cim - course notes - chapter 3

7/29/2019 CIM - Course Notes - Chapter 3

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Chapter 3 Manufacturing Models and Metrics

A variety of metrics help manage the operations ofmanufacturing companies. Manufacturing metrics aredivided into two basic categories:

1. Production performance measuresProduction rate, plant capacity, proportion uptime onequipment (reliability measure), manufacturing lead time

2. Manufacturing costs

Labor and material costs, the costs of producing theproducts, the costs of operating a given piece ofequipment


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3.1 MATHEMATICAL MODELS OF PRODUCTION PERFORMANCE

3.1.1 Production Rate

Cycle time Tc: The time that one work unit spends being

processed or assembled. It is the time

between when one work unit begins

processing or assembly and when the nextunit begins.

Typical cycle time for a production operation:Tc= To + Th + Tth

where Tc= cycle time (min/pc), To = processing time for theoperation (min/pc), Th = handling time(min/pc), (e.g., loadingand unloading the production machine), and Tth = toolhandling time (min/pc), (e.g., time to change tools).


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Batch production: batch time Tb = Tsu + QTc

Average production time per work unit Tp = Tb/Q

Production rate (pc/min) Rp= 1/Tp or Production rate (pc/hr)Rp= 60/Tp

where Tb = batch processing time (min), Tsu = setup time

to prepare for the batch (min), Q = batch quantity (pc),Tc= cycle time per work unit (min/cycle).


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Job shop production:

For quantity Q = 1, Tp = Tsu + Tc

For job shop production when Q is greater than one, the

production rate is determined as in batch production case.

where Tp = production time per work unit, Tsu = setup time,

Tc= cycle time.


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Forhigh quantity production ormass production, the

production rate equals the cycle rate of the machine

(reciprocal of operation cycle time) because the effects

of setup time become insignificant, i.e., as Q becomes

very large, Tsu/Q 0.

Rp = Rc= 60/Tc

where Rc= operation cycle rate of the machine (pc/hr),

Tc= operation cycle time (min/pc).


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Forflow line production, the production rate approximates

the cycle rate of the production line, i.e., neglecting setup

time.

Tc= Tr+ Max Toand Rc= 60/Tc

where Tc= cycle time of the production line (min/cycle),Tr= time to transfer work units between stations eachcycle (min/cycle), Max T

o

= operation time at thebottleneck station (the maximum of the operation times forall stations on the line, min/cycle),Rc= theoretical or idealproduction rate or cycle rate (cycle/hr).


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3.1.2 Production Capacity

Definition

The maximum rate of output that a production facility (orproduction line, work center, or group of work centers)

is able to produce under a given set of a assumed

operation conditions. It usually refers to a plant or factory

so that it is also termedplant capacity.


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Plant capacity for facility in which parts are made in oneoperation (no = 1):

PCw= nSwHshRpwhere PCw= weekly plant capacity (unit/wk), n = number

of machines or work centers in the facility, Sw= number of

shifts per week, Hsh = number of hours per shift, Rp = hourlyproduction rate of each work center (unit/hr).

Plant capacity for facility in which parts require multipleoperations (no > 1):

PCw=o

pshw

n

RHnS

where no

= number of operations in the routing.


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Example 3.1

Production Capacity

The turret lathe section has six machines, all devoted to theproduction of the same part. The section operates 10 shift/wk.The number of hours per shift averages 8. Average production

rate of each machine is 17 unit/hr. Determine the weekly

production capacity of the turret lathe section.

Solution

PC= 6 10 8 17 = 8160 output unit/wk


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For short term:

Change the number of shifts per week Sw to affect plant capacity

Change the number of hours worked per shift Hsh to affect plant

capacity

For long term:

Increase the number of work centers n in the shop to increase plantcapacity

Reduce the number of operations no required per work unit by usingcombined operations, simultaneous operations, or integration ofoperations to increase plant capacity


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3.1.3 Utilization and Availability

Utilization UIt refers to the amount of output of a production facility relative to itscapacity.

U=

where Q = quantity actually produced, PC= plant capacity

Utilization can be assessed for an entire plant, a single machine in the

plant, or any other productive resources, i.e., labor. It is also defined asthe proportion of time that the facility is operating relative to the timeavailable under the definition of capacity.

PC

Q


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Example 3.2

Utilization

A production machine operates 80 hr/wk (2 shifts, 5 days) atfull capacity. Its production rate is 20 unit/hr. During a certain

week, the machine produced 1000 parts and was idle the

remaining time. (a) Determine the production capacity of the

machine. (b) What was the utilization of the machine duringthe week under consideration?


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Solution(a) PC= 80 20 = 1600 unit/wk

(b) The ratio of the number of parts made by the machine

relative to its capacity

U= 1000/1600 = 0.625 = 62.5% or

The hours required to produce the given output

hr

His the time during the week that the machine was actually used.

5020

1000H

%5.62625.080

50U


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AvailabilityA

It is a common measure of reliability for equipment.

It is especially appropriate for automated

production. Mean time between failure (MTBF)

Average length of time the piece of equipment runs betweenbreakdowns

Mean time to repair (MTTR)Average time required to service the equipment

and put it back into operation when a breakdown

occurs.


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Availability:A =MTBF

MTTRMTBF


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Example 3.3

Effect of Utilization and Availability on Plant Capacity

The turret lathe section has six machines, all devoted to the production

of the same part. The section operates 10 shift/wk. The number ofhours per shift averages 8. Average production rate of each machine is

17 unit/hr. The availability of the machine is 90% and the utilization of

the machine is 80%. Determine the weekly production capacity of the

turret lathe section.

SolutionQ =AU(nSwHshRp) = 0.9 0.8 6 10 8 17 = 5875 output unit/wk


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3.1.4 Manufacturing Lead Time

Definition: Manufacturing lead time (MLT) is the total time

required to process a given part or product

through the plant, including any lost time due to

delays, time spent in storage, reliabilityproblems, and so on.

Activities of production: Operation Performed on a work unit when it is in the production

machine Nonoperation Handling, temporary storage, inspection, and other

sources of delay when the work unit is not in the

production machine


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where MLTj= manufacturing lead time forPart orProductj(min), Tsuji= setup time for operation i(min),Qj= quantity of part or productjin the Batch beingprocessed (pc), Tcji= operation cycle time for

operation i(min/pc), and Tnoji= nonoperation timeassociated with operation i(min), and iindicates theoperation sequence in the processing; i= 1, 2,, noj,noj= number of operations on partj.

ojn

i

nojicjijsu jij TTQTMLT1


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Simplified model:All setup times, operation cycle times, and

nonoperation times are equal for the nojmachines. Batch quantities

of all parts or products processed through the plant are equal and

they are processed through the same number of machines, i.e.,noj= no.

MLT= no (Tsu + QTc+ Tno)

where MLT= manufacturing lead time for a part or product,no = number of operations, Tsu = setup time, Q = batch

quantity, Tccycle time per part, and Tno = nonoperation time


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Averaging procedure

In an actual batch production factory, the terms no, Q, Tsu,

Tc, and Tno would vary by product and by operation. These

variations can be accounted for by using properly weighted

average vales of the various terms.

The average procedure is explained in Appendix.


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Example 3.4

Manufacturing Lead Time

A certain part is produced in a batch size of 100 units. The batch must be

routed through 5 operations to complete the processing of the parts.

Average setup time is 3 hr/operation and average operation time is 6 min

(0.1 hr). Average nonoperation time due to handling, delays, inspections,

etc., is 7 hr for each operation. Determine how many days it will take

to complete the batch, assuming that the plant runs one 8 hr shift/day.

Solution

MLT= no (Tsu + QTc+ Tno)

= 5 (3 + 100 0.1 + 7) = 100 hr = 100/8 days = 12.5 days


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For job shop production, Q = 1

For mass production, Q term in the MLT equation is verylarge and dominates the other terms. In the case ofno = 1,the MLT simply becomes the operation cycle time.

MLT= no (Tsu + Tc+ Tno)

MLT= QTc


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ForFlow Line mass production, the entire production lineis set up in advance. Also, the nonoperation time betweenprocessing steps is simply the transfer time Tr to move thepart or product from one workstation to the next.

MLT= no (Tr+ MAX To) = noTc or

MLT= n (Tr+ MAX To) = nTc

where MLT= time between start and completion of a given work unit on

the line, no = number of operations on the line, n = number of stationson the line, no = n, because each station completes one operation,

Tr= transfer time, Max To = operation time at the bottleneck station,

Tc= cycle time of the production line.


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3.1.5 Work-in-Process

WIP=

where WIP= work-in-process (pc),A = availability, U= utilization,PC= ideal plant capacity (pc/wk), MLT= manufacturing lead time(hr), Sw= shifts per week, Hsh = hours per shift (hr/shift).

w sh

AU PC MLT

S H

Definition:Work-In-Process (WIP) is the quantity of parts or products

currently located in the factory that either are being

processed or are between processing operations. It is

inventory that is in the state of being transformation from raw

material to finished product.


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3.2 MANUFACTURING COSTS

3.2.1 Fixed and Variable Costs

Two major categories of manufacturing costs:

1. Fixed costs - Remain constant for any output

level, cost of the factory building and productionequipment, insurance, property taxes

2. Variable costs - Vary in proportion to productionoutput level; increase with output, direct labor, raw

materials, electric power to operate the productionequipment


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3.2.1 Fixed and Variable Costs

Adding fixed and variable costs

TC= FC+ VC(Q)

where TC= total costs, FC= fixed costs (e.g., building,equipment, taxes), VC= variable costs (e.g., labor,materials, utilities), Q = output level.

When comparing automated and manual production

methods, it is typical that the fixed cost of the automatedmethod is high relative to the manual method, and thevariable cost of automation is low relative to the manualmethod.


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3.2.1 Fixed and Variable CostsFixed and variable costs as a function of production output


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3.2.2 Direct Labor, Material, and Overhead

Alternative classification of manufacturing costs:

1. Direct labor - Wages and benefits paid to workers

2. Materials - Costs of raw materials

3. Overhead - All of the other expenses associated with

running the manufacturing firm

Factory overhead

Corporate overhead


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Typical factory overhead expenses


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Typical corporate overhead expenses


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3.2.2 Direct Labor, Material, and OverheadCosts for a manufactured product


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Allocation of overhead costs:

Direct labor cost

Material cost

Direct labor hours

Space

Most common in industry is direct labor cost, which will

be used to illustrate how overheads are allocated andsubsequently used to compute factors such as sellingprice of the product.


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3.2.2 Direct Labor, Material, and OverheadOverhead rates

Factory overhead rate (FOHR):

FOHR=

Corporate overhead rate (COHR):

COHR=

where DLC= annual direct labor costs, FOHC= annual factoryoverhead costs, COHC= annual corporate overhead costs.

If material cost were used as the allocation basis, then material costwould be used as the denominator in both ratios.

DLC

FOHC

DLC

COHC


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Example 3.5

Determining Overhead Rates

Suppose that all costs have been compiled for a certain

manufacturing firm for last year. The summary is shown in

the table below. The company operates two different

manufacturing plants plus a corporate headquarters.

Determine (a) the factory overhead rate for each plant, and(b) the corporate overhead rate. These rates will be used

by the firm to predict the following years expenses.


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Solution

(a) For plant 1,

For plant 2,

(b)

%2505.2108

1025

6

1

1

1

DLC

FOHCFOHR

%27575.2104

101.15

6

2

2

2

DLC

FOHCFOHR

%6006102.1

102.76

6

DLC

COHCCOHR


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Example 3.6

Estimating Manufacturing Costs and Establishing Selling

Price

A customer order of 50 parts is to be processed through plant of

Example 3.5. Raw materials and tooling are supplied by the

customer. The total time for processing the parts (including setup and

other direct lobor) is 100 hr. Direct labor cost is $ 10/hr. The factory

overhead rate is 250% and the corporate overhead rate is 600%.(a) Compute the cost of the job. (b) What price should be quoted to a

potential customer if the company uses a 10% markup.


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Solution

(a) The direct labor cost for the job is 100 10 = $1000.

The allocated factory overhead charge, at 250% of direct labor, is

1000 2.5 = $2500.

The total factory cost of the job, including allocated factory overhead

is 1000 + 2500 = $3500.

The allocated corporate overhead charge, at 600% of direct labor, is

1000 6 = $6000.

The total cost of the job including corporate overhead is$3500 + $6000 = $9500.

(b) If the company uses a 10% markup, the price quoted to the customerwould be 1.1 9500 = $10450.


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3.2.3 Cost of Equipment Usage

Deficiency of overhead rates

Based on labor cost only

Equipment factor neglected

Therefore, it is appropriate to divide the cost of a worker

running a machine into two components:

Direct labor

Machine

These costs apply not to the entire factory operations, but to

individual work centers.


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A work center can be any of the following:

One worker and one machine

One worker and several machines

Several workers operating one machine

Several workers and machines

The direct labor cost consists of the wages and benefits paidto operate the work center.


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Applicable factory overhead expenses allocated to direct

Labor cost include

State taxes

Certain fringe benefits

Line supervision

The machine annual cost is the initial cost of the machine

apportioned over the life of the asset at the appropriate rateof return used by the firm.


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Equivalent uniform annual cost is expressed as

niPAICUAC ,,/where IC= initial cost of the machine, (A/P, i, n) = capital recovery

factor that converts initial cost at year zero into a series of equivalent

uniform annual year-end values, where i= annual interest rate and

n = number of years in the service life of the equipment.

11

1,,/

n

n

i

iiniPA


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The uniform annual cost can be expressed as an hourlyrate by dividing the annual cost by the number of annualhours of equipment use.

The machine overhead rate is based on those factoryexpenses that are directly assignable to the machine,including power to drive the machine, floor space,maintenance and repair expenses, and so on.

The total cost rate for the work center is the sum of laborand machine costs.


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For a work center consisting of one worker and one machine,

hourly cost of worker-machine system:

Co = CL(1 + FOHRL) + Cm(1 + FOHRm)

where Co = hourly rate to operate the work center,

CL = direct labor wage rate, FOHRL = factory overhead rate

for labor, Cm = machine hourly rate, FOHRm = factory

overhead rate applicable to the machine.


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Example 3.7

Hourly Cost of a Work Center

The following data are given for a work center consisting of one

worker and one machine: direct labor rate = $10/hr, applicable

factory overhead rate on labor = 60%, capital investment in

machine = $105, service life of the machine = 8 yr,

rate of return = 20%, salvage value in 8 yr = 0, and applicable

factory overhead rate on machine = 50%. The work center will be

operated one 8 hr shift, 250 day/yr. Determine the appropriate

hourly rate for the work center.


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Solution

Labor cost per hour is

CL(1 + FOHRL) = 10 (1 + 0.6) = $16/hr

The number of hours per year = 8 250 = 2000 hr/yr.

/hr

2606.012.01

2.012.011

1,,/8

8

n

n

i

iiniPA

26060$2606.010,,/ 5 niPAICUAC

03.13$2000

26060mC


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Machine cost per hour is

Cm(1 + FOHRm) = 13.03 (1 + 0.5) = $19.55/hr

Total cost rate for the work center is

Co = CL(1 + FOHRL) + Cm(1 + FOHRm)

= 16 + 19.55

= $35.55/hr

cim - course notes - chapter 3

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