Models & Metrics

1. Ch 3 Manufacturing Models
and Metrics
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
Learning Objectives:
By the end of the lecture the student should be able to:
■ Apply mathematical models of production
performance problems.
■ Explain the concepts of fixed and variable
manufacturing costs

2. Production Concepts and
Mathematical Models
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No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
■ Production rate Rp
■ Production capacity PC
■ Utilization U
■ Availability A
■ Manufacturing lead time MLT
■ Work-in-progress WIP

3. Operation Cycle Time
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No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
Typical cycle time for a production operation:
Tc = To + Th + Tth
where Tc = 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)

4. Production Rate
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
Batch production: batch time Tb = Tsu + QTc
Average production time per work unit Tp = Tb/Q
Production rate Rp = 1/Tp
Job shop production:
For Q = 1, Tp = Tsu + Tc
For quantity high production:
Rp = Rc = 60/Tp since Tsu/Q  0

5. Production Capacity
Plant capacity for facility in which parts are made in
one operation (no = 1):
PCw = n Sw Hs Rp
where PCw = weekly plant capacity, units/wk
Plant capacity for facility in which parts require
multiple operations (no > 1):
PCw
=
nSwHsRp
where no = number of operations in the routing
o
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
n

6. 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
PC
Q
MTBF
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
MTBF  MTTR

7. Availability -
MTBF and MTTR Defined
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.

8. Manufacturing Lead Time (Batch)
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
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

9. Work-In-Process
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
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
AU PCMLT 
Sw Hsh

10. Costs of Manufacturing Operations
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
■ 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.

11. Fixed and Variable Costs
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.

12. Manufacturing Costs
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
■ 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

13. Typical Manufacturing Costs
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.

14. Overhead Rates
Factory overhead rate:
FOHR =
Corporate overhead rate:
COHR =
where DLC = direct labor costs
DLC
FOHC
DLC
©2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book
Automation, Production Systems, and Computer-Integrated Manufacturing, Third Edition, by Mikell P. Groover.
COHC