 G EAR T RANSPORTATION

Job shop locations are modeled as Station modules. Accordingly, every gear entity proceeds to the Station module, called Arrive_Dock, to model its physical arrival at the

, job shop s arrival dock. From here, gear entities will be transported to the job shop floor

to start the first step in their operations sequence. To this end, a gear entity enters the Request module (from the Advanced Transfer template panel), called Request a Truck, whose dialog box is displayed in Figure 13.52. The Transporter Name field indicates a request for a Fork Truck transporter. If multiple transporters are available, the modeler can specify how to select one in the Selection Rule field. Such selections may be cyclical, random, preferred order (as listed in the Transporter module), smallest distance, largest distance, or a specific transporter. Here the selection rule requests the transporter nearest to the arrival dock. Furthermore, the Save Attribute field specifies that the ID of the selected transporter be saved in the Truck_ID attribute of the requesting gear entity. The saved ID will be used in due time

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Figure 13.52 Dialog box of the Request module Request a Truck.

to free that particular truck. Since requesting transporters from multiple locations is a form of contention for resources, the Priority field allows the modeler to assign

a priority to requests issued at multiple Request modules (here a high priority is assigned in order to clear the arrival dock as soon as possible). The Entity Location field indicates

, the location of the requesting entity, and the Velocity field specifies the transporter s

velocity, which is 100 feet/minute in our case. Finally, gear entities requesting transpor- tation at the same Request module are instructed in the Queue Name field to wait in the queue, called a Truck.Queue, until a transporter becomes available.

As soon as a gear entity grabs a truck, it proceeds to the Transport module, called Transport to Shop Floor, whose dialog box is displayed in Figure 13.53. The Trans- porter Name and Unit Number fields specify the type and ID of the selected transporter,

which here is the truck whose ID is kept in the Truck_ID attribute of the requesting gear entity. The transporter/gear destination is specified in the Entity Destination Type field as the By Sequence option, indicating that the destination is determined by the gear entity , s sequence number. This field may also specify a Station module name, using the Station option. It can also specify an attribute or expression. The gear entity and the transporter move as a grouped entity at a velocity of 100 feet/minute as specified in the Velocity field. Note that the velocity may depend on trip type, so that an empty truck and a loaded one can be made to move at different velocities.

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Figure 13.53 Dialog box of the Transport module Transport to Shop Floor.

13.5.3 G EAR P ROCESSING

The gear processing segment encompasses sets of Station modules, each modeling an operation in the sequence, from milling to polishing. Since all sets have the same structure (except for names), we will only walk through the milling operation logic.

When a gear entity is transported to the milling operation, it enters the Station module, called Milling Station. It then proceeds to the Free module, called Free Truck at Mill, whose dialog box is displayed in Figure 13.54. Here, the Transporter Name and Unit Number fields specify the truck to be freed for use by other gear entities, using the Truck_ID attribute of the freeing gear entity.

The association between the transporter and the transported entity is severed: The freed transporter stays at the destination Station module until requested, while the gear entity moves on to the next module. In this case, it enters the Process module, called Milling, whose dialog box is displayed in Figure 13.55. The Seize Delay Release option in the Action field is used to model gear delays at this process. The resource seized is Milling Machine and the processing time is kept in the Milling Time attribute specified in the Sequence module of Figure 13.51. Furthermore, to model four milling machines at the milling workstation, resource Milling Machine has to be declared as having a capacity of four in the spreadsheet view of the Resource module. The capacity of other machine groups is similarly declared.

On completing the milling operation, the gear entity proceeds to the Request module, called Request Truck at Milling, whose dialog box is displayed in Figure 13.56. In this module, the gear entity requests transportation to the next operation, similarly to the

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Figure 13.54 Dialog box of the Free module Free Truck at Mill.

Figure 13.55 Dialog box of the Process module Milling.

first request from the arrival dock to the job shop floor (Figure 13.52). Here, it may have to wait in the queue, called Request Truck at Milling.Queue, which serves as the output buffer for the milling process. The transport operation takes place when a truck arrives and both gear and transporter enter the Transport module called Transport From Milling.

Gear entities move from one operation to another according to their specified sequences. It should be pointed out that Arena handles all sequencing details at run-

, time. The internal Arena attribute IS keeps track of each gear entity s step number in its

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Figure 13.56 Dialog box of the Request module Request Truck at Milling.

sequence. Whenever a sequential transport is requested, Arena increments the IS attribute and indexes into the appropriate Steps module spreadsheet to determine the destination location and travel time. The IS attribute may also be modified by the modeler. Eventually the gear entity arrives at the Station module, called Shop Exit, which is always the last location in each operations sequence.

Next, the transporting truck is freed in the Free module, called Free Truck at Exit, and the finished gear entity is ready to record some statistics and then depart from the model at a Dispose module.

Figure 13.57 displays the dialog box of the Record module, called Tally Flow Time. Here, flow times are tallied with the aid of the ArrTime attribute of each finished gear entity. Note that these flow times are tallied by gear type, using the tally set mechanism. The Tally Set Name field indicates that tallies are to be entered in the Flow Times set. Each gear entity indexes into this set using its Type attribute, specified in the Set Index field. The Flow Times set is specified in the Set module spreadsheet from the Basic Process template panel. Figure 13.58 displays the Set spreadsheet and the members of the Flow Times set.

Arena computes travel times of transporters among Station modules based on their distances and transporter speeds. Figure 13.59 introduces Fork Truck transporters into the model and specifies their parameters in the Transporter module spreadsheet. These

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Figure 13.57 Dialog box of the Record module Tally Flow Time.

Figure 13.58 Dialog spreadsheet of the Set module (bottom) and the Members dialog spreadsheet of the Flow Times set (top).

Figure 13.59 Dialog spreadsheet of the Transporter module (bottom) and the Initial Position Status dialog spreadsheet (top).

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of Units), a Distance Set field for specifying the name of a Distance module allowing the user to specify distances between pairs of Station modules, a Velocity and Units fields that specify the transporter speed (in our case, in feet per minute), and an Initial Position Status column of buttons, which pop up the Initial Position Status dialog spreadsheet (top of Figure 13.59). The latter is used to specify the location at which a transporter resides initially (at simulation time 0). In particular, the top dialog box in Figure 13.59 indicates that all Fork Truck transporters reside initially in the Station module called Arrive_Dock. Note that the transporter speed is the default speed. Arena allows the modeler to override this value and to further distinguish between the speed of an empty transporter (specified in a Request module) and a loaded transporter (specified in a Transport module).

Next, Figure 13.60 displays the dialog spreadsheet of the Distance module (left), as well as a corresponding Stations dialog spreadsheet (right), which pops up on clicking a button under the former , s Stations column.

Finally, the collection of fork truck utilization (a Time-Persistent statistic) and flow- time statistics (Tally statistics) is specified in the Statistic spreadsheet module, as shown in Figure 13.61. Observe that the Arena variable nt(transporter_name) is used to collect transporter utilization, in our case, nt(Fork Truck).

Figure 13.60 Dialog spreadsheet of the Distance module (left) and the Stations dialog spreadsheet (right).

Figure 13.61 Dialog spreadsheet of the Statistic module for collecting fork truck utilization and flow-time tallies.

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13.5.4 S IMULATION R ESULTS FOR THE G EAR M ANUFACTURING J OB S HOP M ODEL

The job shop model was simulated for 1 year and the resulting output report is displayed in Figure 13.62. The Time per Entity section lists the statistics of gear waiting times for each operation. As expected, the average waiting time at the paint shop is very large as compared to the other operation locations, since spray times are quite long. The Usage section displays resource utilizations at individual operation locations. For

Figure 13.62 Simulation results for the gear manufacturing job shop model.

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Figure 13.63 Simulation results for the modified gear manufacturing job shop model.

instance, the utilization of a drilling machine is about 0.0898. The User Specified section displays fork truck utilization statistics and flow-time statistics by gear type. The fact that the average flow times are much larger than the total processing time bears witness to excessive delays in resource queues.

To reduce the wait at the paint shop, we modify the job shop model by increasing the number of paint booths from two to three. The impact of this modification on gear delays and flow times is indicated in the simulation results of Figure 13.63. Clearly, the addition of a paint booth has significantly reduced the delay at the paint shop but slightly increased the delay at the polishing area, because speeding up an operation increases congestion downstream. The overall effect on gear flow times, however, is a slight reduction.