meng448mdtrm1spring16solution

8/16/2019 MENG448MDTRM1Spring16solution

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Spring 2016 “MENG4448: Facilities Planning”Mechanical Engineering Department !"#

!$ !$ Elimam

Name % &D: 80 min'tes

Please write your answers neatly on this sheet. Make sure to have all what you need. Youare NOT allowed to borrow any item. ABSOLUTLY NO !UST"ONS a#ter the #irst $%minutes. &ood Lu'k

1. a. Part Z requires machiningon the same lathe type withoperation B following operation

A as shown next.

Operation StandardTime, min

fficiency, !elia"ility, ! Scrap

A # $%& $' & ( &

B ) *'& $+ & % &

-ind the num"er of lathes required to produce #+++ part Z per wee. Assume that the company will "eoperating ' days per wee, * hours per day.

(perati)n *e+'ire,('tp't

Scrap-

*e+'ire,&np't

!.aila/leime

Stan,ar,ime

E * ) M#s

3 4000 %& 4081$6 2400 6 *'& $+& 1$865! 4081$625 (& 4205$86 2400 4 $%& $'& 8$024178

". /hat is the impact of dou"ling the wor schedule to two shifts on the num"er of machines0/hat is the new num"er of milling machines0

(perati)n *e+'ire,('tp't

Scrap-

*e+'ire,&np't

!.aila/leime

Stan,ar,ime

E * ) M#s

3 4000 %& 4081$6 4800 6 *'& $+& 6$664! 4081$625 (& 4205$86 4800 4 $%& $'& 4$01205

c. Part A is produced in machine 12345 followed "y 123%5. Part B is produced in 123(5. Parts Aand B are assem"led in worstation # to create part 3, which is painted in worstation '. 6t isrequired to deli7er #+++ painted 3 parts. 8i7en the following scrap percentages, determine the

num"er of units in each stage.Stage M# 1 M# 2 M# !ssem/l Painting

- scrap 0$07 0$01 0$02 0$0 0$0

&np't 9'antit 4720$20 424$2 48$01 4271$248 412$51

('tp't 9'antit 424$1 4271$2 4271$27 412$511 4000

%. a. A 2usical instrument company produces a Piano with the following demand and in7entory costs9 Annual :emand ; '+++ units Setup 3ost ; < #++ per order =olding 3ost ; % & of price per piano Piano 7alue ; < %++++

:etermine the conomic lot si>e and the corresponding total cost. /hat is the impact of the lot si>e on thelayout0 ?@ points

E(9 100)tal #)st 40000

he larger l)t sie ;)'l, re+'ire e


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as long as the num"er of accepta"le quality castings is at least 4+ units. 6f fewer than 4+accepta"le castings are produced, none are purchased "y the customer. =owe7er, a penaltyclause in the contract results in the foundry ha7ing to pay the customer < 4'+ per unit short 1"elowthe 4' castings5. The pro"a"ility distri"utions for the num"er of good castings produced in a lot of7arying si>es are gi7en "elow9

G)),#astings

Lot Size: Number of Castings Scheduled

15 16 17 18

10 0$07 0 0 011 0$07 0$07 0 0

12 0$17 0$07 0$07 0

1 0$2 0$17 0$07 0$07

1! 0$27 0$2 0$17 0$07

15 0$ 0$27 0$2 0$17

"15 0 0$ 0$77 0$57

Sum 1 1 1 1

i. State the cost, re7enue and profit functions for this foundry ?4# points#)st: >?9 )r all 'ncti)ns

#@9>A B 600 9 i >C10#@9>A B 600 9 100 > 170 @17>A i 10 ?>?17#@9>A B 600 9 100 @17A i > 17*e.en'e:*@9>A B 57 9 i >C10*@9>A B 1200 > 57 @9>A i 10 ?>?17*@9>A B 1200 @17A 57 @917A i > 17Pr)it:P@9>A B 727 9 i >C10P@9>A B 1157 > 727 9 2270 i 10 ?>?17P@9>A B 1757 727 9 i > 17

ii. :etermine the expected profit for a lot si>e ; 4@ castings ?' points

#)st H*e.en'e

HPr)it

H

1170 12727 757

1100 1670 1570

11870 14557 227

11800 1700 4100

11570 15027 7257

11500 18170 6470

11500 18170 6470

E


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". se the !an Order 3lustering 1"inary5 2ethod to form cells for the machineCpart matrix shown"elow. 6f conflicts exist propose alternati7e approaches for resol7ing the conflict 1show all yourwor5. ?4+ pointsParts Machines DE

PartsMachines 3= Parts Machines DE

! 3 # D ! 3 # D ! 3 D #

1 1 1 6 2 1 1 8 2 1 1 12

2 1 1 12 4 1 1 4 4 1 1 10

1 1 1 1 1 2 1 1 1 7

4 1 1 1 1 1 1 1 3= 8 4 2 1 DE 12 10 7 3= 8 4 2 1

!s sh);n / the ell); c)l)rs ;e )rm t;) man'act'ring cells:#ell &: Machines ! an, 3 t) pr)cess parts 2 an, 4#ell &&: Machines D an, # t) pr)cess parts 1 an, $;) /)ttlenecJs still e B 5070707 B 267Pr),'ct L B 5050120147 B 407

3

A

B C

D

E


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'. Suppose you need to decide on the num"er of machines to "e assigned to one operator. 6ttaes one minute to tra7el "etween machines, 4 minute to load or unload a machine, ' minutes ofautomatic machine time and 4 minute to inspect and pac a finished part. The operator hour costs

meng448mdtrm1spring16solution

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