Ch 3 Manufacturing Models and Metrics Sections: 1.Mathematical Models of Production Performance 2.Manufacturing Costs 1.

Ch 3 Manufacturing Models and Metrics

Sections:

1. Mathematical Models of Production Performance

2. Manufacturing Costs

1

Why use metrics

“A system of related measures that facilitates the quantification of some particular characteristic”

To track performance in successive periods, Try out new technologies and systems to determine their

merits, identify their problems, To compare alternative methods, and To make good decisions.

2

Production Concepts and Mathematical Models

Production performance metrics:

Production rate Rp for an individual processing or assembly operation is usually expressed as an hourly rate, that is, number of work units completed per hour (pc/hr).

Cycle time Tc is defined as 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 next unit begins.

3

Production Concepts and Mathematical Models

Production performance metrics:

Production capacity PC Utilization U Availability A Manufacturing lead time MLT Work-in-progress WIP

4

Operation Cycle Time

Typical cycle time for a production operation:

Tc = To + Th + Tth

where

Tc = cycle time (min/pc),

To = processing time for the operation (min/pc),

Th = handling time (min/pc) (e.g., loading and unloading the production machine), and

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

5

Production Rate (batch/job shop/flow)

Batch production:

Batch time Tb = Tsu + QTc 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)

Average production time per work unit Tp

Tp = Tb/Q= Tsu/Q + Tc

Hourly production rate Rp = 60/Tp 6


Job shop production:

For Q = 1, Tp = Tsu + Tc

For Q > 1, Tp is determined as in batch production

Mass production:

Rp Rc = 60/Tc since Tsu/Q 0 (Q is very large)where

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

Tc = operation cycle time (min/pc)

7


Flow line production: Bottleneck station is the station with the largest operation

time (with highest utilization)

Tc = Tr + Max To

Tc = cycle time of the production line (min/cycle)

Tr = time to transfer work units between workstations each cycle (min/cycle)

Max To = operation time at the bottleneck station (min/cycle)

Rc = 60/Tc

Rc = theoretical (ideal) production rate (cycles/hr) 8

Production Capacity

“Max rate of output that a production facility is able to produce under a given set of assumed operating conditions”

Operating conditions: Number of shifts per day Number of days per week Employment levels

A work center is a manufacturing system in the plant typically consisting of one worker and one machine.

9

Production Capacity

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

PC = n Sw Hsh Rp where PC = weekly plant capacity (units/wk)n = number of work centers working in parallel

Sw = number of shifts per week

Hsh = hr/shift

Rp = hourly production rate of each work center (output units/hr)

10

Production Capacity

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

PCw =

where no = number of operations in the routing

w sh p

o

nS H R

n

11

Production Capacity

This capacity model assumes that all n machines are producing 100% of the time and there are no bottleneck operations due to variations in process routings to inhibit smooth flow of work through the plant.

There are some operations that are fully utilized while other operations occasionally stand idle waiting for work.

That is, utilization varies.

12

Utilization and Availability

Utilization: U =

where Q = quantity actually produced, and PC = plant capacity

“the amount of output of a production facility relative to its capacity”

Utilization can be assessed for an entire plant, a single machine in the plant or any other productive resource.

PC

Q

13

Utilization and Availability

Availability: A =

where MTBF = mean time between failures, and

MTTR = mean time to repair

“a common measure for reliability of equipment”

MTBF

MTTRMTBF

14

Availability - MTBF and MTTR Defined

15

Manufacturing Lead Time

where

MLTj = manufacturing lead time for part or product j (min)

Tsuji = setup time for operation i (min)

Qj = quantity of part or product j in the batch being processed (pc)

Tcji = operation cycle time for operation i (min/pc)

Tnoji = non-operation time (handling, temporary storage, inspections) associated with operation i (min)

“the total time required to process a given part/product through the plant including any lost time due to delays, time spent in storage, reliability problems, and so on”

1

ojn

j suji j cji nojii

MLT T Q T T

16


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 (handling, temporary storage, inspections)

17


Job shop when Q=1

MLT = no (Tsu + Tc + Tno)

Mass production when QMLT = no QTc

Flow line

MLT = no (Tr + Max To) = no Tc

18

Work-In-Process

WIP =

where WIP = work-in-process, pc;

A = availability,

U = utilization,

PC = plant capacity, pc/wk;

MLT = manufacturing lead time, wk;

Sw = shifts per week,

Hsh = hours per shift, hr/shift

“quantity of parts or products currently located in the factory that are either being processed or between processing operations”

“the inventory in the state of being transformed from raw material to finished product”

w sh w sh

AU PC MLT Q MLT

S H S H

19

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.

20

Fixed and Variable Costs

21

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 with running the manufacturing firm Factory overhead consists of the costs of operating

the factory other than direct labor and materials. Corporate overhead is the cost not related to the

company’s manufacturing activities.

22

Typical Manufacturing Costs

23

Overhead Rates

Factory overhead rate: FOHR =

Corporate overhead rate: COHR =

where

FOHC=annual factory overhead costs ($/yr)

COHC= annual corporate overhead costs ($/yr)

DLC = annual direct labor costs ($/yr)

FOHC

DLC

DLC

COHC

24

Example 3.5

Determine

a. The factory overhead rate for each plant

b. The corporate overhead rate

Expense category

Plant 1 ($) Plant 2 ($) Headquarters ($) Totals ($)

Direct labor

800,000 400,000 1,200,000

Materials 2,500,000 1,500,000 4,000,000

Factory expense

2,000,000 1,100,000 3,100,000

Corporate expense

7,200,000 7,200,000

Totals 5,300,000 3,000,000 7,200,000 15,500,000

25

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

26

Averaging Procedures for Production Models

number of batches of the various part/product stylesQn

1

Average batch quantity

batch quantity for part/product style 1,...,

Qn

jj

Q

j Q

Q

Qn

Q j j n

27


1

Average number of operations in the process routing

number of operations in the process routing of

part/product style

Qn

ojj

oQ

oj

n

nn

n

j

28


1

Average setup time for part/product

setup time for operation in the processing sequence

for part/product style

ojn

sujkk

sujoj

sujk

j

TT

n

T k

j

29


1

1

Grand average setup timeQ

Q

n

oj sujj

su n

ojj

n T

T

n

30


1

Average operation cycle time for item

cycle time for operation for item

1, 2,...,

ojn

cjkk

cjoj

cjk

oj

j

TT

n

T k j

k n

31


1

1

Grand average cycle time for all items

Q

Q

Q

n

oj cjj

c n

ojj

n

n T

T

n

32


1

Average nonoperation time for item

nonopertion time for operation for item

ojn

nojkk

nojoj

nojk

j

TT

n

T k j

33


1

1

Grand average nonoperation timeQ

Q

n

oj nojj

no n

ojj

n T

T

n

34

Ch 3 Manufacturing Models and Metrics Sections: 1.Mathematical Models of Production Performance 2.Manufacturing Costs 1.

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