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Manufacturing Models and Metrics

Sections:

1. Mathematical Models of Production Performance

2. Manufacturing Costs

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Production Concepts andMathematical Models

Production rate Rp Production capacity PC

Utilization U

AvailabilityA

Manufacturing lead time MLT

Work-in-progress WIP

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Operation Cycle Time

Typical cycle time for a production operation:

Tc= To + Th + Tth

whereTc= cycle time,

To = processing time for the operation,

Th = handling time (e.g., loading and unloading the

production machine), and

Tth = tool handling time (e.g., time to change tools)

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Production Rate

Batch production: batch time Tb = Tsu + QTcAverage production time per work unit Tp = Tb/Q

Production rateRp = 1/Tp

Job shop production:For Q = 1, Tp = Tsu + Tc

For quantity high production:

Rp = Rc= 60/Tp since Tsu/Q 0

For flow line production

Tc= Tr+ Max To and Rc= 60/Tc

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In FLOW LINES, it is easy to calculate OVERALL PRODUCTION

RATE (units/hour) and Capacity (units/month).

12 Units/Hr

5 Mins/Unit

10 Units/Hr

6 Mins/Unit

12 Units/Hr

5 Mins/Unit

Overall Production Rate = 10 Units per Hour

Slowest Work Centre (BOTTLENECK) Determines

OVERALL PRODUCTION RATE OF THE SYSTEM.

Work

Centre

2

Work

Centre

3

Work

Centre

1

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CAN WE EASILY CALCULATE PRODUCTION RATE

OF A JOB SHOP (which has FUNCTION LAYOUT)?

In function layouts, there are more than one product type.

Each product type has a unique routing and process plan.When product mix or new product types are introduced to

the system, changes, the overall production rate also

changes. There is NO single production rate for the

function layout. There may be more than one bottleneck inthe system. The bottleneck(s) also change(s) in the system.

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Production Capacity

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

PCw= n SwHsRpwhere PC

w= weekly plant capacity, units/wk

Plant capacity for facility in which parts requiremultiple operations (no > 1):

PCw

=

where no = number of operations in the routing

o

psw

n

RHnS

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Utilization and Availability

Utilization: U=

where Q = quantity actually produced, and

PC= plant capacity

Availability:A =

where MTBF= mean time between failures, and

MTTR= mean time to repair

PCQ

MTBF

MTTRMTBF

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Availability -MTBFand MTTRDefined

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Manufacturing Lead Time

MLT= no (Tsu + QTc+ Tno)

where MLT= manufacturing lead time,no = number of operations,

Tsu = setup time,

Q = batch quantity,

Tc= cycle time per part, and

Tno = non-operation time

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Work-In-Process

WIP=

where WIP= work-in-process, pc;

A = availability, U= utilization,

PC= 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

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Costs of Manufacturing Operations

Two major categories of manufacturing costs:

1. Fixed costs - remain constant for any output level

2. Variable costs - vary in proportion to production

output level 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.

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Fixed and Variable Costs

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Manufacturing Costs

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 withrunning the manufacturing firm

Factory overhead

Corporate overhead

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Typical Manufacturing Costs

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Overhead Rates

Factory overhead rate:

FOHR=

Corporate overhead rate:

COHR=

where DLC= direct labor costs

DLC

FOHC

DLC

COHC

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Cost of Equipment Usage

Hourly cost of worker-machine system:

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

where Co = hourly rate, $/hr;CL = labor rate, $/hr;

FOHRL = labor factory overhead rate,

Cm = machine rate, $/hr;

FOHRm = machine factory overhead rate