Numerical Operations From PU

8/13/2019 Numerical Operations From PU

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NUMERICAL QUESTIONS:

1. The PU plumbing supply company stocks a particular type of brass valve. The company operates 250 daysin a year and sells approximately 1 000 valves per year at a constant rate .The valve costs !s."0 from thesupplier and the lead time delivery is five #ork days .$t costs PU %ompany !s.200 in fixed costs to placeand order and the annual holding cost is 25& of the item's cost .find the economic order (uantity for thecompany .%alculate the total annual costs for the company. %ompare the cost #ith the total annual stockingcost that #ould result from a policy of ordering in a month. )etermine the reorder point also.

200* fall2. + manufacturing company has monthly demand for one of its product as follo#s,

-. onth )emand onth )emand

/ebruary ". 520 5. une . 00*. arch . "30 3. uly 10. "2011. +pril 12. 550 1-. +ugust 1". 510

15. ay 1 . 5 0 1*. 4eptember1 . 10)evelop three period simple moving average forecast and a three period #eighted moving averageforecast #ith #eights of 0.50 0.-0 and 0.20 for the most recent demand values in that order. %alculate

+) for each forecast and indicate #hich forecast is better.200*

fall-. lectro 6amp %orporation manufactures emergency lights. The 7uality %ontrol anager 8as

collected the follo#ing data from a day's production to check #hether the lights do light or not,49. 1 2 - " 5 * 3 10

9o. oflampstested

200 200 200 200 200 200 200 200 200 200

9o. of

lampsnotlighting

20 2 1 11 1 12 10 1" 1

)ra# a suitable (uality control chart for 33.*-& confidence interval :;hat is your comment aboutthe process?

200*fall

". >hat are the characteristics of (ueuing system? 4tudents arrive at the +dministrative 4ervice @ffice atan average of one every 15 minutes and their re(uests take on average of 10 minutes to be processed. Theservice counter is staffed by only one clerk r. !amesh Aarki #ho #orks eight hour per day. +ssumePoisson xponential service times.i. #hat percentage of time is !amesh idle?ii. >hat is probability that an arriving student #ill find at least one other student #aiting in line?

200* fall

5. 10 samples of 15 parts each #ere taken from an ongoing process to establish a control chart. Thesamples and the number of defectives in each are sho#n in the follo#ing table,

4ample no. 9o. of defectives 4ample no. 9o of defectives1 - 22 1 * 0- 0 -


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" 1 3 15 2 10 0

i. )evelop a suitable control chart for 35& confidence level :;hat comments you can make?

200 4pring

. 8istorical demand for a product is,onth )emandanuary 12

/ebruary 11arch 15

+pril 12ay 1une 15

i. Using a #eighted moving average #ith #eights 0." 0.2 and 0.1 find the uly forecast.ii. Using a simple three month moving average. /ind the uly forecast.iii. By observing +) for each of the above methods state #hich method is preferable and #hy?

200 4pring

*. The maintenance department of large hospital uses about 1 cases of li(uid cleanses annually. @rdering cost isC12 carrying cost is C" per case a year and the ne# price schedule indicates that orders of less than 50 cases #illcost C23 per case 50 to *3 cases #ill cost C1 per case 0 to 33 cases #ill cost C1* per case and larger orders #illcost C1 per case. )etermine the optimal order (uantity and the total cost.

200 4pring

. +ssume a driveDup #indo# at a fast food restaurant. %ostumers arrive at the rate of 25 per hour. The employeecan serve one costumer every t#o minutes. +ssume Poisson arrival and exponential service rates. Determine:

i. >hat is the average utiliEation of the employee?ii. >hat is the average number of costumers in line?

iii. >hat is the average number of costumers in the system?iv. >hat is the average #aiting time in line?200 4pring

3. + police department carried out an investigation survey by taking a sample of 1000 people each month in a cityhaving a population of 200000. The crime incidence #as as follo#,

onth %rime incidence %rime ratean * .00*

/eb 3 .003arch * .00*

+pril " .00"ay * .00*

une 3 .003uly * .00*+ug 10 .0104ept .00@ct 11 .011

9ov 10 .010)ec .00i. %onstruct a 35& confidence interval control chart. :;hat is your comment? $s the police patrolling effective in controlling crime in the city?


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200" /all10. + photocopy firm uses an average of "0 packages of paper per day. The firm operates 2 0 days a year. 4torageand handling costs for the paper are !s. - per year per pack and it costs approximately !s. to order and receive ashipment of paper. i. calculate the optimal order siEe.ii. %ompute the total annual cost of carrying and holding paper.

200" fall11. The manager of a department store is interested in providing good service to senior citiEens #ho shop in hisstore. There is a separate checkDout counter for senior citiEens. @n average -0 senior citiEens arrive per hour at thecounter according to Poisson distribution and they are served at an average rate of -5 customers per hour #ithexponential service times. /ind outi. average utiliEation of the check out clerk.ii. +verage number of customer in line.iii. The average time spent #aiting in line.

200" /all

12. + ultinational %ompany : 9%= is planning to establish a manufacturing plant for its products. The 9% hasselected follo#ing sites for the product unit.

6ocation /ixed costs :!s.= Fariable costs per unit :!s.=+ 2500 *B *000 5% 10000 -

)etermine the volume ranges for #hich the selected locations suit the best.

200" 4pring1-. $n a process 10 samples of 200 items each #ere taken from a day's production. The number of defective items ineach sample #as recorded as follo#s,4ample

9o.1 2 - " 5 * 3 10

9o. ofdefectives

1" 20 "2 22 1 2 2 12

)ra# a suitable (uality control chart and give your comments about the process. 200" 4pring1". $n the product tree structure sho#n in the figure one unit of finished one unit of finished product ; is made oft#o units of + and four units of B. + is made of three nits of % and four units of ).

6eadDout for fabrication or purchase is, ; takes 2 #eeksG + % and ) take one #eek each and B takes - #eeks. /iftyunits of ; are re(uired in period 10. )evelop an !P schedule sho#ing gross and net re(uirements order releaseand order receipt dates. 200" 4pring

Z

A (2) B (4)

C D (4)


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15. ))% re(uires 12000 units of material annually. $f ordering cost are !s. 250 per expected lead time is 5 daysunit cost is !s. 25 per unit and annual inventory holding cost are charged at 20& and the company operates 250 daysin a year. %ompute @7 and !@6.

200* 4pring

1 . 10 samples of 15 parts each #ere taken from an ongoing process to establish a chart for control. The samples andno of defectives in each are sho#n in the follo#ing table.4ample 1 2 - " 5 * 3 10

9o ofdefective sample

- 1 0 0 0 2 0 - " 0

)ra# a suitable (uality control chart for 35& confidence interval. %omment on the information provided by thechart.

200* 4pring

1*. %ool 4pring ineral >ater Pvt. 6td. is thinking to expand its production unit to meet increasing market demand.%urrently it has three options to build large medium and small plant. $f it builds large plant and market demandturned out to be high then revenue :present value of future profits= of !s. 5 000 000 could be realiEed in case ofmarket demand is lo# then revenue of !s. " 000 000 could be realiEed. 8o#ever a medium unit #ould yieldrevenue of !s. " 000 000 in case of high market demand and revenue of !s. 2 000 000 for lo# market demand. +small unit on other the hand #ould result in the revenue of !s.2 000 000 for high market demand and revenue of!s. 500 000 for lo# market demand. The cost estimated to build large medium and small plant is !s. - 000 000 !s.2 500 000 and !s. 1 000 000 respectively. !ecent market research indicates that there is 0." probability of high market demand and 0. probability of lo#market demand. >ith this information make a decision tree for %ool 4pring ineral >ater Pvt. 6td. to find out #hatoption should it go for.

200* 4pring

1 .$n a manufacturing concern the demand for an item #as observed as follo#s,onth +ctual demand:9o of

units=+pril 250

ay 100une 220uly 2"0

The forecast for the month +pril #as 130 units. Using a smoothing constant of 0.2 and using the first orderexponential smoothing compute the forecast for +ugust.8o# does the choice of smoothing constant affect the forecast?

200* 4pring13. /ive Hobs a#ait processing on a machine. The setup cost sho#n belo# depends upon the se(uence in #hich the

Hobs are processed. +pply the next best rule to determine the se(uence for these Hobs if Hob $ is processed first.4etup cost in !s.

Predecessor Hob $ $$ $$$ $F F$ D 1-0 10 30 -0$$ 100 D 20 *0 0$$$ 10 50 D 110 30$F 50 0 30 D "0F 0 20 0 -0 D

200* 4pring

20. $n a process 10 samples of 100 items each #ere taken from a day's production. The number of defective items ineach sample #as recorded as follo#s,


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4ampleno.

1 2 - " 5 * 3 10

9o. ofdefective

12 15 21 5 5 * 15 3 1 1

)ra# a suitable 33& confidence (uality control chart and give your comment about the control of the process.

200* 4pring

21. a maintenance service facility has Poisson arrival rates and negative exponential service times operates on the/$/@ discipline. Breakdo#ns occur on an average - per day and maintenance cre# can service on an average machines per day. /ind.a. UtiliEation factor of the service facility.

b. ean #aiting time in the system. c. mean number of machines in the system. d. ean #aiting time of the machines in the (ueue.

200* 4pring

22. +ssume that product ; is made of t#o units of + and four units of B + is made of three units of % and four ).) is made of t#o units of . 6ead times for the fabrication of each units of each to final assembly are ; takes t#o#eekG + B % ) takes one #eek each and takes three #eeks. /ifty units are re(uired in period 10. :+ssume thatthere is no inventory on hand of any of these items=

i. 4ho# the B@ :product tree structure=ii. )evelop !P schedule sho#ing net re(uirements order release and order receipt dates.

200* 4pring

2-. The follo#ing tabulations are actual sales of six months starting from anuary.Months Actual

anuary 12/ebruary 10*

arch 100+pril 0

ay 100une 121

%alculate forecast for uly using - period simple moving average methods.+lso calculate forecast for uly using exponential smoothing methods. :take alpha < 0.-=@ut of above forecast #hich forecast is more reliable and #hy? 200* Spring

2". The maintenance department of large hospital uses about 1 cases of li(uid cleanses annually. @rdering cost isC12 carrying cost is C" per case a year and the ne# price schedule indicates that order of less than 50 cases #illcost C 20 per case 50 to *3 cases #ill cost C1 per case 0 to 33 cases #ill cost C1* per case and larger orders #illcost C1 per case. )etermine the optimal order (uantity and the total cost.

2007 spring25. Assume a drive up window a a !as !ood res auran . Cos umers arrive a "era e o! 25 per "our. #"e emplo$ee %an serve one %us omer ever$ wo minu es.Assume &oisson arrival and e'ponen ial servi%e ra es.

De ermine i. "a is "e average u ili*a ion o! "e emplo$ee+ii. "a is "e average num,er o! %us omers in line+iii. "a is "e average num,er o! %us omers in "e s$s em+iv. "a is "e average wai ing ime in line+

2007 spring


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Numerical Operations From PU