Optimal pricing strategy of hotel for long-term stay. Liuyi Ling, Xiaolong Guo and Lina He*

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1 7 In. J. Services Technology and Managemen, Vol. 7, No., 0 Opimal pricing sraegy of hoel for long-erm say Liuyi Ling, Xiaolong Guo and Lina He* School of Managemen, Universiy of Science and Technology of China, 96 Jinzhai Road, Hefei, Anhui, China lyling@usc.edu.cn gxl@mail.usc.edu.cn helina@mail.usc.edu.cn *Corresponding auhor Absrac: Along wih he economic developmen and ourism prosperiy, long-erm say in hoel is very common in realisic pracice in recen years. This paper does some research on how hoel pricing for long-erm say. By developing an operaional opimisaion model, his paper derives he opimal pricing sraegy for long-erm say, and demonsraes ha his sraegy is beneficial o hoel as well as is cusomers. Moreover, his paper furher analyses he effecs on he opimal room rae and hoel revenue, of sandard room rae, variable cos, hoel capaciy, he number of individual cusomers, as well as he properies of long-erm say. Evenually, a numerical experimen is employed, and he resuls are consisen wih realiy. Keywords: service managemen; long-erm say; hoel pricing; opimal sraegy; Poisson disribuion. Reference o his paper should be made as follows: Ling, L., Guo, X. and He, L. (0) Opimal pricing sraegy of hoel for long-erm say, In. J. Services Technology and Managemen, Vol. 7, No., pp Biographical noes: Liuyi Ling is a Senior Lecurer of School of Managemen a Universiy of Science and Technology of China wih ineress in ourism economics, supply chain managemen, and opimisaion. Xiaolong Guo is a PhD candidae of managemen science and engineering a Universiy of Science and Technology of China wih ineress in ourism supply chain, service supply chain managemen, and game heory. Lina He is a Maser suden a Universiy of Science and Technology of China, wih ineress in ourism managemen, and hoel pricing. Inroducion Nowadays, hoel plays an imporan role in ourism, business and academic exchange, ec. However, few researchers sudy hoel pricing problem based on mahemaical mehod. Pricing is an imporan business behaviour. Price and service are imporan facors affecing he buying decisions of cusomers (Xiao and Yang, 008). Moreover, Sohail Copyrigh 0 Inderscience Enerprises Ld.

2 Opimal pricing sraegy of hoel for long-erm say 73 e al. (007) indicae pricing is currenly he ourism s compeiive advanage. Gu (997) esablishes he pricing model o improve he profiabiliy of hoel rooms. Ling e al. (0) build a sraagem pricing model for he small or medium sized hoels o cooperae wih a hird pary organisaion. Kimes and Chase (998) consider ha room rae is he imporan revenue lever of hoel. Lai and Ng (005) srucure he nework opimisaion model for hoel pricing in uncerain environmen. Schwarz (006) analyses he relaionship beween hoel room reservaion and revenue, and pus forward a policy o increase hoel revenue. Pan (007) invesigaes he impacs on hoel opimal room rae, of marke demand and he number of available rooms. van der Res and Harris (008) prove ha discoun is he ideal hoel pricing sraegy under he high variable cos and rigid demand. Along wih economic developmen and ourism populariy, long-erm say (LTS) in a hoel is very common in realiy. For insance, when an employee is assigned by his company o se up a branch in a ciy, he would ren a hoel room as office and bedroom for several days; people say in hoel in a holiday resor o enjoy his vacaion for many days. In order o improve is revenue, a hoel responds posiively o he demand for LTS. Silver House Hoel provides differen room raes for LTS according o is duraion, such as 58 euros/day for longer han monhs, 59 euros/day for monhs, 65 euros/day for 8 9 days. Chicago Hoel uses a real discoun rae of 30% for he cusomer who says more han hree days. Four Seasons Hoel in Miami develops LTS business a full seam, Sarwood Hoel promoes LTS business named Beer Tomorrows, and Hoels in Philadelphia provide discouned room rae for LTS. Besides hoels, aparmens also pay heir aenions o LTS. The room raes of Barbacan Palace Aparmens in Vilnius s for LTS varies along wih duraion of say, such as 45 euros/day for longer 30 days, 70 euros/day for 5 9 days, 70 euros/day for 8 4 days, 5 euros/day for four o seven days and 50 euros/day for one o hree days. Alhough LTS is common in realiy, and imporan o improve occupancy rae and revenue of a hoel, few researchers pay aenion o i. Collins and Parsa (006) poin ou ha pricing is he sraegy lever of hoel revenue. This paper is ineresed in answering he following quesions, Why does a hoel provide low room rae for LTS? Wha is he opimal pricing sraegy of a hoel for LTS? 3 Wha are he effecs on revenue and he room rae for LTS, of a hoel capaciy, sandard room rae, variable cos, vacancy rae, duraion of say, and he number of rooms for LTS? To he bes of our knowledge, his paper is organised as follows. Secion saes he problem of LTS, and gives some assumpions; Secion 3 derives he opimal room rae ha a hoel provides for a LTS cusomer and he increased revenue brough by his cusomer; Secion 4 analyses he effecs on opimal room rae and hoel revenue, of hoel capaciy, sandard room rae, daily variable cos, he number of regular cusomers, and ha of rooms rened by LTS cusomers, and duraion of say; Secion 5 makes a conclusion for his paper and presens he problems of LTS o be solved in he fuure research.

3 74 L. Ling e al. Problem saemen A hoel has idenical rooms, and is daily variable cos per occupied room is C. Then we classify he hoel cusomers o wo groups: one is regular cusomers who pay he hoel a a rae of P/day/person, and he oher is LTS cusomers who pay he hoel a a lower discoun rae of P /day/person. The number of regular cusomers of he hoel per day is x, and each of hem needs one room. x follows Poisson disribuion (Baker and Collier, 003; Ling e al., 009), and is densiy funcion is denoed as f(x). Then f(x) is expressed as follows, λ k λ e f( x = k) = () k! where λ is he expeced value of he number of regular cusomers. The parameers, variables and assumpions of his LTS problem are given in he following conen. C x λ P n m hoel capaciy daily variable cos per occupied room he number of regular cusomers per day rae of densiy funcion f(x) sandard room rae for regular cusomers he number of rooms required by a LTS cusomer he duraion of LTS P discouned room rae for he LTS cusomer. LTS cusomer rens n rooms of a hoel for m days, receives room rae P. g( ) is denoed as he probabiliy ha he LTS cusomer acceps he room rae, and expressed as follows, P g( P ) = h( m, n) () P h(m, n) is an adjusmen funcion in equaion (). h(m, n) decreases along wih m or/and n. Equaion () indicaes ha a LTS cusomer expecs lower room rae, when he rens more rooms or/and for longer period (see Figure ). I is reasonable in realiy. For example, a cusomer will ask for a lower price if he buy more. He is likely o give up he idea of rening rooms from he hoel, if he mus receive sandard room rae. Hence, equaion () is reasonable and consisen wih realiy. From equaion (), we obain hmn (, ) (3) So g( ) is a non-increasing convex funcion of m or/and n. From he above equaion, a LTS cusomer rens he hoel rooms wihou hesiaion, g(p ) =, if he hoel provides free accommodaion, P = 0.

4 Opimal pricing sraegy of hoel for long-erm say 75 Figure Accepance probabiliy of he room rae for LTS cusomer This paper solves he LTS problem based on following assumpions, Assumpion: P > C and P > C n <. Assumpion ells ha boh sandard room rae and he one for a LTS cusomer are higher han variable cos. If no, he hoel would raher accommodae none. Assumpion ells ha he number of rooms needed by LTS cusomers is less han he hoel capaciy. In pracice, i is very rare ha a cusomer rens all he rooms of a hoel. Hence, assumpion exiss in mos case. 3 Opimal pricing sraegy for LTS Wheher a LTS cusomer rens rooms depends on he room rae ha a hoel provides for him. In his paper, a cusomer could be firs saisfied if he has a check prioriy. We consider ha LTS cusomers could enjoy he check prioriy. LTS cusomers should be firs saisfied in hoel. By building models, his secion deermines he opimal pricing sraegy of a hoel for a LTS cusomer. Wihou LTS, he average daily revenue of he hoel is as follows, R = ( P C) xf( x) + ( P C) f( x) (4) x= 0 x= + where he firs and second erms are he revenues when he number of regular cusomers is, respecively, less and greaer han hoel capaciy. Wih LTS, he daily revenue brough by LTS is as follows, r3 = ( P C) n (5) Afer meeing he requiremen of LTS cusomers, ( n) rooms are lef for regular cusomers. If he number of he lef rooms is greaer han ha of regular cusomers, he daily revenue bough by regular cusomers is

5 76 L. Ling e al. r = ( P C) xf( x) (6) oherwise, i is n x= 0 r = ( n)( P C) f( x) (7) x= n+ According o equaions (5), (6) and (7), he daily revenue of he hoel is as follows, R = r+ r + r3 (8) According o equaions (4) and (8), he increased revenue brough by LTS is as follows, ( ) D = m R R (9) Considering he accepance probabiliy g(p ) of he room rae for a LTS cusomer, he average increased revenue is as follows, D = g( P ) D (0) Proposiion : D has he maximum value and he global opimal soluion of P exiss. Proposiion indicaes ha he hoel may maximise is revenue by providing a suiable room rae for a LTS cusomer. The proof is given in he Appendix, and all he proofs of he laer proposiions are all in he Appendix. From he derivaive of equaion (0) wih respec o P, we obain he opimal room rae for a LTS cusomer as follows, * P P C P = ( x) f( x) n f( x) + hmn (, ) n x= n+ x= n+ () According o equaions (), he discouned rae is relaed o he sandard room price, P, or he duraion of LTS, m, and he once booking room quaniy, n. And he number of regular cusomers also affecs he discouned rae. According o equaions (0) and (), obain he maximal increased revenue brough by LTS as follows, * mh( m, n) np D = ( P C ) ( x ) f ( x ) n ( P C ) f ( x ) cn+ 4 Pn h( m, n) x= n+ x= n+ () Proposiion : P * < P and D * > 0. Proposiion saes ha LTS is beneficial o boh sides, a LTS cusomer obains discouned room rae and he hoel improves revenue. According o equaions (4) and (), he maximal oal revenue of he hoel wih LTS during m days (called oal revenue hereafer) is as follows, * Δ π = D + mr (3)

6 Opimal pricing sraegy of hoel for long-erm say 77 4 Effecs of he parameers on opimal room rae and revenue This secion analyses he effecs on he opimal room rae and hoel revenue, of hoel capaciy, sandard room rae, daily variable cos, he number of regular cusomers, and ha of rooms rened by LTS cusomers, and duraion of say. Noe: The numerical examples in his secion are implemened in MATLAB and wih parameers as follows: P = 00, C = 0, m = 0, n = 0, λ = 0, = 00. We adop hmn (, ) = 4 ln mn hrough simulaion experimen in his paper. e h(m, n) is an adjusmen funcion and i saisfies ha g( ) is a non-increasing convex funcion of m or/and n. I is reasonable and consisen wih equaion (). Proposiion 3: P * is an increasing funcion of P. In Figures and 3, opimal room rae and LTS revenue boh increase along wih he sandard one, jus as Proposiion 3 shows, since a high sandard room rae implies high-level faciliies and comforable service. This indicaes ha higher-level hoel gains more revenue. Figure Effec of P on P * (see online version for colours) Figure 3 Effec of P on D * (see online version for colours)

7 78 L. Ling e al. Proposiion 4: P * is a decreasing funcion of m. This proposiion indicaes ha he cusomer wih longer duraion of say receives lower opimal room rae, jus as Figure 4 shows, since he brings more revenue o he hoel, jus as Figure 5 shows. Proposiion 4 coincides wih he room raes ha Silver House Hoel and Barbacan Palace Aparmens provide for LTS (see Secion ). According o equaion (), Proposiion 4 exiss obviously. Figure 4 Effec of m on P * (see online version for colours) Figure 5 Effec of m on D * (see online version for colours) Proposiion 5: There exiss an opimal value of n, which minimises he opimal room rae. Proposiion 5 implies ha LTS cusomers rening more rooms does no always receive lower opimal room rae. In Figures 6 and 7, if he number of rooms for LTS is less han 50, he opimal room rae decreases along wih i, and LTS revenue increases, because LTS increases he occupancy rae of he hoel; oherwise, he conrary is he case, because grea loss is caused by he refusal o he accommodaion reques from regular cusomers. Hence, i is beer for a LTS cusomer o cooperae wih several hoels or he hoel wih low occupancy rae, if he rens a large number of rooms.

8 Opimal pricing sraegy of hoel for long-erm say 79 Figure 6 Effec of n on P * (see online version for colours) Figure 7 Effec of n on D * (see online version for colours) Proposiion 6: P * is an increasing funcion of C. This proposiion indicaes ha, in order o mainain is revenue, he hoel increases he opimal room rae along wih daily variable cos, jus as Figure 8 shows. High opimal room rae reduces he possibiliy of LTS, and consequenly he LTS revenue decreases, jus as Figure 9 shows. Hence, he hoel should improve managemen level o cu down he daily variable cos, and hereby improves he revenue brough by regular cusomers and LTS cusomers. Proposiion 7: P * is an increasing funcion of λ. Proposiion 7 implies ha he opimal room rae increases along wih he number of regular cusomers, jus as Figure 0 shows. If he oal number of regular and LTS cusomers is greaer han is capaciy, he hoel has o refuse accommodaion requess from regular cusomers o mee he requiremen of LTS. Frequenly, LTS revenue decreases, jus as Figure shows, because a LTS cusomer obains lower room rae. In his case, more regular cusomers, greaer loss caused by LTS he hoel underook. In order o reduce he loss, he hoel increases he opimal room rae for a LTS cusomer.

9 80 L. Ling e al. Figure 8 Effec of C on P * (see online version for colours) Figure 9 Effec of C on D * (see online version for colours) Figure 0 Effec of λ on P * (see online version for colours)

10 Opimal pricing sraegy of hoel for long-erm say 8 Figure Effec of λ on D * (see online version for colours) Proposiion 8: P * is a decreasing funcion of. This proposiion predics ha opimal room rae for a LTS cusomer decreases along wih hoel capaciy. Wih a fixed number of regular cusomers, he number of vacan rooms increases along wih hoel capaciy. In order o reduce vacancy rae and improve is revenue, he hoel aracs LTS cusomers wih low opimal room rae. Figure Effec of on P * (see online version for colours) Figure 3 Effec of on D * (see online version for colours)

11 8 L. Ling e al. In Figures and 3, along wih hoel capaciy, he opimal room rae decreases, LTS revenues increases, and hey boh keep sable if hoel capaciy is greaer han he number of rooms needed by regular and LTS cusomers. Hence, he hoel wih low occupancy rae provides LTS cusomers wih low opimal room rae. 5 Conclusions and fuure research As we all known, along wih economic developmen, all of he companies are facing fierce compeiion in every indusry. Hoel indusry is no excepion. Hoel companies ofen use managemen sraegies o achieve cerain arges. LTS in a hoel is very common in realisic pracice wih he enhancing mobiliy, bu few papers are concerned abou i. This paper sudies he opimal pricing sraegy of a hoel for LTS cusomers, analyses he effecs on opimal room rae and LTS revenue, of hoel capaciy, sandard room rae, daily variable cos, he number of regular cusomers, and ha of rooms rened by LTS cusomers, and duraion of say. According o he analysis of he preceding secions, several managemen implicaions are suggesed as follows, A LTS cusomer rening more rooms does no always receive lower opimal room rae. Hence, i is beer for a LTS cusomer o cooperae wih several hoels or he hoel wih low occupancy rae, if he rens a large number of rooms. A hoel wih low occupancy rae provides LTS cusomers wih low opimal room rae. Moreover, a LTS cusomer wih longer duraion of say also receives lower opimal room rae. In realiy, a hoel should make grea effors o increase he occupancy, for ha can improve is marginal revenue. 3 A high-level hoel provides high room rae for LTS cusomers and gains more revenue. Hence, a hoel could obain more revenue by offering beer service. 4 In order o improve he revenue brough by regular cusomers and LTS cusomers, a hoel should improve managemen level o cu down he daily variable cos. However, here are some problems abou LTS o be solved in fuure research, he average number of regular cusomers varies during he duraion of LTS a hoel provides oher services for a LTS cusomer, such as meeing arrangemen 3 a hoel has several ypes of rooms 4 a hoel accommodae several LTS cusomers 5 he sandard price of a hoel can be considered as a decision variable, ec. Acknowledgemens The auhors would like o hank he ediors and he anonymous referees for heir encouraging commens and suggesions. The qualiy of his aricle was improved

12 Opimal pricing sraegy of hoel for long-erm say 83 subsanially as a resul of hese suggesions. This work was suppored by he Naional Naural Science Foundaion of China under gran Nos and References Baker, T.K. and Collier, D.A. (003) The benefis of opimizing prices o manage demand in hoel revenue managemen sysems, Producion and Operaions Managemen, Vol., No. 4, pp Collins, M. and Parsa, H.G. (006) Pricing sraegies o maximize revenues in he lodging indusry, Inernaional Journal of Hospialiy Managemen, Vol. 5, No., pp Gu, Z. (997) Proposing a room pricing model for opimizing profiabiliy, Inernaional Journal of Hospialiy Managemen, Vol. 6, No. 3, pp Kimes, S.E. and Chase, R.B. (998) The sraegic levers of yield managemen, Journal of Service Research, Vol., No., pp Lai, K-K. and Ng, W-L. (005) A sochasic approach o hoel revenue opimizaion, Compuers & Operaions Research, Vol. 3, No. 5, pp Ling, L., Guo, X. and Liang, L. (009) Opimal pricing sraegy of hoel for cooperaive ravel agency, 009 Inernaional Conference on Compuaional Inelligence and Sofware Engineering, CiSE 009, December 009 o 3 December 009, IEEE Compuer Sociey, Wuhan, China. Ling, L., Guo, X. and Liang, L. (0) Opimal pricing sraegy of a small or medium-sized hoel in cooperaion wih a web sie, Journal of China Tourism Research, Vol. 7, No., pp.0 4. Pan, C-M. (007) Marke demand variaions, room capaciy, and opimal hoel room raes, Inernaional Journal of Hospialiy Managemen, Vol. 6, No. 3, pp Schwarz, Z. (006) Advanced booking and revenue managemen: room raes and he consumers sraegic zones, Inernaional Journal of Hospialiy Managemen, Vol. 5, No. 3, pp Sohail, M.S., Roy, M.H., Saeed, M. and Ahmed, Z.U. (007) Deerminans of service qualiy in he hospialiy indusry: he case of Malaysian hoels, Journal of Accouning, Business & Managemen, Vol. 4, No., pp van der Res, J-P.I. and Harris, P.J. (008) Opimal imperfec pricing decision-making: modifying and applying Nash s rule in a service secor conex, Inernaional Journal of Hospialiy Managemen, Vol. 7, No., pp Xiao, T. and Yang, D. (008) Price and service compeiion of supply chains wih risk-averse reailers under demand uncerainy, Inernaional Journal of Producion Economics, Vol. 4, No., pp Appendix D Proof of Proposiion : According o equaion (), = 0, if P = P *. P We obain he second order derivaive of equaion (0) as follows, D P nh( m, n) = P According o equaion (3), he above equaion is greaer han zero. Hence, Proposiion exiss.

13 84 L. Ling e al. Proof of Proposiion : We define Δ A= ( x) f( x) n f( x) x= n+ x= n+ A + = ( x) f( x) f( x) + n n x= n+ x= n+ n = ( x) f( x) + f( x) > 0 n x= n+ x= 0 (B-) * P P C C P P = A+ P hmn (, ) n P P C A = hmn (, ) + n (B-) According o Assumpion (), equaions (3) and (B-), equaion (B-) is greaer han zero, ha is, P * < P. According o Assumpion (), equaion () is greaer han zero, ha is, D * > 0. Hence, Proposiion exiss. Proof of Proposiion 3: We obain he derivaive of equaion () wih respec o P as follows, * P = + ( x + n) f( x) + n f( x) P h( m, n) n x= n+ x=+ (C-) According o equaion (3), he above equaion is greaer han zero, ha is, * P > 0 P Hence, Proposiion 3 exiss. Proof of Proposiion 5: We define Δ * * DP( n) = P ( n + ) P ( n) P P = ( x) f( x) ( n+ ) f( x) h( m,( n+ ) ) ( n+ ) x= n x= n P P + ( x) f( x) n f( x) hmn (, ) n x= n+ x= n+ (D-) P P P C P C = + f ( n) + ( x) f( x) h( m,( n+ ) ) h( m, n) ( n+ ) n( n+ ) x= n+ P P P = + ( x) f( x) h( m,( n+ ) ) hmn (, ) nn ( + ) x= n

14 Opimal pricing sraegy of hoel for long-erm say 85 And we define TP( n) = DP( n) DP( n ) Δ P P P = + + h m,( n ) h( m, n) h m,( n ) ( + ) ( ) P C P C f ( n) + ( x) f( x) ( n+ ) ( n )( n+ ) x= n+ (D-) According o assumpion, we could obain hmn (, ) < 0 n (D-3) According o Assumpion (), equaions (D-) and (D-3), TP(n) > 0. Hence, Proposiion 5 exiss. Proof of Proposiion 6: From equaion (), * P = ( x) f( x) + n f( x) n C n x= n+ x= n+ = ( x) f( x) f( x) 0 n + > x= n+ x= n+ Hence, Proposiion 6 exiss. Proof of Proposiion 7: From equaions () and (), * λ x λ x λ x λ x P P e λ + e xλ e λ + xe λ = ( x) n λ n x! x! x= n+ x= n+ P C = ( x) [ f( x) f( x ) ] n [ f( x) f( x ) ] n + + x = n+ x= n+ P = ( x) f( x) ( x) f( x) + f( x) + nf( n) n x= n+ n x= n P = nf ( n ) + f ( x ) nf ( n ) n + x= n P C = f( x) > 0 n x= n Hence, Proposiion 7 exiss.

15 86 L. Ling e al. Proof of Proposiion 8: + * * P P P ( + ) P ( ) = ( x ) f( x) n f( x) hmn (, ) n + x= n+ x= n+ P P C + ( x) f( x) n f( x) hmn (, ) n x= n+ x= n+ P = f( x) ( n ) f( n ) nf( n ) n x= n+ Hence, Proposiion 8 exiss. P C = f( x) < 0 n x= n+