ICIE - TMA 2015 Submission 15

8/16/2019 ICIE - TMA 2015 Submission 15

1/19

PERFORMANCE BASED LEASECONTRACT

INVOLVING DISCRETE PMEka K.A Pakpahan1 and B. P. Iskandar2

1Harapan Bangsa Institute of Technology, Indonesia

2Bandung Institute of Technology, Indonesia

Presented on:

International Conference on Indstrial En!ineerin!" T#eor$"Met#odolo!$ and A%%lication &ICE'TMA(

)o!$a*arta" +,'+- Octo.er +/01


2/19

BAC2GRO3ND•

ince 1!!", #usinesseschoose to lease e$uip%entinstead of o&ning the%.

• 'essee #uys o%erationalti4e instead of e5i%4ent fro% lessor, and o&ner isresponsi#le on assuring higho%erational ti4e through

4aintenance

• The relationship a%onglessee and lessor are de(ned

on lease contract 2


3/19

PRELIMINAR) ST3DIES

• 'iteratures dealing &ith %aintenanceof leased e$uip%ent)

*

•

+eh, .H., and -hen, -.K. 2""• +eh, .H., -hang, /.'., and 'o,H.-. 2"1"

• -hang, /.'., and 'o, H.-. 2"11• +eh, .H., Kao, K.-., and -hang,

/.'. 2"11•

+eh, .H., -hang, /.'., and 'o,H.-., 2"11• 0aturonnatee, 0., urthy, .3.P., and

Boondiskulchok, . 2""4.

• 3iya%osoth, T., and Pongpech, 0. 2""5.

• +eh, .H., Kao, K.-., and -hang, /.'.

2""!.• +eh, .H., and -hang, /.'. 2""5.

• -onsider only thelessor point of 6ie&

• Penalty stipulation onlease contract

• eter%ine ho& lessor

can achie6e %a7i%u%pro(t #y c#oosin! t#eo%ti4al PM %olic$

ARM Based

FRRM Based


4/19

RESEARC6 MOTIVATION

• This paper takes the perspecti6e of lessee andai%s to deter%ine the opti%al leasing price to #eo8ered to the lessor

• The price should %oti6ate lessor to do t&o things) – Accept the lease o8er – Perfor% the opti%al %aintenance e8ort, thus ensuring

the opti%al operational ti%e of the e$uip%ent

• /e adopt %rinci%al a!ent t#eor$ and%erfor4ance .ased 4aintenance concept


5/19

MODELLING FRAME7OR2 :

PRINCIPAL AGENT T6EOR)

LESSEE LESSOR

E9:IPE3T

;PEATI;3

Lessee8sdecision:• 'ease Price

Lessor8sdecision:• aintenance

e8ort

E$uip%ent<s;perational

e6enue

• Branch of ga%e theory =tole, 1!!!>• epict the %rinci%al8s atte%pt to push a!ent to

do so%ething as the principal

Self interest:Mini4al %a$4entfor #i!#esto%erational ti4e


6/19

LEASE PRICE SC6EME

•

/e consider this lease price sche%e)

4

• 'essee leased e$uip%ent fro% lessor for years

and paid a price of paid at the #eginning of leaseperiod.

• To achie6e high operational ti%e, lessee control

lessor #y specifying perfor%ance related pay%ent – &hen e$uip%ent do&nti%e => e7ceeds li%it, lessor ispenali@ed.

– &hen e$uip%ent do&nti%e => is lo&er than li%it,incenti6e is gi6en.

=1>


7/19

E93IPMENT FAIL3RE MAINTENANCE EFFORT•

-onsider e$uip%ent, ha6ing as its failure distri#utionfunction, as its failure density function and as its failurerate. ailure is rectify through 4ini4al correcti;e4aintenance<

• To reduce the likelihood of failure, lessor takes %eriodicalPM action. Each P is conducted #y a (7ed degree of%aintenance e8ort le6el =, &here .

• P e8ect)

•

5

=2>

=*>


8/19

MAINTENANCE COST

• P cost along lease period

• - cost along lease period

=>

=?>

=4>


9/19

E93IPMENT DO7NTIME

• If the nu%#er of failure occurs along lease periodis and each failure causes do&nti%e, then thetotal do&nti%e in the lease period, ( >, is gi6en #y)

•

=5>

• E7pected total do&nti%e and 6ariance

=C>

=!>


10/19

E93IPMENT OPERATIONAL REVEN3E

•

'essee uses e$uip%ent for #usiness purpose&hich generates re6enue =dollarDyears>.

• E7pected operational re6enue and 6ariance)

•

1"

=1">

=11>


11/19

PERFORMANCE RELATEDPA)MENT•

The 6alue of perfor%ance related pay%ent can #eeither positi6e =incenti6e>, or negati6e =penalty>.

• Incenti6e occurs &hen the reali@ation ofdo&nti%e is lo&er than a predeter%ined li%it ,

&hile penalty occurs &hen the opposite happens.

• E7pected 6alue of perfor%ance related pay%entand its 6ariance are gi6en #y)

•

11

=12>

=1*>


12/19

LESSEE AND LESSOR 3TILIT) F3NCTION

•

'essee and lessor &ill try to %a7i%i@e their utility) /here r is the degree of risk

aversion,• r = /, sho&s risk neutrality• r > /" sho&s risk a6erse

•

'essee utility)

• 'essor utility)

12

=1>

=1?>


13/19

LESSEE DECISION MODEL

1*


14/19

SOL3TION MET6OD

1

Step 1 : Use constraint c.2, determine as function of by taking the first derivative of

lessor’s utility function towards m, we then have m().Step 2 : Take constraint c.1 which is binding at and m(), substitute them into utility

function (Eqn. 15). This creates lessee’s utility as function of .

Step : etermine that ma!imi"es lessee’s utility function#$heck for feasibility of ).%f is not feasible# &T'.%f is feasible# continue to ste *

Step ! : +ind the ,alue of m# gi,en from ste -$heck for the feasibility of m ()%f is not feasible# &T'.%f is feasible# continue to ste 5.

Step " : +ind by substituting m (from ste *) and (from ste -) into (c.1) which is binding at .$heck feasibility of ( /).%f is not feasible# &T'.%f is feasible# continue to ste 0.

Step # : enote # # and as solutions of the model

Step 1 :

Step 2 :

Step :

Step ! :

Step " :

Step # :


15/19

N3MERICAL E?AMPLE &0(• /e consider e$uip%ent &ith failure %odeled #y t&o

para%eter /ei#ull distri#ution, . The 6alue of = 1 yearsand.

• 'ease contract period is planned for years. Each failurecauses do&nti%e &ith para%eter . ;ther para%eters are

gi6en #elo&.

•

uring the contract, lessor is responsi#le to conduct P and-. Penalty is gi6en if the e$uip%ent


16/19

N3MERICAL E?AMPLE &+(

14

)isk *ttitude Setting U Lessee U Lessor

+oth )isk eutral 5*.12 /.203 /.14- -/5.03 10.1-2

)isk *verse -essor 1/3.-2 /./10 /.14 53.4*- 15./-2

)isk *verse -essee 5/./45 /.335 /.14 -/5./5 12.143


+oth )isk eutral 5*.12 /.203 /.14- -/5.03 10.1-2

)isk *verse -essor 1/3.-2 /./10 /.14 53.4*- 15./-2

)isk *verse -essee 5/./45 /.335 /.14 -/5./5 12.143

Reslt

• By si%ple calculation &e could notice that for 1, putting%aintenance e8ort le6el &ould #e suFcient to hinderlessor fro% penalty, #ut result on ta#le a#o6e sho&s thatthe opti%al is al&ays greater than @ero.

• This sho&s that under pay%ent sche%e o8ered, lessor@old .e indced to %erfor4 .etter t#an tar!et<


17/19

• The result pattern sho&n for 6arious risk attitude

setting ) – &hen #oth parties are risk neutral, there is no lost due to risk

pre%iu%, co%#ination of (7ed price and perfor%ance relatedpay%ent are opti%al to induce .

– &hen lessor is risk a6erse, they &ould a6oid risk due to

uncertainty of inco%e, the 6alue of on this second setting is%uch s%aller than on the (rst

– &hen lessee is risk a6erse, they &ould then push risk to thelessor sho&ed #y the 6alue of &hich is %uch larger than onthe (rst.

•

15


+oth )isk eutral 5*.12 /.203 /.14- -/5.03 10.1-2)isk *verse -essor 1/3.-2 /./10 /.14 53.4*- 15./-2

)isk *verse -essee 5/./45 /.335 /.14 -/5./5 12.143


+oth )isk eutral 5*.12 /.203 /.14- -/5.03 10.1-2)isk *verse -essor 1/3.-2 /./10 /.14 53.4*- 15./-2

)isk *verse -essee 5/./45 /.335 /.14 -/5./5 12.143

Reslt


18/19

CONCL3SIONS•

/e ha6e deter%ined the o%ti4al lease%a$4ent sc#e4e =(7ed price and perfor%ancerelated pay%ent> to #e o8ered #y the lessor atthe #eginning of a lease contract.

• This lease pay%ent %eets lessor


19/19

T6AN2S FOR T6EATTENTION

1!

Documents

ICIE - TMA 2015 Submission 15