HAMPTONSHIRE EXPRESS
PROBLEM #1 A. The simulated function given in the Excel speadsheet !"amptonshie Expess Po$lem%#1& allo's the use to find the optimal (uantit) of ne'spapes to $e stoc*ed at the ne'l) fomed "amptonshie Expess +ail) ,e'spape. Anna -heen estimated estimated the dail) demand of of ne'spapes to $e on a nomal standad standad disti$ution stating that dail) demand 'ill have a mean of /00 ne'spapes pe da) 'ith a standad deviation of 100 ne'spapes pe da). sing the function povided2 the optimal stoc*ing (uantit)2 (uantit)2 'hich maximi3es expected pofit2 is detemined to $e appoximatel) 584 ne'spapes. 4f /56 ne'spapes 'ee to $e odeed2 "amptonshie Expess 'ill net an expected pofit of $331.436 pe da) 'ith an expected fill ate of 98%. An) invento) odeed odeed a$ove /56 'ill poduce a loss of pofit pofit due to stoc*ing stoc*ing invento) ove expected demand causing an im$alance $et'een the gains and losses due to the espective oveage and undeage costs. The ta$le $elo' outlines the optimal amount of dail) expected pofit. Pofits ise until the /56 ne'spape ma* an) potential incease in (uantit) stoc*ed 'ill decease dail) expected pofit fo eve) ne'spape odeed a$ove /56. -toc*ing 7uantit) +ail) Expected Pofit /8/ ne'spapes 991.9:9 /8; ne'spapes 991.968 /88 ne'spapes 991.9;< /85 ne'spapes 991.958 /8< ne'spapes 991.609 /50 ne'spapes 991.61/ /51 ne'spapes 991.6:/ /5: ne'spapes 991.691 /59 ne'spapes 991.69/ /56 ne'spapes 991.69; /5/ ne'spapes 991.69/ /5; ne'spapes 991.690 /58 ne'spapes 991.6:9 /55 ne'spapes 991.619 /5< ne'spapes 991.600 /<0 ne'spapes 991.95/ =alculations => =u ? @=u=o 'hee => citical atio. =u>1 C 0.: > 0.5 =o>0.: Theefoe2 => 0.5 ? @0.50.: > 0.5 'hich is e(ual to .56 @3 value on the standad nomal disti$ution function ta$le. To find the optimal stoc*ing (uantit) that maximi3es expected pofit2 'e 'ill use mean and standad deviation in fomula sho'n 7>mean 3D@-+ /00.56D100>/56. B. sing the ,e'svendo omula given2 7>FGC1@=u?=u=o 7>FGC1@=u?=u=o H2 'hee 7>optimal (uantit) F> mean of expected demand H> standad disti$ution of expected demand IC1> the invese of the standad nomal disti$ution function =u> undeage costs @-ale pice J cost2 o @K1.00CK0.:0 =o> oveage costs @cost J salvage value2 o @K0.:0 C K02
e can estimate the optimal stoc* (uantit). The values allo' us to input the 3 statistic2 and the oveage?undeage costs in the given e(uation to deive the e(uation and ans'e sho'n $elo'. The output of the ,e'svendo e(uation2 'hile diffeent than the excel function @due to ounding eo2 is consistent 'ith the optimal stoc*ing (uantit) found $) the Excel model. 7> /00 @0.5;01
[email protected]? 0.50 0.:0 D 100 > /<9.01:66
PROBLEM #: A. The given simulation model in the Excel speadsheet !"amptonshie Expess Po$lem%#:& allo's the use to find the optimal num$e of hous pe da) to $e invested into ceating the pofile section to maximi3e expected pofits fo the "amptonshie Expess +ail) ,e'spape. Loo*ing at the ta$le $elo'2 Anna can spend 6 hous2 'hee @">62 "ous -pent @" :.00 :.:/ :./0 :.8/ 9.00 9.:/ 9./0 9.8/
Optimal Expected Pofit K9;8.<1 K9;5.56 K9;<./5 K980.18 K980.;1 K980.<6 K981.1; K981.:<
4.00
$371.33
6.:/ 6./0 6.8/ /.00
K981.:< K981.15 K981.01 K980.88
B. Anna -heens choice of effot is at the point 'hee the maginal cost of spending the exta time to develop the pofile section > maginal $enefit of spending the exta time to develop the pofile section o the point 'hee pofit is maximi3ed. 4f she spends the exta time to develop the pofile section past 'hee maginal cost > maginal $enefit2 she 'ont $e a$le to ceate enough demand fo he ne'spape2 $ut if she spends less time than 'hee maginal cost > maginal $enefit2 she 'ont have a (ualit) ne'spape and misses out on additional sales2 'hich leads to inceased pofits. To find the optimal pofit level2 )ou 'ould set K10 > to the maginal $enefit2 o K10> @@0.5 D/0 ? @:h and solve fo " 'hich > 6 hous. =. sing a ta$le to compae the diffeence $et'een po$lem #1 and po$lem #:2 espectivel)2 'e can see the o$vious diffeences $et'een the optimal stoc*ing (uantit) and dail) expected pofit figues. -toc*ing 7uantit) /56 ;5/
+ail) Expected Pofit 991.66 981.99
The stoc*ing (uantit) and expected pofits ae highe in the second scenaio $ecause of the exta time spent to impove the (ualit) of pofile section. B) spending the exta time to impove the pofile section2 Anna -heen inceased the oveall (ualit) of he ne'spape2 'hich 'ill2 most li*el)2 lead to an inceased po$a$ilit) of demand fo he ne'spape aound theaea. This inceased demand 'ill aise Anna -heens stoc*ing (uantit) and the dail) expected pofits that ae associated 'ith that individual stoc*ing (uantit).
Po$lem #9 A. Assuming the num$e of hous Anna -heen 'ill spend d eveloping the pofile section 'ill > 6 Ralph Amentouts optimal stoc*ing (uantit) is /1;2 as pota)ed in the ta$le $elo' -toc*ing 7uantit) +ail) Expected Pofit /19 ;:.191 /16 ;:.19< /1/ ;:.169 /1; ;:.16/ /18 ;:.166 /15 ;:.160 /1< ;:.199 /:0 ;:.1:6 B. Ralph Amentouts optimal stoc*ing (uantit) is less than Anna -heens in Po$lem #: due to the etailing extension of the suppl) chain. Amentouts oveage cost @K0.50 as he puchases them fom -heen minus K0 of salvage value is highe than his undeage cost @K0.:0 K1 sale pice minus K0.50 puchasing cost. +ue to this2 Amentout has less oom than -heen fo a pofit magin ma*ing it a highe is* fo him to ca) a geate amount of invento)2 'hich ultimatel) affects the fill ate of the suppl) chain. =. The optimal time spent to impove the (ualit) of the pofile section is detemined $) the ta$le. The pofit -heen 'ill stand to ma*e in the com$ined suppl) chain is optimal at :.:/ hous spent pe da). -heens pofit ises 'ith each 1/ minute inteval until : hous and 1/ minutes is eached. The maginal $enefit2 fom the additional time spent to impove the pape2 'ill incease expecteddemand of ne'spape2 ho'eve2 if too much time is spent2 the maginal costs2 associated 'ith the additional time2 'ill out'eigh the associated maginal $enefits. Expected demand is moe esistant to high levels of time spent2 $asicall)2 -heen is huting pofits a$ove :.:/ hous spent pe da) on impovements. -heens optimal amount of hous spent is lo'e2 in this diffeentiated channel2 as compaed to Po$lem #:2 due to -heens lo'e maginal $enefit $eing eceived due to the split suppl) chain. 4t 'ouldnt ma*e sense fo -heen to spend moe time to impove he ne'spape if she has to split a pecentage of the pofits 'ith Amentout. +ue to this2 she 'ill put less effot in and get moe expectation of demand. +. Tansfe P .80 .8/ .8< .50 .51 .5/ .<0
-toc*ing 7 /10 /01 6<9 6<1 655 685 6/<
Pofit 999 9:8 9:1 91< 918 905 :<:
Ralphs P 106 51 ;: /8 /9 96 11
Annas P ::<.95 :6;.;6 :/<.11 :;:.10 :;6.6: :86.:< :50.;5
Annas E 1./;9 1.5<1 :.18; :.:/ :.9:; :.;61 9.0;9
ill Rate 5
4f the tansfe pice2 fom -heen to Amentout2 'ould decease2 Amentout 'ould ultimatel) gain a lage maginal $enefit out of the puchasing deal 'ith -heen. +ue to the incease of Amentouts pofit magin2 he 'ould tend to stoc* moe ne'spapes2 'hich 'ould incease the suppl) chains fill ate. "o'eve2 this2 in tun2 'ould cause -heens pofits2 fom the deal2 to decease and 'ould ultimatel) lo'e he motivation to impove the ne'spape2 'hich leads to a decease in expected demand and loss of potential pofits. E. Effots and stoc*ing levels 'ill $e lo'e in a diffeentiated channel than in an integated fim due to the multiple entities that ae pesent in the suppl) chain. The multiple etailing and manufactuing entities2 in the suppl) chain2 allo' the pofits to $e split $) pecentage athe than
totaled to one fim 'ho does $oth functions. Po$lem #6 A. The optimal stoc*ing (uantit) fo Amentout2 in this scenaio2 'as detemined to $e 60<. The optimal stoc*ing (uantit) is lo'e at 60<2 in this scenaio2 as compaed to /1; in Po$lem #9a. The optimal stoc*ing (uantit) is lo'e2 $ecause Amentout has an altenative to The Expess 'ith Ralphs Pivate E)e. B. The stoc*ing (uantit) mainl) diffes fom Po$lem #12 #:2 and #92 $ecause Amentout undeage costs have deceased2 in this scenaio2 due to the consumes altenative to puchase Pivate 'hen Expess has a stoc* out to consumes. "o'eve2 thee ae mao diffeences that one should conside. The fist t'o po$lems use an integated point of vie'2 as elated to the suppl) chain2 'hich allo's fo a highe optimal stoc*ing (uantit). On the othe hand2 Po$lems 9 and 6 use a diffeentiated channel. "o'eve2 4n Po$lem 92 'hile Amentout tied to *eep is* lo' $) odeing a lo'e optimal stoc*ing (uantit)2 'hich 'as fueled $) his lo' expected magins @due to his im$alanced undeage and oveage costs2 Amentouts optimal stoc*ing (uantit) changes 'hen Pivate is intoduced into the mix. 4n Po$lem 62 Amentout ma*es moe pofit on Pivate2 $ut thee is a lo'e expectation of demand fo Pivate. +ue to this2 he must still stoc* Expess to maximi3e pofits. To demonstate this phenomenon2 'hich 'ill ultimatel) decease optimal stoc*ing (uantit)2 the ne' oveage cost 'ould have to $e set. 4n the Po$lem 6 scenaio2 =o> K0.:0 J 6 0N D K0.60 > K0.1;. The ,e'svendo model 'ill also allo' one to aive at these conclusions. =. Amentouts oveage cost 'ould incease $) K0.09 to K0.592 'hile his undeage costs 'ould $e K.01. @,e' Expess pofit K0.18 J ,e' Pivate pofit K0.1; The im$alance 'ould educe the citical atio2 'hich 'ould lead to a eduction of the optimal stoc*ing (uantit) to a decentl) lo'e amount. Po$lem #/ A. The $u)C$ac* pice initiative allo's -heen to dop Amentouts oveage costs2 'hich leads to an incease in his optimal stoc*ing (uantit) and a 'inC'in situation fo -heen and Amentout. 4f -heen 'ould set the $u)C$ac* pice at K.8/2 this 'ould maximi3e the total suppl) chains pofits as sho'nin the ta$le $elo'. At K.8/2 Amentouts optimal stoc*ing (uantit) 'ould $e ;/< ne'spapes. B. The com$ination of $u)C$ac* pice and tansfe pice is oughl) K1.0: and K1.0:/2 espectivel)2 as sho'n in the ta$le $elo'. The optimal level of expected pofit is maximi3ed 'hen -heen2 the manufactue2 in this scenaio2 has a high expected pofit magin2 'hile Amentout2 the etaile2 has a negative expected pofit. Amentout is $asicall) a nonCfacto in this suppl) chain and allo's this scenaio to act as one integated chain although technicall) it is diffeentiated. =. The fixed fanchise fee 'ould not $e factoed into Amentouts oveage and undeage costs2 so it 'ouldnt have an effect on his stoc*ing decisions. 4f -heen 'ee a$le to impose a fanchise fee to Amentout2 ho'eve2 she 'ould not have a eason to sell ne'spapes at all2 since he pofits 'ould $e coming fom fanchising athe than ne'spape sales.
Po$lem #; A. The !M4& plan 'ould allo' -heen to $e a$le to esta$lish the optimal levels of effot and allo' he to set the optimal stoc*ing (uantit) in elation to he maximi3ing the diffeence $et'een he maginal $enefits and he maginal costs $asicall) she is in contol of the stoc*ing decision ights of the Expess to maximi3e total pofits. -ince she has contol ove stoc*ing (uantit)2 Amentout could not ma*e much of a pofit using a diffeentiated suppl) chain model. "o'eve2 due to poposed slotting allo'ance2 Amentout has the a$ilit) to ma*e moe of a pofit than he 'ould have $attling against -heen fo stoc*ing ights of the Expess2 if he 'ould go fo moe of an integated model and allo' -heen to contol the Expess. B. -ince Amentout 'ould not cae a$out sales diectl) @due to him collecting a slotting fee egadless of a sale o not2 unde the M4 plan vesus the diffeentiated model2 Amentout might lose potential sales he might have gotten if he had a sa) in the dail) stoc*ing (uantit) of the Expess. 4f Amentout had the chance to ma*e a potential pofit off of the consumes2 he might t) hade to pa) attention to demand. Because of thisealit) of manufactue vesus etaile2 -heen might not undestand the local demand of the aea as 'ell as Amentout2 due to him $eing the !gound level etaile& and 'itnessing the su$tle changes in dail) demand.
