A2 19A - solutions - OIDD 101 - 2019 - Introduction to Operations, Information and Decisions Professors: PDF

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OIDD 101 - 2019 - Introduction to Operations, Information and Decisions
Professors: Gérard Cachon/Sergei Savin, Santiago Gallino...

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University of Pennsylvania The Wharton School Operations, Information and Decisions Department

Assignment 2: OIDD 101, Spring 2019 Instructions: • • • • • • •

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You must submit this assignment by 11:30pm, Monday, February 18 2019 Late submissions receive zero credit. You must submit your own assignment. Your assignment is submitted only once you click the "submit" button! Do NOT forget to click submit. Once you click submit, you will NOT be allowed to submit a different set of answers – you will only be able to submit once! There are 10 questions in this assignment, each worth 1 point. There is no partial credit.

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Q1.!Framous!Framers!makes!custom!frames!for!beautiful!artworks!of!various!shapes!and! sizes.!On!average,!they!can!make!3!custom!frames!per!hour.!However,!15%!of!the!frames! end!up!having!quality!issues.!The!ones!with!quality!issues!need!to!be!redone,!which!takes! an!additional!12!minutes!per!frame.!Assuming!they!prioritize!re-doing!the!frames!that!have! quality!issues!(i.e.,!if!there!are!frames!that!need!to!redone,!they!would!prioritize!those! rather!than!making!new!frames),!how!many!custom!frames!per!hour!can!they!successfully! complete?! ! ! At!a!rate!of!3!per!hour,!they!require!60/3!=!20!minutes!per!frame.!12! ! minutes!are!needed!to!redo!frames!with!quality!issues.!! frames/hour! !! ! ! So,!the!average!processing!time!for!successfully!completed!frames!is! 2.75! ! 0.85!x!20!+!0.15!x!(20!+!12)!=!17!+!4.8!=!21.8!minutes.! !! ! Therefore,!they!can!complete!60/21.8!=!2.75!frames!per!hour.! ! ! ! ! Q2-Q3.!The!OIDD!department!is!looking!to!recruit!their!incoming!cohort!of!PhD!students! this!admissions!season.!They!have!a!three-stage!admissions!process:! !

! ! In!the!first!stage,!the!admissions!committee!screens!all!applications.!Of!these,!14%!move!on! to!the!interview!stage.!Of!the!applicants!who!receive!an!interview,!35%!receive!an!offer!of! admission!to!the!PhD!program.!30%!of!applicants!who!receive!the!offer!decline!the!offer.! The!remaining!students!(who!receive!an!offer!and!do!not!decline!it)!join!the!incoming! cohort!of!PhD!students.!! ! Q2.!The!admissions!committee!would!like!to!have!an!incoming!cohort!of!at!least!5!new!PhD! students.!On!average,!how!many!applications!should!they!make!sure!they!receive!to!attain! this!goal?!! ! ! Input!needed!=!target!output!/!process’!yield! applications! ! Process’!yield!=!0.14!x!0.35!x!0.70!=!0.0343! ! ! Input!needed!=!5!/!0.0343!=!145.77!applications! 145.77! ! !

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Q3.!Suppose!the!admissions!committee!receives!20!applications!per!day!during!the! admissions!season.!During!this!time,!the!committee!has!the!capacity!to!screen!16! applications!per!day,!interview!2!applicants!per!day,!and!send!4!offers!per!day.!! ! What!is!the!implied!utilization!(in!%)!of!the!bottleneck!step!of!the!admissions!process?!! !! ! %! !! ! A!resource’s!yield!=!flow!rate!of!good!output!/!flow!rate!of!input! ! 140! Screen!yield!=!0. 14 ! ! ! Interview!yield!=!0.35! ! Total!demand!at!screen!=!20!apps/day! Total!demand!at!interview!=!20!apps/day!x!0.14!=!2.8!apps/day! Total!demand!at!offer!=!2.8!apps/day!x!0.35!=!0.98!apps/day! ! Total!capacity!at!screen!=!16!apps/day!! Total!capacity!at!interview!=!2!apps/day!! Total!capacity!at!offer!=!4!apps/day!! ! Implied!utilization!=!Demand!/!Capacity! Implied!utilization!at!screen!=!20/16!=!1.25! Implied!utilization!at!interview!=!2.8/2!=!1.4! Implied!utilization!at!offer!=!0.98/4!=!0.245! ! The!resource!with!the!highest!implied!utilization!is!the!bottleneck.!Thus,!interview!is!the! bottleneck!of!the!admissions!process,!which!has!an!implied!utilization!of!1.4!or!140%.!

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Q4.!An!insurance!agency!needs!to!process!three!types!of!customer!calls:!New!customers! looking!to!buy!insurance!(New),!existing!customers!looking!to!renew!their!insurance! (Renew),!and!existing!customers!looking!to!file!an!insurance!claim!(Claim).!They!have!three! departments!that!serve!these!customers:!Customer!Service,!Application!Processing,!and! Claims!Processing.!Each!type!of!customer!has!its!own!path!through!the!process!and!does! not!necessarily!visit!all!departments.!The!following!table!shows!the!different!amounts!of! time!that!are!involved!in!processing!the!different!types!of!customers!at!the!different! departments:!! ! ! Customer! Application! Claims! ! Service! Processing! Processing! Number!of!staff! ! 6! 20! 5! Processing!time! New! 5! 25! -! Customer! (min/customer)! Renew! ! 3! 15! -! Customer! Claim! ! 4! -! 40! Customer! ! On!average,!250!“New”!customers,!490!“Renew”!customers,!and!75!“Claim”!customers! arrive!per!day.!The!insurance!agency!is!open!from!8:00am!to!5:00pm!each!day.!! ! What!is!the!implied!utilization!of!the!Application!Processing!department!(in!%)?! ! %! Because!we!have!flow!unit!dependent!processing!times,!we!define!! ! ! ! the!flow!unit!as!a!“minute!of!work”.!! 125.93! ! ! Implied!utilization!=!Demand!/!Capacity! ! Total!demand!on!Application!Processing!in!minutes!of!work/hour!! =!25!mins!x!250!cust/9!hrs!+!15!mins!x!490!cust/9!hrs!! =!25!mins!x!27.7778!cust/hr!+!15!mins!x!54.4444!cust/hr!! =!1511.11!minutes!of!work/hr! ! Total!capacity!of!Application!Processing!in!minutes!of!work/hour!! =!60!mins!x!20!staff! =!1200!mins!of!work/hr! ! Implied!utilization!of!Application!Processing! =!1511.11!minutes!of!work/hr!/!1200!mins!of!work/hr!! =!1.2593!=!125.93%! !

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Q5-Q7.!Jake’s!Contracting!renovates!kitchens!and!bathrooms.!They!order!marble!tiles!from! a!supplier!that!charges!a!flat!fee!of!$50!per!order!and!$2!per!tile.!Their!annual!inventory! holding!cost!percentage!is!25%.!They!need!1500!marble!tiles!per!week!to!satisfy!demand.!! ! Q5.!How!many!tiles!should!Jake’s!Contracting!purchase!with!each!order,!such!that!they!can! minimize!the!ordering!and!inventory!holding!costs?!! ! ! ! Cost!per!tile!=!$2! tiles! ! K!=!$50! ! ! h!=!weekly!holding!cost!per!tile!=!(25%/52!weeks)!x!$2!=!$0.009615! 3949.68! ! R!=!weekly!demand!=!1500!tiles!per!week! ! EOQ!=!sqrt(2xKxR/h)!=!3949.68!tiles!per!order! !! ! ! Q6.!Suppose!Jake’s!Contracting!orders!8000!tiles!at!a!time!(i.e.,!each!order!is!for!8000!tiles).! What!would!be!the!interval!of!time!(in!weeks)!between!orders?!! ! !! Time!between!orders!in!weeks!=!Q!/!R!! weeks! ! =!8000!tiles!/!1500!tiles!per!week!=!5.33!weeks! ! ! 5.33! ! ! ! ! ! Q7.!Suppose!the!supplier!is!running!a!promotion,!in!which!they!give!a!10%!discount!off!the! regular!price!of!$2!per!tile!if!they!purchase!8000!or!more!tiles.!What!is!the!per!tile!ordering! and!inventory!holding!costs!($)!if!they!were!to!place!an!order!of!10000!under!this! promotion?! ! Per!pound!ordering!and!inventory!holding!costs!=!C(Q)!/!R! $! ! With!the!promotion,!the!weekly!holding!cost!per!pound!(h)!is!now!! (25%/52!weeks)!x!($2!x!(1-0.10))!=!$0.008654! 0.0338! Q!=!10000! ! C(Q)!=!(K!x!R)!/!Q!+!(1/2)!x!h!x!Q!=!$50.7692! ! C(Q)!/!R!=!$0.0338! !

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Q8-Q10.!Perfect!Paints!produces!paint!in!Philadelphia.!They!focus!their!production!on!four! popular!colors:!white,!grey,!yellow,!and!green.!They!produce!white!paint,!then!grey!paint,! then!yellow!paint,!then!green!paint,!and!then!they!repeat!that!sequence.!When!running,!the! paint!machine!produces!at!a!rate!of!1200!gallons!per!hour!no!matter!what!color!of!paint!it! is!producing.!So!that!the!colors!are!perfect,!they!need!30!minutes!to!set!up!the!paint! machine!before!switching!to!the!next!color!(i.e.,!30!minutes!to!switch!to!white,!30!minutes! to!switch!to!grey,!30!minutes!to!switch!to!yellow,!and!30!minutes!to!switch!to!green).!The! demand!for!each!of!the!paint!colors!are!given!in!the!table!below:! ! ! White! Grey! Yellow! Green! Demand!(gallons/hour)! 450! 250! 200! 50! ! Q8.!Suppose!Perfect!Paints!wants!to!minimize!their!inventory!while!still!satisfying!demand.! How!many!gallons!of!white!paint!should!they!produce!with!each!batch?!! ! ! Production!cycle:!Setup!white!–!make!white!–!setup!grey!–!make!grey!–!setup!yellow!–! ! make!yellow!–!setup!green!–!make!green! gallons! ! Flow!unit:!1!gallons!of!paint!(of!any!color)! ! !! 4320! ! Total!demand!=!Target!capacity!=!450!+!250!+!200!+!50!=!950!gallons/hr! !! ! Total!setup!time!per!production!cycle!=!(4!x!30!min)!/!60!min/hr!=!2!hrs! ! Processing!time!per!flow!unit!=!1!gallon!/!1200!gallons/hr!=!0.0008333!hrs! !! ! Batch!size!=!(Capacity!x!Setup!time)!/!(1!–!Capacity!x!Processing!time)!=!(950!gallons/hr! ! x!2!hrs )!/!(1!–!950!gallons/hr!x!0.0008333!hrs)!=!9120!gallons! !! ! ! Batch!size!of!white!paint!=!9120!x!(450/950)!=!4320! ! ! Q9.!Suppose!Perfect!Paints!produces!5400!gallons!of!white!paint,!3000!gallons!of!grey! paint,!2400!gallons!of!yellow!paint,!and!600!gallons!of!green!paint!in!a!production!cycle.! How!many!gallons!per!hour!of!paint!(of!any!color)!can!they!produce?!! ! ! Batch!size!=!5400!+!3000!+!2400!+!600!=!11400!gallons! gallons/hour Total!setup!time!per!production!cycle!=!(4!x!30!min)!/!60!min/hr! ! ! =!2!hrs! 991.3! Processing!time!per!flow!unit!=!1!gallon!/!1200!gallons/hr!=! 0.0008333!hrs! ! Capacity!with!batches!=!B!/!(Setup!time!+!B!x!Processing!time)!=! 11400!/!(2!+!11400!x!0.0008333)!=!991.30!gallons/hr!

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Q10.!Suppose!Perfect!Paints!produces!6300!gallons!of!white!paint,!3500!gallons!of!grey! paint,!2800!gallons!of!yellow!paint,!and!700!gallons!of!green!paint!in!a!production!cycle.! Say!they!are!demand!constrained!(see!the!information!in!the!table!above).!What!is!their! average!inventory!of!yellow!paint!(in!gallons)?! ! Average!inventory!=!½!x!batch!size!x!(1!–!R!x!p)! ! Batch!size!of!yellow!paint!=!2800!gallons! “Demand!constrained”!implies!flow!rate!=!demand! Flow!rate!=!demand!of!yellow!paint!=!200!gallons/hr! Processing!time!per!flow!unit!=!1!gallon!/!1200!gallons/hr!=! 0.0008333!hrs! Average!inventory!of!yellow!paint!=!½!x!2800!x!(1!–!200!x!0.0008333)! =!1166.67!gallons! ! ! ! ! ! ! !

gallons! !

1166.67! ! ! ! ! ! ! !...