Q7.8 (KingaDollCompany)KingaDollCompanymanufactureseightversionsofitspopulargirl doll,Shari.Thecompanyoperatesona40-hourworkweek.Theeightversionsdifferindollskin,hair,andeyecolor,enablingmostchildrentohaveadollwithasimilarappearancetothem.It currentlysellsanaverageof4,000dolls(spreadequallyamongitseightversions)perweekto boutiquetoyretailers.Insimplifiedterms,dollmaking atKingainvolvesthreebasicoperations: moldingthebodyandhair,paintingtheface,anddressingthedoll.Changingoverbetween versionsrequiressetuptimeatthemoldingandpaintingstationsduetothedifferentcolorsof plasticpellets,hair,andeyecolorpaintrequired.The tablebelowliststhesetuptimes forabatch andtheactivitytimesforeachunitateachstep.Unlimitedspaceforbufferinventoryexists betweenthesesteps.

Assumethat (i)setupsneedtobecompletedfirst,(ii)a setupcanonlystartoncethe batchhas arrivedattheresource,and(iii) allflowunitsofabatchneedtobe processedataresourcebefore anyoftheunitsofthebatchcanbemovedtothenextresource.

a.Whatistheprocesscapacityinunitsperhourwithabatchsizeof500dolls?

b.Whatisthetimeittakesforthefirstbatchof500dollstogothroughanemptyprocess?

c.Whichbatchsizewouldminimizeinventorywithoutdecreasingtheprocesscapacity?

d.Whichbatchsizewouldminimizeinventorywithoutdecreasingthecurrentflowrate?

Process Step 1 Molding 2 Painting 3 Dressing Setup time 15 min. 30 min. No setup Activity time 0.25 min./unit 0.15 min./unit 0.30 min./unit