Product and Equipment Analysis

Chapter 2

Data required for developing good layouts

• Product Analysis

• Process Analysis

Input Data and Activities• What data are critical to the facility plan?

• Muther categorizes the information as:

P – Product (what?)

Q – Quantity (how much?)

R – Routing (where?)

S – Support (with what?)

T – Timing (when?)

Product Analysis

• Bill of Materials

• Assembly Charts

• Engineering Drawing

• Operation Process Chart

• Route Sheet

• QFD product development

• TRIZ

• CAD/CAM

Input Data and Activities• Tompkins, White, et. al., categorize it as:

Product Design – what is to be produced?

Process Design – how is it to be produced?

Schedule Design – when and how much?

Product

ScheduleProcess

Facility

Product Design

• Based on– Function– Aesthetics– Costs– Materials– Manufacturing Methods

• Key point– The product design MUST be finalized before

designing the facility. Otherwise a flexible facility is needed.

Driven by market demand

Tools Used in Product Design

• Product/Part Drawings– 2-D, 3-D visualization

• Exploded Assembly Diagrams

Part drawing

Tools Used in Process DesignA partial list (dependent on product and service):• Process Flowcharts and Process Maps• Make vs. Buy • Parts Lists • Bill of Materials• Route Sheets• Assembly Charts• Operations Process Charts• Precedence Diagrams

Process Flowcharts

Reserve Storage

Quality Assurance

Back to Vendor

UPS

Parcel Post

Next-Day UPS

Mono-gramming

Embroid-ering

Hemming

Gift Boxing

Receiving Active Bins Picking Packing Shipping

Process Maps

Place order

Drink

Eat salad or soup

Eat dinner

Receives check

Gives payment to waiter

Collect change, leave tip

Fill in tip amount

Give order to waiter

Prepare dinner order

Prepare soup or salad order

Give order to waiter

Is order complete?

Give soup or salad order to chef

Give dinner order to chef

Get drinks for customer

Deliver salad or soup order to customer

Deliver dinner to customer

Deliver check to customer

Receive payment for meal

Cash or Credit?

Bring change to customer

Run credit card through

Return credit slip to customer

Collect tip

Y

N

Credit

Cash

CustomerCustomer WaiterWaiter Salad ChefSalad Chef Dinner ChefDinner Chef

Make vs. Buy?

Can item be purchased?

MAKE

Can we make the

item?

BUY

Is it cheaper for us to make?

BUY

Is the capital available?

MAKE

Yes

No

YesYes

No

NoNo

BUY

Yes

Parts List

• A listing of component parts.

Company: TW Inc. Prepared By: JSUProduct: Air Flow Regulator Date: 6/30/2003

Part No. Name Drwg. No. Qty/unit Material Size Make/Buy1050 Pipe plug 4006 1 Steel 0.5" x 1.00" Buy2200 Body 1003 1 Aluminum 2.75" x 2.5" x 1.5" Make3250 Seat Ring 1005 1 Stainless Steel 2.97" x 0.87" Make3251 O-Ring - 1 Rubber 0.75" diam. Buy3252 Plunger 1007 1 Brass 0.812" x 0.715" Make3253 Spring - 1 Steel 1.4" x 0.225" Buy3254 Plunger Housing 1009 1 Aluminum 1.6" x 0.225" Make3255 O-Ring - 1 Rubber 0.925" diam. Buy4150 Plunger Retainer 1011 1 Aluminum 0.42" x 1.2" Make4250 Lock Nut 4007 1 Aluminum 0.21" x 1.00" Buy

PARTS LIST

Bill of Materials• Many different types of “structured parts lists”

Company: TW Inc. Prepared By: JSUProduct: Air Flow Regulator Date: 6/30/2003

Level Part No. Name Drwg. No. Qty/unit Make/Buy0 0021 Air Flow Regulator 0999 1 Make1 1050 Pipe plug 4006 1 Buy1 6023 Main assembly - 1 Make2 4250 Lock Nut 4007 1 Buy2 6022 Body Assembly - 1 Make3 2200 Body 1003 1 Make3 6021 Plunger Assembly - 1 Make4 3250 Seat ring 1005 1 Make4 3251 O-Ring - 1 Buy4 3252 Plunger 1007 1 Make4 3253 Spring - 1 Buy4 3254 Plunger Housing 1009 1 Make4 3255 O-ring - 1 Buy4 4150 Plunger retainer 1011 1 Make

BILL OF MATERIALS

Bill of Materials

12 Computer Device

11 Keyboard Assembly (Purchased) 10 Color Video Display Device

8 Video Panel (Purchased) 7 Circuit Board

9 Main CPU Unit 6 Power Supply Kit (Purchased)

5 PC Board Assembly 3 Main PC Board (Purchased) 4 Disk Drive Unit

2 Floppy Drive 1 Hard Drive

Route Sheet

Oper. No.

Operation Description

Machine

Type

Tooling Setup

(hr.)

Oper. Time (hr.)

Mtls.

Parts

0104 Shape, drill, cut off

Auto sc. Machine

.5 in dia coller, cir. Form tool, .45” diam center drill

5 0.0057 Alum

1”x12’

0204 Machine Slot and thread

Chucker 0.045” slot saw, turret slot

2.25 0.0067

0304 Drill 8 holes Auto dr. unit

0.078” diam twist drill

1.25 0.0038

0404 Debur and Blow out

Drill press Deburring tool with pilot

0.5 0.0031

SA 1 Enclose subassembly

Dennison hydraulic press

None 0.25 0.0100

Company: ARC Inc.

Produce: Air Flow Regulator

Part: Plunger Housing

Part No. 3254

Prepared by: JSU

Part No. 6/6/03

Routing sheet MASTER ROUTING LIST MASTER ROUTING LIST--PART NUMBER-- ---------DESCRIPTION---------- DATE ALT CODE BUYER/PLANNER --PART NUMBER-- ---------DESCRIPTION---------- DATE ALT CODE BUYER/PLANNER DRAWING REVISIONDRAWING REVISIONH6709 HANDLE,DENSPLY PROBE 6/25/92 B 239 H6709 HANDLE,DENSPLY PROBE 6/25/92 B 239 G G --------STANDARD-------- --------STANDARD-------- TIME MOVETIME MOVEOPER WORK OPER SETUP CREW MACH --TOOLING REF-- --SETUP- -LABOR- -MACHINE-- I/O OPER WORK OPER SETUP CREW MACH --TOOLING REF-- --SETUP- -LABOR- -MACHINE-- I/O BASIS TIME -----EFFECTIVE----BASIS TIME -----EFFECTIVE----& ALT CENTER CODE CODE FACTOR GROUP NUMBER HOURS HOURS HOURS & ALT CENTER CODE CODE FACTOR GROUP NUMBER HOURS HOURS HOURS CDE/-QTY- -DAYS- FROM TOCDE/-QTY- -DAYS- FROM TO 10 01226 1.0 01226 T9330 12.000 336.880 336.880 4 10 01226 1.0 01226 T9330 12.000 336.880 336.880 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- MAKE @ AUTO 804843P MAKE @ AUTO 804843P C 804843P B C 804843P B A A02247 A A A02247 A 15 02053 1.0 02053 T9712 1.500 41.670 83.330 4 15 02053 1.0 02053 T9712 1.500 41.670 83.330 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- DRILL & TAP 804843P1 DRILL & TAP 804843P1 B 804843P1 A B 804843P1 A 20 02053 1.0 02053 T9713 1.500 8.330 16.670 4 20 02053 1.0 02053 T9713 1.500 8.330 16.670 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- KNURL OD KNURL OD 30 03029 1.0 .000 33.330 33.330 4 30 03029 1.0 .000 33.330 33.330 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- SCOTCHBRITE/BELT SCOTCHBRITE/BELT 40 03105 1.0 03105 .000 3.000 3.000 4 40 03105 1.0 03105 .000 3.000 3.000 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- PASSIVATE PASSIVATE 50 03005 1.0 .000 54.170 54.170 4 50 03005 1.0 .000 54.170 54.170 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- BUFF BUFF 60 03007 1.0 03007 .000 50.000 50.000 4 60 03007 1.0 03007 .000 50.000 50.000 4 1000 .000 0/00/00 99/99/991000 .000 0/00/00 99/99/99PARTIAL AHEAD QTYPARTIAL AHEAD QTY ----------ROUTING DESCRIPTIONS---------- ----------ROUTING DESCRIPTIONS---------- GLASSBEAD KNURL/ SHIP GLASSBEAD KNURL/ SHIP

Analog model of the assembly

process.

• Circles denote components

• Links denote

operations/subassemblies

• Squares represent inspections

operation

• Begin with the original product

and to trace the product

disassembly back to its basic

components.

Assembly Chart2200

3254

3253

3252

3251

3250

3255

4150

4250

A-1

Pack

SA-1

A-2

A-3

I-11050

A-4

Assembly Charts

９５

６

７

８

1１

1０

1２

３

1

２

４

Found by superimposing

the route sheets and the

assembly chart, a chart

results that gives an

overview of the flow within

the facility.

Operations Process Chart

Volume Variety ChartsProduct Units/year Percent

C 14000 47%F 6000 67%G 3250 78%J 3000 88%K 1120 92%A 1000 95%E 650 98%D 450 99%B 100 99%H 100 100%I 81 100%

0

2000

4000

6000

8000

10000

12000

14000

16000

C F G J K A E D B H I

Products

Un

its/

yr

0%

20%

40%

60%

80%

100%

120%

Per

cen

t

Volume Variety ChartProduct Units/year Percent

P 800 13%F 766 26%C 600 36%J 542 45%G 513 53%O 498 62%K 475 69%A 423 76%Q 418 83%E 322 89%D 234 93%B 100 94%H 100 96%N 100 98%I 81 99%L 52 100%M 16 100%

0

100

200

300

400

500

600

700

800

900

P F C J G O K A Q E D B H N I L M

Products

Un

its/

Yr

0%

20%

40%

60%

80%

100%

120%

Per

cen

t

Production Requirements – Yield Loss

)1( i

ii s

OP

i

Pisi

OiPi

Pi – Production input to operation i

si – Fraction of Pi lost (scrap)

Oi – output of process i

)1( iii

iiii

sPO

sPPO

Production Requirements – Series Systems

1

P1s1

2 n OnP1

Pnsn

. . .

)1()1)(1( 211

n

n

sss

OP

P2s2

Example

• 5 processes in series• Need 2000 units out

2190)03.1)(02.1)(01.1)(02.1)(01.1(

20001

P

Process Loss Out In5 3% 2000 20624 2% 2062 21043 1% 2104 21252 2% 2125 21691 1% 2169 2190

Production Requirements – Non SeriesPart A Part B

M1s1=1% 1

M22s2=2%

M2s3=2% 3

M3s4=1% 4

M4s5=4% 5

100,000 units

451,10899.

366,107

1

366,10798.

219,105

1

366,10798.

219,105

1

219,10599.

167,104

1

167,10496.

000,100

1

1

11

2

22

3

33

234

44

45

55

s

OP

s

OP

s

OP

OOs

OP

Os

OP

Work backward from end of the line.

Simple equipment selection model

• P desired prod rate

• t time (in hours)

to process one part• m/c avail time

(in hours)• m/c efficiency

tPNM

Simple equipment selection model

• Nol Number of good units at output of stage l

• Nil Number of units reqd at input of stage l

• Sl Scrap at stage l

1ol

ill

NN

S

Simple example1. Consider a simple job shop manufacturing system that makes three

major “Class A” products requiring three types of machines. The three products include seven parts shown in Table 2.1. Table 2.1 also shows the time standards in units per hour.

2. Assume an hour has only 55 minutes of productive time and that 5 minutes are lost due to operator or machine unavailability and machine downtime.

3. Dividing the value 55 by the values in Table 2.1, we get the as well as time per unit.

4. Determine the quantities of machines of each type required to make the standard time per unit.

5. Assuming 12000 “representative” parts are to be made and that only 440 minutes of productive time is available per shift, we can find that we need 12000*0.1799/440= 4.9 units of machine A, 5.85 units of machine B, and 4.3 units of machine C.

6. Rounding up these numbers gives us 5, 6, and 5 units of machine types A, B, and C, respectively.

Table 2.1

PartMachine

1 2 3 4 5 6 7

A 2000 - 1200 1500 - 2300 1200

B 1200 1800 1200 - 1600 2000 1000

C - - 1200 2000 1200 - 1400

Table 2.2

PartMachine

1 2 3 4 5 6 7 Total Time

A 0.0275 - 0.0459 0.0367 - 0.0239 0.0459 0.1799

B 0.0459 0.3056 0.0459 - 0.0344 0.0275 0.0550 0.2143

C - - 0.0459 0.0275 0.0459 - 0.0393 0.1586

Calculating Equipment Requirements

How many pieces of equipment do we need?Pi Production rate for operation i (pcs/period)

Ti Time per piece for operation i (time/pc)

Ci Time available to run operation i (time/period)

Ei Efficiency of machine while running

Ri Reliability of machine

Mj Number of type j machines required

xj Set of operations run on machine j

periodtime

pctime

periodpc

REC

TPM

jXi iii

iij

Example• Consider Machine 2

• x2={2,3}

• Do similar calculation for other machines

• Other factors to consider– Number of shifts– Setup times– Customer lot sizes (smaller require more setups)– Layout type– Maintenance activities

Oper (i) Pi (pcs/yr) Ti (hr/pc) PiTi (hrs/yr) Ci (hrs/yr) Ei Ri CiEiRi (hrs/yr) No. Mach.

2 107,366 0.043 4616.7 2000 0.98 0.99 1940.4 2.383 107,366 0.022 2362.1 2000 0.90 0.99 1782.0 1.33

M2= 3.70

Operator-Machine Charts• Tool for showing activity of

both operator and machine along a time line

• Also called “multiple activity chart”

Example:1 minute to load

1 minute to unload

6 minute run cycle

0.5 minute to inspect and pack

0.5 minute to travel to another machine

Time Operator M10.5 U1 UNLOAD1 U1 UNLOAD

1.5 L1 LOAD2 L1 LOAD

2.5 I&P RUN3 RUN

3.5 RUN4 RUN

4.5 RUN5 RUN

5.5 IDLE RUN6 RUN

6.5 RUN7 RUN

7.5 RUN8 RUN

Cycle Time 8 minOper Idle 5.5 minMach. Idle 0 minProd. Rate 0.125 pc/min

ONE MACHINE

Operator Machine Charts

Time Operator M1 M2 Time Operator M1 M2 M20.5 U1 UNLOAD RUN 0.5 U1 UNLOAD RUN RUN1 U1 UNLOAD RUN 1 U1 UNLOAD RUN RUN

1.5 L1 LOAD RUN 1.5 L1 LOAD RUN RUN2 L1 LOAD RUN 2 L1 LOAD RUN RUN

2.5 I&P RUN RUN 2.5 I&P 1 RUN IDLE RUN3 T-2 RUN RUN 3 T-2 RUN IDLE RUN

3.5 U2 RUN UNLOAD 3.5 U2 RUN UNLOAD RUN4 U2 RUN UNLOAD 4 U2 RUN UNLOAD RUN

4.5 L2 RUN LOAD 4.5 L2 RUN LOAD RUN5 L2 RUN LOAD 5 L2 RUN LOAD RUN

5.5 I&P RUN RUN 5.5 I&P 2 RUN RUN IDLE6 T-1 RUN RUN 6 T-3 RUN RUN IDLE

6.5 RUN RUN 6.5 U3 RUN RUN UNLOAD7 RUN RUN 7 U3 RUN RUN UNLOAD

7.5 IDLE RUN RUN 7.5 L3 RUN RUN LOAD8 RUN RUN 8 L3 RUN RUN LOAD

8.5 I&P 3 IDLE RUN RUNCycle Time 8 min 9 T-3 IDLE RUN RUNOper. Idle 2 minMach Idle 0 min Cycle Time 9 minProd Rate 0.25 pc/min Oper. Idle 0 min

Mach Idle 1 minProd Rate 0.333333 pc/min

TWO MACHINES THREE MACHINES

Parameters for an LP equipment selection model

• Oi Operation type i, i=1,2,...,o• Mi Production equipment type i, i=1,2,...,m• Pi Part type i, i=1,2,...,p• MHi Material handling system type i, i=1,2,...,n• cij cost of performing operation Oi on production equipment type Mj

• hij cost of handling part type Pi using material handling system type MHj

• tij time required to perform operation Oi on production equipment type Mj

• sij time required to transport part type Pi using material handling carrier type MHj

• τj time available on production equipment type Mj

• σj time available on material handling carrier type MHj

• NOi number of operations Oi to be performed• NPi number of units of part type Pi to be manufactured• Cj cost of production equipment type Mj

• Hj cost of material handling system MHj

• B total budget available

Decision Variables for LP equipment selection model

• xij number of operations Oi to be performed on production equipment type Mj

• yij number of units of part type Pi to be transported on material handling system type MHj

• NMj number of units of production equipment type Mj selected

• NMHj number of units of material handling system type MHj selected

• MIDTERM,May3rd

LP equipment selection model

• Min

• Subject to1

=1,2,...,m

ij ij

x NO i o

1 1 1 1 1 1

po m n m n

ij ij ij ij i i i ii j i j j i

c x h y C NM H NMH

1

=1,2,...,o

ij ij j ji

t x NM j m

1

=1,2,...,n

ij ij

y NP i p

1

=1,2,...,p

ij ij j ji

s y NMH j m

LP equipment selection model (cont)

1 1

m n

i i i ii i

C NM H NMH B

0 and integer 1, 2,..., ; 1, 2,...,ijx i o j m

0 and integer 1, 2,..., ; 1, 2,...,ijy i o j m

0 and integer 1, 2,...,jNM j m

0 and integer 1, 2,...,jNMH j m

Example

An automobile engine cylinder manufacturing company that supplies high precision engines to a multinational car manufacturer plans to manufacture several models of cylinder.For planning purposes, it uses the following pseudo products - a standard(basic) engine cylinder, a high-technology model, an engine cylinder for sports cars and a luxury car cylinder.The marketing department has demand forecast figures which have been aggregated for the four pseudo models. It has been determined that 2000, 1500, 1800 and 1000 units of the basic, high-tech, sports and luxury models will be demanded during the next six months.

Example

The models require one or more of three operations, referred to as O1, O2, and O3.Three machine types and two material handling systems available for performing the three operations and transporting the models. These are denoted as M1, M2, M3 and MH1, MH2, respectively.Each machine and handling system may be assumed to be available for 90 percent of the time.The cost of machines M1, M2, and M3 are $230,000; $250,000; $310,000. The number of operations needed of each machine is 200,200 and 150 respectively.The cost of material handling carriers MH1, MH2 are $90,000 and $130,000The available budget is $10,000,000.The following two matrices show the cij's and hij's - that is, the cost of performing operation Oi on production equipment type Mj and cost of handling part type Pi using material handling system type MHj, respectively. (Units/ 10 unit time)

Data for example

6 12 8 10 5

[cij]= 4 20 4 [hij]= 12 6

12 10 5 18 9

6 3

LP Model for example• MIN 90000 NMH1 + 130000 NMH2 + 230000 NM1 + 250000 NM2• + 310000 NM3 + 6 X11 + 12 X12 + 8 X13 + 4 X21 + 5 X22• + 4 X23 + 12 X31 + 5 X32 + 5 X33 + 10 Y11 + 5 Y12 + 12 Y21• + 6 Y22 + 18 Y31 + 9 Y32 + 6 Y41 + 3 Y42• SUBJECT TO• C1) X11 + X12 + X13 >= 200• C2) X21 + X22 + X23 >= 200• C3) X31 + X32 + X33 >= 150• C4) - 300 NM1 + 1.67 X11 + 2.5 X21 + 0.83 X31 <= 0• C5) - 300 NM2 + 0.833 X12 + 2 X22 + 2 X32 <= 0• C6) - 300 NM3 + 1.25 X13 + 2.5 X23 + 2 X33 <= 0• C7) Y11 + Y12 >= 2000• C8) Y21 + Y22 >= 1500• C9) Y31 + Y32 >= 1800• C10) Y41 + Y42 >= 1000• C11) – 300 NMH1 + 0.1 Y11 + 0.0833 Y21 + 0.056 Y31 + 0.167 Y41 <= 0• C12) - 300 NMH2 + 0.2 Y12 + 0.167 Y22 + 0.11 Y32 + 0.33 Y42 <= 0• C13) 90000 NMH1 + 130000 NMH2 + 230000 NM1 + 250000 NM2• + 310000 NM3 <= 1000000• END• GIN 5

LP Model Solution• VARIABLE VALUE REDUCED COST• NMH1 2.000000 90000.000000• NMH2 .000000 105454.546875• NM1 2.000000 228562.875000• NM2 1.000000 248353.593750• NM3 .000000 308353.593750• X11 200.000000 .000000• X12 .000000 2.571524• X13 .000000 .860030• X21 59.880245 .000000• X22 140.119751 .000000• X23 .000000 1.744012• X31 140.119751 .000000• X32 9.880246 .000000• X33 .000000 .000000• Y11 2000.000000 .000000• Y12 .000000 11.363637• Y21 1500.000000 .000000• Y22 .000000 7.663636• Y31 1800.000000 .000000• Y32 .000000 .000000• Y41 1000.000000 .000000• Y42 .000000 24.000002

Parameters for LP equipment selection model

• rik number of times operation Oi is to be performed on part type Pk

• cijk cost of performing operation Oi using production equipment type Mj on part type Pk

• tijk time required to perform operation Oi using production equipment type Mj on part type Pk

• xijk number of units of operation Oi performed using production equipment type Mj on part type Pk

• Cj purchase cost of production equipment type Mj prorated over the planning period

LP equipment selection model

• Min

• Subject to1

=1,2,..., ; =1,2,...,m

ijk ik kj

x r NP i o k p

1 1 1 1

po m m

ijk ijk j ji j k j

c x C NM

1 1

=1,2,...,po

ijk ijk j ji k

t x NM j m

0 and integer 1, 2,..., ; 1, 2,..., ; 1, 2,...,ijkx i o j m k p

0 and integer 1, 2,...,jNM j m

Queuing Model

Manufacturing engineers at the Widget Manufacturing Company recently convinced their manager to purchase a more expensive, but flexible machine that can do multiple operations simultaneously. The rate at which parts arrived at the machine that was replaced by the flexible machines follows a Poisson process with a mean of 10 parts per hour.The service rate of the flexible machine is 15 parts per hour compared with the 12 units per hour service rate of the machine it replaced. (All service times follow an exponential distribution.)

Queuing ModelThe engineers and manager were convinced that the company would have sufficient capacity to meet higher levels of demand, but just after a two months of purchasing the machines it turned out that the input queue to the flexible machine was excessively long and part flow times at this station were so long, that the flexible machine became a severe bottleneck.The engineers noticed that more parts were routed through this machine, and that the parts arrival rate to the flexible machines had increased from 10 per hour to about 14 per hour, but were puzzled why the part flow time at this station doubled from 30 minutes to one hour and the work-In-process (WIP) inventory increased nearly threefold from 5 to 14 when the arrival rate only increased 40%.Use a queuing model to justify the results observed at Widget Manufacturing Company.

M/M/1 Model Solution

Parameters Replaced Machine Flexible MachineArrival rate 10 14

Service Rate 12 15Machine Utilization

0.83 0.93

WIP 5 14

Flow Time 0.5 1

Parameters Replaced Machine Flexible MachineArrival rate 10 14

Service Rate 12 15Machine Utilization

0.83 0.93

WIP 5 14

Flow Time 0.5 1

Personnel requirements analysis

• n number of types of operations

• Oi aggregate number of operation type i required on all the pseudo (or real) products manufactured per day

• Ti standard time required for an average operation Oi

• H total production time available per day

• η assumed production efficiency of the plant

1

ni i

i

TON

H

Queuing ModelThe American Automobile Drivers’ Association (AADA) is the only office serving customers in New York’s greater capital district area. Ahead of the busy summer season, the office manager wants to hire additional staff members to help provide these services to members effectively - summer travel planning, membership renewal, disbursing traveler’s checks, airline, hotel, and cruise booking, and other travel related services.It is anticipated that each customer typically requires 10 minutes of service time and customers arrive at the rate of one customer every three minutes.The arrival process is Poisson and the service times are exponentially distributed.Determine how many staff members are required if the average wages and benefits per staff member are $20 per hour and the “cost” to AADA for every hour that a customer waits to be served is $40.

M/M/m Model Solution

Number of staff members (m) 4 5 6Arrival rate 20 20 20

Service Rate 6 6 6

Machine Utilization 0.83 0.67 0.56

Time in queue 0.1447 0.0261 0.0075Hourly Cost $195.74 $120.85 $126.01

Number of staff members (m) 4 5 6Arrival rate 20 20 20

Service Rate 6 6 6

Machine Utilization 0.83 0.67 0.56

Time in queue 0.1447 0.0261 0.0075Hourly Cost $195.74 $120.85 $126.01

Production space requirement sheet

Department Name

WorkCenterName

WorkCenterCode

Length(feet)

Width(feet)

Area(feet2)

Auxiliary Area(feet2)

Operator Space(feet2)

Material Space(feet2)

Sub-Total(feet2)

Allowance (feet2)

Totalspace permachine(feet2)

NumberofMachines

TotalSpace MachineType(feet2)

GeneralMachining

VerticalMilling

1202 15 15 225 70 30 50 375 150% 565 2 1130

Planer 2005L 25 5 125 40 20 40 225 125% 290 1 290

PunchPress

3058 10 10 100 30 20 20 170 140% 240 2 480

InjectionMolding

6078 20 10 200 60 50 100 410 150% 615 3 1845

OtoscopeCell

NC-Machine

9087 20 8 160 50 30 30 270 125% 340 2 680

Lathe 1212 15 8 120 40 20 30 210 150% 315 1 315

Auto-Chucker

2056 5 5 25 10 5 5 45 125% 60 1 60