Industrial Management & Data Systems

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1 Inustrial Management & Data Systems Supply Chain Contrating Coorination for Fresh Prouts with Fresh-Keeping Effort Inustrial Management & Data Systems Journal: Inustrial Management & Data Systems Manusript ID IMDS-0-0-0R Manusript Type: Researh Paper Keywors: Fresh prout, Supply hain, Contrat, Coorination, Fresh-keeping effort

2 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Supply Chain Contrating Coorination for Fresh Prouts with Abstrat Fresh-Keeping Effort Purpose Fresh prout loss rates in supply hain operations are partiularly high ue to the nature of perishable prouts This paper aims to maximize profit through the ontrat between retailer an supplier The optimize pries for the retailer an the supplier, taking the fresh-keeping effort into onsieration, are erive Design/methoology/approah To aress this issue, we onsier a two-ehelon supply hain onsisting of a retailer an a supplier (ie, wholesaler for two senarios: entralize an eentralize eision-making We start from investigating the optimal eision in the entralize supply hain an then omparing the results with those of the eentralize eision Meanwhile, a fresh-keeping ost-sharing ontrat an a fresh-keeping ost- an revenue-sharing ontrat are esigne Numerial examples are provie, an managerial insights are isusse at en Finings The results show that (a the entralize eision is more profitable than the eentralize eision; (b a fresh prout supply hain an only be oorinate through a fresh-keeping ost- an revenue-sharing ontrat; ( the optimal retail prie, wholesale prie an fresh-keeping effort an all be ahieve; ( the profit of a fresh prout supply hain is positively relate to onsumers sensitivity to freshness an negatively orrelate with their sensitivity to prie Originality/value Few stuies have onsiere fresh-keeping effort as a eision

3 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems variable in the moelling of supply hain In this paper, a mathematial moel for the fresh-keeping effort an for prie eisions in a supply hain is evelope In partiular, fresh-keeping ost sharing ontrat an revenue-sharing ontrat are examine simultaneously in the stuy of the supply hain oorination problem Keywors Fresh prout; Supply hain; Contrat; Coorination; Fresh-keeping effort Paper type Researh paper Introution One of biggest hallenges in fresh prout supply hain (FPSC is maintaining prout freshness Aoring to Cai et al (00, in evelope ountries, there is up to a % loss of prout ue to amage an spoilage In eveloping ountries, this loss rate is muh higher Overoming this problem requires retailers an suppliers to work losely by oorinating operations aross the supply hain FPSC retailers an suppliers are severely affete by onsumer value an prout freshness an prie; these onsierations oul invaliate suh ompanies original oorination shemes in ases laking a ontrat Therefore, researh on the issue of oorinating FPSC management through ontrat is both meaningful an ritial There have been numerous researh on FPSC The majority of researh has fouse on inventory management, priing an orering strategies Dye (00 evelope a time-varying eterioration rate to formulate an inventory moel for perishable prouts by assuming a onstant loss rate for fresh prouts Loree an Uzohukwu (00 investigate the inventory management of fresh prouts by assuming that

4 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems onsumer eman hanges with the prout eterioration rate Ferguson an Koenigsberg (00 stuie a two-perio moel in whih inventory is left over from the first perio an a firm must eie whether to arry all, some or none of the leftover inventory to the next perio Suh eisions affet reations to new prout proution an priing strategies Cahon an Kök (00 re-examine the newsvenor problem by assessing the prout salvage value an then making optimal eisions on orer quantity Akay et al (00 investigate the optimal joint ynami priing of various perishable prouts when onsiering strategi onsumers using an algorithm of multinomial time Wang an Li (0 argue that, although it is iffiult to foreast the quality of perishable prouts, it is possible to evelop a priing metho to maximize profit base on more exat quality information Gallego an Hu (0 presente a joint priing approah for ompetitive prouts in a speial market environment, with perishable prouts onsisting of substitutable an omplementary prouts Nakanala et al (0 evelope an optimization moel for onsiering quality an transportation an etermine optimal priing eisions to minimize total ost for fresh foo Halim et al (00 introue the orering strategy of stohasti eman in ases of prout shortage using a fuzzy number eterioration rate In these stuies, inventory management an priing an orering strategies were stuie separately Some researhes have onsiere the three fators in ombination Li et al (00 stuie the optimal levels of priing an inventory simultaneously for perishable prouts, eveloping an optimal inventory replenishment strategy to reue loss

5 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Kanhanasuntorn an Tehanitisawa (00 evelope an inventory moel for perishable prouts with fixe life yles, examining how prout perishability an stokout influene supply hain profit, ost, servie an inventory Pasternak (00 presente a hierarhial moel to etermine optimal priing strategies an return poliies for perishable prouts with short shelf or eman lives Dong et al (00 etermine optimal eisions for inventory an priing when onsiering strategi onsumers using a polynomial moel Herbon et al (0 examine a replenishment poliy in regular time for perishable prouts an evelope a ynami priing strategy to attrat more onsumers an generate greater profit Chen et al (0 analyse the issue of joint priing an inventory ontrol for perishable prouts with fixe lifetimes over a finite horizon Li et al (0 onsiere strategies of inventory ontrol an joint ynami priing for perishable prouts in a stohasti inventory system Chew et al (0 investigate optimal eision making for perishable prouts with multiple-yle lifetimes, inluing eisions regaring prie an orer quantity Avinaav et al (0 evelope an optimization moel for onsiering time-epenent an prie-epenent eman an etermine optimal orer quantities, priing eisions an replenishment perios for perishable prouts Sainathan (0 onsiere perishable prouts with two-perio shelf lives in an infinite horizon an erive optimal priing eisions an orering strategies None of these stuies onsiere ways to oorinate FPSC with a ontrat The literature on FPSC ontrat oorination is very sparse Most stuies have fouse on non-perishable prouts Feng an Lu (0 stuie a two-ehelon

6 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems supply hain onsisting of retailers an manufaturers an analyse ontrating behaviours in ifferent ompetitive senarios Xu et al (0 investigate how the risk aversion of ual-hannel supply hain partners influenes the oorination of ontrats using a mean-variane mathematial moel Sommer an Loh (00 suggeste that employee effort an be motivate by inentive ontrats in ases of unpreitable events Xiao et al (0 examine how to oorinate the supply hain whih ontains a manufaturer an a retailer by revenue-sharing ontrat, propose a prout quality assurane poliy, an onsumer s utility is use in the moel Krishnan et al (00 investigate the effets of retailer promotional effort on onsumer eman an evelop a ontrat for hannel oorination through onsieration of this promotional effort Shang an Yang (0 investigate the hoie of profit-sharing oeffiient an the istribution of inrease profit when the ual-hannel supply hain is oorinate by profit-sharing ontrat, an risk preferene an negotiation ability ha an effet on the two fators Jiang an Chen (0 presente a newsvenor moel to oorinate the supply hain, an haraterize expetations equilibrium to obtain the optimal solutions when onsiering onsumer s strategi behaviour Lee et al, (0 propose prourement strategies an erive optimal prourement quantity so as to maximize firm s profit by forwar ontrat, an finally realize the oorination of supply hain Cahon an Lariviere (00 evelope a newsvenor moel for one supplier an one retailer using a revenue-sharing ontrat an ompare the profits generate by this ontrat to profits generate by other ontrats in one perio He an Zhao (0 investigate

7 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems the oorination of multi-tier supply hains when supply an eman are not efinite, showing that supply hains an be oorinate through wholesale prie ontrats with return strategies Lau et al (00 suggeste that purhase ontrats are esigne to oorinate supply hains when onsiering prie-sensitive eman, thus allowing the ominant retailer to generate greater profit Chen an Bell (0 examine supply hain oorination with buy-bak ontrats using fixe perentages of onsumer returns Sana an Chauhuri (00 analyse how to oorinate supply hains to maximize profit using reit an prie-isount ontrats when onsiering time-epenent emans Ma et al (0 isusse the issue of hannel oorination in a two-tier supply hain, proposing an innovative supply hain ontrat to inue effort on the parts of both the retailer an the manufaturer Xiao et al (00 oorinate a supply hain using a buybak ontrat an a markown money ontrat, respetively, uner a partial refun poliy Furthermore, they analyse how hanges to some moel parameters affete supply hain profit However, their moels i not onsier the harateristis of fresh prouts A few stuies have examine the oorination of FPSC in onsieration of prout loss rates Ketzenberg an Ferguson (00 investigate the value of information sharing between retailers an suppliers for perishable prouts, onsiering the effets of information sharing on eterioration an eman for supply hain oorination Blakburn an Suer (00 presente a ombine strategy involving mixe prout spee an effiieny for perishable prouts to oorinate FPSC Rong et al (0 moelle the proution an istribution of perishable foo items an stuie

8 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems their quality an ost in a supply hain with mixe-integer linear programming Cai et al (0 esigne an inentive sheme to oorinate the FPSC, examining whether the inentive ontrat oul remove the ouble marginalization that exists in supply hains an enourage partners to at in a oorinate way Wang an Webster (00 showe that perent markown money ontrats an quantity markown money ontrats an oorinate the supply hains for perishable goos with learane priing However, the extant literature has not yet simultaneously examine fresh-keeping ost sharing ontrats an revenue-sharing ontrats in the stuy of the FPSC oorination problem From the above review, it suggests: first, the foo supply hain is a relative less stuie area; seon, taking freshness of the foo into onsieration is rather sare; thir, simultaneously examining fresh-keeping ost an revenue issues is rare This motives our researh in eveloping a moel by taking these two tatis, ie fresh-keeping ost sharing an revenue-sharing, into onsieration This paper examines the oorination of a two-ehelon supply hain onsisting of a retailer an a supplier by onsiering fresh-keeping effort as a eision variable in the moelling of supply hain In this researh, the supplier refers to the wholesaler We present a mathematial moel for the fresh-keeping effort an for prie eisions in entralize an eentralize FPSC, respetively; provie optimal solutions for both supplier an retailer, inluing with respet to retail prie, wholesale prie an fresh-keeping effort; an analyse the impats of onsumer sensitivities to prie an freshness on FPSC profit We investigate how FPSC oorination an a win-win

9 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems outome an be ahieve through ost-sharing an revenue-sharing ontrats between retailer an supplier We also erive the optimal ost-sharing an revenue-sharing oeffiients to realize a win-win result Figure emonstrates the researh framework for a FPSC Inset: Figure Researh Framework for a FPSC The rest of the paper is organize as follows Setion esribes the moel an assumptions Setion stuies a entralize an a eentralize oorination moel for a FPSC oorinate without a ontrat Setion investigates two types of ontrats for oorinating between the retailer an the supplier: a fresh-keeping ost sharing ontrat an a fresh-keeping ost- an revenue-sharing ontrat Setion uses some numerial examples to illustrate the moel Setion onlues Moel esription We onsier a FPSC onsisting of one supplier an one retailer It osts per unit for the supplier to proure the prout The supplier then sells the prout to the retailer at a wholesale prie w, an the retailer sells the prout to onsumers at a retail prie p We use a ontinuous variable τ to measure the level of effort (Cai et al, 00 use by the retailer to preserve the fresh prout This effort is alle the fresh-keeping effort The relationships of events in FPSC are presente in Figure Insert: Figure Relationships of Events uner Consieration Let θ enotes a freshness inex in the range of [0,], with θ an θ 0 representing a fully fresh an ompletely eaye prout, respetively We aopt the freshness inex funtion evelope by Avinaav et al (0:

10 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems θ ( t t 0 η ( θ, t [ 0, T] ( T where T is the sale perio of the fresh prout; θ 0 is the initial value of freshness; an η is the prout s perishability rate From Eq (, we know that if the perishability rate η inreases, the prout freshness will erease sharply at the en of the sale perio Furthermore, η is a funtion of τ, as follows: η( kτ η0 (Dan et al, 0, where k is the oeffiient of τ, an k (0,, τ (0, A fresh-keeping effort implies a ertain ost, whih is enote as τ ( Aoring to Ma et al (0, we assume that the fresh-keeping ost funtion is where m is the fresh-keeping ost oeffiient The assumptions in the moel are: ( τ τ m, ( Orer quantity of retailer an supplier is equal to the eman (Ma et al, 0a; Xiao an Xu, 0; Zhang et al, 0 ( In a sale perio T, the onsumer arrival rate δ at any time is onstant ( In any yle, the lea time is negligible, an shortages are not allowe ( The retailer an supplier are risk-neutral, therefore they always purse the maximum profit Similar to Xu et al (0, we assume that the utility fae by the onsumer is a linear funtion of retail prie an freshness of prout The utility funtion of fresh prout is given as: U( t U α p+ βθ( t ( 0 where U0 represents the initial value of the fresh prout an follows a uniform

11 Inustrial Management & Data Systems Page 0 of Inustrial Management & Data Systems istribution of [0,], α enotes onsumers sensitivity to the prout prie an β enotes onsumers sensitivity to the prout freshness The following notation is use in the moel: : supplier s prourement ost per unit of fresh prout; Q : retailer s orering quantity in the entralize FPSC; p : retail prie of the fresh prout in the entralize FPSC; π : total profit in the entralize FPSC; w : wholesale prie of the supplier in the eentralize FPSC; i Q : retailer s orering quantity in the eentralize FPSC; p : retail prie in the eentralize FPSC; π : retailer profit in the eentralize FPSC; ri π : supplier profit in the eentralize FPSC; si π : total profit in the eentralize FPSC; i i : i without a ontrat; i for a fresh-keeping ost-sharing ontrat; i for a fresh-keeping ost- an revenue-sharing ontrat A oorination moel without ontrat In this setion, we examine the optimal eisions for retail prie an fresh-keeping effort in a entralize an a eentralize FPSC without ontrat Deisions in entralize FPSC In the entralize FPSC, the supplier an retailer are treate as one entity They make optimal eisions to maximize their total profit From a onsumer point of view, the eision to purhase a fresh prout is base

12 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems on the expetation of a positive utility funtion ie U ( t > 0 ; otherwise, the onsumer will walk away Therefore, the market eman of a fresh prout at any time t is D( t δ P( U t > 0 P( U t > 0 is the probability when onsumers utility funtion is positive Substituting Eq ( an Eq ( into the market eman funtion, we obtain: t D( t δ P( U0 α p+ β ( θ0 η( > 0 T t t δ P( U0 > α p β ( θ0 η( δ ( α p+ β ( θ0 η( T T Eq ( represents the whole market eman in the FPSC at any time Therefore, in a sale perio T, the atual orering quantity of fresh prout is: Then, the total profit funtion t Q D( t ( p ( ( t T T T δ α + β θ0 η 0 ( 0 π in the entralize FPSC is given by: π [( p w + ( w ] Q ( τ T t ( p δ ( α p ( 0 + β θ0 η( t mτ T In Eq (, we notie that wholesale prie w We seek to etermine the optimal eisions for the prie effort τ to oorinate the supply hain ( ( isappears in the entralize FPSC p an the fresh-keeping Theorem In the entralize FPSC, for any given parameters ( α, β, η0, k, the m( α+ B + B optimal retail prie of a fresh prout is p (α B an the optimal δβtη0k( B α fresh-keeping effort of the fresh prout is τ, where α B B ( + βθ βη, 0 0 Proof B δtβ η k 0

13 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems To fin the optimal retail prie an fresh-keeping effort to maximize ifferentiate π 0 p π with respet to π an 0 τ m( α+ B + B p (α B δβtη0k( B α τ α B p an π, we τ, setting both them equal to 0 Solving, we fin that the optimal retail prie is an the optimal fresh-keeping effort is However, to ensure that the first orer erivation is the optimal result, we nee to prove that the funtion is onave The Hessian matrix is π π η 0βTδ k αδ T p p τ H This shows that the Hessian matrix π η π 0βTδ k m τ p τ of π is a negative efinite for all values of η βtδ k αδ > Therefore, total profit π is onave to 0 Tm ( 0 Hene, theorem hols Substituting p an entralize FPSC as follows: Sine αδ 0 Tm ( 0 η βtδ k p an τ if p an τ τ into Eq (, we obtain the optimal total profit in δtm( B α π (α B >, we an obtain α B > 0 Therefore, the optimal total profit is positive α δ η β T ( 0 k 0 ( >, whih is Note that α B > 0 is onsiere in the rest paper In aition, the optimal α B fresh-keeping effort τ (0, ; thus, we an erive that 0< B α < δβtη k 0

14 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Deisions in eentralize FPSC In this subsetion, we onsier a eentralize supply hain in whih the retailer an supplier make their eisions inepenently This setion aims to etermine the optimal retail prie, the optimal fresh-keeping effort an the optimal wholesale prie to maximize expete iniviual profit Optimal eisions of the fresh prout retailer In the eentralize FPSC, the retailer makes optimal eisions aoring to the wholesale prie w, whih is given by the supplier The retailer s proess of euing its market eman funtion an orering quantity funtion is similar to that in the entralize supply hain Thus, the profit funtion of a fresh prout retailer is: π ( p w Q ( τ r T t ( p w δ ( α p ( 0 + β θ0 ( kτ η0( t mτ T From Eq (, we an obtain the optimal retail prie an the optimal fresh-keeping effort Lemma In the eentralize FPSC, for any given supplier s wholesale prie w, the m( α w + B + Bw optimal retail prie is p ( w an the optimal fresh-keeping (α B δβtη0k( B αw effort is τ ( w α B Proof As in the proof of Theorem, to fin the optimal retail prie an the optimal fresh-keeping effort to maximize π r, we ifferentiate π r with respet to τ, respetively, setting these equal to 0 ( p an

15 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems η 0βTδ k αδ T The Hessian matrix is H This shows that the Hessian η 0βTδ k m matrix of π r returns a negative efinite for all values of 0 ( 0 p an τ if η βtδ k αδt > Therefore, we fin that the optimal retail prie is ( βθ0 αw βη0( kτ p ( τ + + an the optimal fresh-keeping effort is α ( p w βη0tδ k ( p Simultaneously, from the two equations, we an obtain m τ m( α w + B + B w p ( w (α B δβtη k( B α w 0 an τ ( w α B Lemma shows that the optimal retail prie an the optimal fresh-keeping effort are funtions of the supplier s wholesale prie w The supplier etermines its optimal wholesale prie aoring to the retailer s reation funtion Optimal eisions of the fresh prout supplier For any given wholesale prie w of a fresh prout supplier, the retailer has a orrespone orering quantity The profit funtion of a fresh prout supplier is: Substituting p ( w π ( w Q s T t ( w δ ( α p ( 0 + β θ0 ( kτ η0( t T an τ ( w ( into Eq (, we obtain the optimal supplier profit in the eentralize FPSC The profit funtion has only one eision variable: w Lemma In the eentralize FPSC, the optimal wholesale prie of a fresh prout m( B + α + B supplier is w ( α B Proof

16 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Taking the first erivative of Eq ( with respet to wholesale prie w, we set it equal to 0 Taking the seon erivative of Eq ( with respet to w, we have π w s δαt < 0, whih is the fresh prout supplier s profit funtion π s an whih is onave to w Therefore, we fin that the optimal wholesale prie is m( B + α + B w ( α B Lemma gives an optimal wholesale prie w By substituting w into Lemma, we an obtain the optimal retail prie an the optimal fresh-keeping effort Theorem In the eentralize FPSC, the optimal retail prie of the fresh prout is m( B + α + B p ( α B δβtη0k( B α τ ( α B Proof an the optimal fresh-keeping effort of fresh prout is Substituting the optimal wholesale prie of the fresh prout supplier m( B + α + B w ( α B m( B + α + B p ( α B Substituting p, τ an into p ( w δβtη0k( B α an τ ( α B an τ ( w, we obtain w into ( an (, we obtain the retailer s optimal profit an the supplier s optimal profit in the eentralize FPSC: δtm(α B ( B α π r ( α B π δαtm ( B α s ( α B ( (0

17 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Beause α B> 0, as given previously, we know that B δtβ η k > 0 0 Hene, α B > 0 ; therefore, p > 0 Similarly, the optimal fresh-keeping effort τ δβtη0k( B α (0,, τ ; thus, we only onsier the situation in whih ( α B α B α B < B α< < δβtη0k δβtη0k 0 Comparison of entralize an eentralize eisions In the above isussions, Theorem provies the optimal retail prie an the optimal fresh-keeping effort for a entralize FPSC, while Theorem provies the optimal retail prie an the optimal fresh-keeping effort for a eentralize FPSC We an obtain Proposition by ontrasting the entralize supply hain an the eentralize supply hain with regar to optimal retail prie, optimal fresh-keeping effort an total profit Proposition τ < τ ; Proof when B < α m< B, p < p ; when α m> B, p > p ; π + π < π r s δβtη k( B α δβtη k( B α Sine the numerator is same, 0 0 τ τ ( α B α B the enominator ( α B α B > α B Thus, we get τ τ < 0 Therefore, τ < τ α B > 0 has been previously given The retail prie is positive; thus, α B > 0 Therefore:

18 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems m( α+ B + B m( α+ B + B p p ( α B (α B m(α B ( B α ( α B (α B Then, we fin that when α B > 0, p > p, while when α B < 0, B < α m< B an p < p Using the sum of the retailer s profit (Eq [] an the supplier s profit (Eq [0], we an etermine the total profit of the eentralize FPSC δtm( B α (α B π τ π τ, π ( p, τ r( p, + s( p, ( α B of the entralize FPSC Therefore, is the total profit π ( p, τ ( α B α m α mb + B >, π τ π τ α α α α r( p, + s( p, ( B ( B m mb+ B giving us: π r( p, τ + π s( p, τ < π ( p, τ Proposition iniates that the total profit of a eentralize FPSC is less than that of a entralize FPSC The optimal fresh-keeping effort in a eentralize supply hain is lower than that in a entralize supply hain This suggests that, in a eentralize FPSC, the total profit is not optimal ue to the ouble marginal effet of supply hain Therefore, it is neessary to esign proper ontrats to oorinate FPSC We highlight that a eision to entralize may ahieve maximum profit In the following setions, we take π as a target for a eentralize supply hain, serving as the motivation behin the supplier-retailer ontrat, that is, both retailer an supplier inten to ahieve iniviual maximise profit whilst also maximise total profit in the supply hain Contrating to failitate oorination

19 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems In this setion, we first examine whether the fresh-keeping ost-sharing ontrat is effetive or not Then, we investigate the best way to oorinate the FPSC by sharing both osts an revenues in fresh-keeping ontrats It is expete that the FPSC will be more effetive if it is bone by a ontrat It is also unerstanable that parties will aept suh a ontrat only when they o not nee to sarify their own profit (ompare to situations with no ontrat Fresh-keeping ost-sharing ontrat From Proposition, we know that τ < τ Therefore, to ahieve the optimal fresh-keeping effort τ in the eentralize supply hain, a retailer must pay a higher fresh-keeping ost; however, the supplier may not have enough motivation to o this Thus, it is neessary to esign a ost-sharing ontrat to oorinate both parties A ost-sharing ontrat typially inlues two parameters The first is the wholesale prie w, whih the retailer pays The seon is the ost-sharing oeffiient of the supplier, represente by ϕ ( 0< ϕ< Aoring to the above esription, we know that the profit funtion of retailer is π ( p w Q ( ϕ ( τ r t ( p w ( p + ( ( k ( t ( m T T δ α 0 β θ0 τ η0 ϕ τ The profit funtion of the supplier is π ( w Q ϕ ( τ s t ( w ( p + ( ( k ( t m T T δ α 0 β θ0 τ η0 ϕ τ Base on the above, we an erive Theorem ( (

20 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Theorem Uner the fresh-keeping ost-sharing ontrat, for any given fresh-keeping ost sharing oeffiient ϕ, the optimal retail prie is m( ϕ( B + α + B p (( ϕ α B δβtη0k( B α τ (( ϕ α B Proof π p, an the optimal fresh-keeping effort is Taking the seon erivative of Eq ( with respet to δα r T < 0, π τ ϕ r m( < 0 p an τ, we get The Hessian matrix is η 0βTδ k αδ T H This shows that the Hessian matrix of π r is a η 0βTδ k m( ϕ negative efinite for all values of p an τ if αδ η βtδ k ϕ > 0 Tm( ( 0 Therefore, we fin that, if π r is onave in p an τ, the optimal solution exists Similarly, taking the seon erivative of Eq ( with respet to w, we get π w s δαt < 0 Here, if π s is onave in w, the optimal solution also exists π s Hene, by solving w 0 π r π r first, then substitute w into 0, 0, we τ an evelop the fresh-keeping ost-sharing ontrat For any given fresh-keeping ost-sharing oeffiient ϕ, the optimal retail prie of the fresh prout retailer is m( ϕ( B + α + B p (( ϕ α B δβtη0k( B α τ (( ϕ α B an the optimal fresh-keeping effort is p

21 Inustrial Management & Data Systems Page 0 of Inustrial Management & Data Systems Theorem gives the optimal retail prie an fresh-keeping effort for FPSC Substituting p an retailer an supplier respetively τ into Eq ( an (, we erive the optimal profit for both δtm(( ϕ α B ( B α π r (( ϕ α B δtm(( ϕ αϕ B ( B α π s (( ϕ α B In the ost sharing ontrat, the retailer has signifiant motivation to engage in fresh-keeping effort beause part of ost is supposely share by the supplier Let the optimal fresh-keeping effort is the same as in the entralize supply hain ie, τ τ By omparing the optimal eisions uner the fresh-keeping ost-sharing ontrat for the senario of a entralize eision without a ontrat, we erive Proposition Proposition When τ τ, p > p ; π r + π s < π Proof δβtη0k( B α δβtη0k( B α From τ τ, we get (( 0 α B α B ϕ 0 m( 0( B + α + B m( α+ B + B Therefore, p > p (( 0 α B (α B p > p Then, we an erive the total profit: ( ( Hene, δtm(( 0 α B ( B α δtm(( 0 α 0 B ( B α π π r + s + (( 0 α B (( 0 α B δtm( B α (α B ( α B

22 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Therefore, π π π > r + s Hene, π r + π s < π Proposition shows that the retail prie uner the fresh-keeping ost-sharing ontrat is higher than that in a entralize supply hain, an the total profit is lower than that without a ontrat Therefore, it is useful for retailer to improve their fresh-keeping effort through fresh-keeping ost-sharing ontrats; however, the FPSC annot be oorinate uner fresh-keeping ost-sharing ontrat Thus, we must onsier how to maximize profits by aing a revenue-sharing ontrat Fresh-keeping ost- an revenue-sharing ontrat To ahieve the optimal retail prie an the same fresh-keeping effort as well as total profit as in the entralize supply hain, we onsier a ase in whih a supplier offers a isount to a retailer (apart from sharing the fresh-keeping ost In suh a ase, the retailer may be willing to reue the prie ue to the lower prourement prie, an it may also be willing to share some revenue with the supplier Fresh-keeping ost- an revenue-sharing ontrats inlue three parameters The first is the wholesale prie w that the retailer pays The seon is the ost share oeffiient of the supplier, represente by ϕ ( 0< ϕ< The thir is the revenue share oeffiient of supplier, represente by ϕ ( 0< ϕ < Aoring to the above esriptions, we know that the profit funtion of the retailer is as follows: ( p Q w Q ( ( π ϕ ϕ τ r T t (( ϕ p w δ α p β θ0 ( kτ η + 0 t ( ϕ mτ T 0 (

23 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Then, the profit funtion of the supplier is: π s ϕ p Q + ( w Q ϕ ( τ t T T ( w + ϕ p δ ( 0 α p + β θ0 kτ η0 t ϕ mτ Base on the above, we an erive Theorem Theorem Uner the fresh-keeping ost- an revenue-sharing ontrat, for any given wholesale prie w, fresh-keeping ost-sharing oeffiient ϕ an revenue-sharing oeffiient ϕ, the optimal retail prie of a fresh prout retailer is ( ϕ( βθ0 ( ϕ βη0( kτ wα p ( τ + + ( ϕ α fresh-keeping effort is Proof π τ (( ϕ p w βη0tδ k τ ( p ( ϕ m Taking the seon erivative of Eq ( with respet to ϕ r ( m< 0, π p r ( T < 0 ϕ δα ( an the optimal p an τ, we have The Hessian matrix is ( ϕ η0βtδ k ( ϕ αδt H This shows that the Hessian matrix of ( ϕ η0βtδ k m( ϕ π r returns a negative efinite for all values of αδ 0 Tm( ( 0 p an τ if η βtδ k ϕ > Therefore, we fin that π r is onave in p τ, suggesting that the optimal solution exists π r Hene, solving 0 τ an π r 0 p ( ϕ( βθ0 ( ϕ βη0( kτ wα p ( τ + + ( ϕ α an, we an erive the optimal retail prie an the optimal

24 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems fresh-keeping effort (( ϕ p w βη0tδ k τ ( p ( ϕ m Let p p an τ τ It is then neessary to ajust the wholesale prie w failitate oorination, leaing us to theorem Theorem If the fresh-keeping ost- an revenue-sharing ontrat ( ϕ, ϕ, w is satisfie by ϕ ϕ, w ( ϕ an αm(α B (α B ( α B ( m B then π r+ π s π is ahieve, an the FPSC an be oorinate Proof w Let p p ; that is ( ϕ Thus, we obtain w ( ϕ Similarly, let τ τ ; thus, we obtain ( ϕ ( p ( ϕ ( p ; therefore, ϕ ϕ ϕ α ( ϕ p w ϕ to p That is, Substituting ϕ ϕ, w ( ϕ an p an τ into Eq ( an Eq (, we erive the optimal total profit of the retailer as follows: The optimal total profit of supplier is: ( ϕ δtm( B α π r (α B ϕδ Tm( B α π s (α B Comparing Eq ( an Eq ( with Eq ( an Eq (0, we get αm(α B (α B ( α B ( m B ϕ α Then, the total profit uner the fresh-keeping ost- an revenue-sharing ontrat is: (, (

25 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems ( ϕ δtm( B α ϕδtm( B α δtm( B α π π r+ π s + (α B (α B (α B It is equal to the total profit π in the entralize FPSC Thus, π r π s π the fresh-keeping ost- an revenue-sharing ontrat makes sense ( +, an Comparing the retailer s profit uner ost- an revenue- sharing ontrat with the ase in eentralize FPSC, we get Beause of ( ϕ δtm( B α δtm(α B ( B α π π r r (α B ( α B ϕ δtm( B α ( ϕ (α B (α B ( α B αm(α B (α B,, ( α B ( α B (α B ϕ ( α B Therefore, π π 0 That is the retailer uner ost- an revenue- sharing ontrat r r an earn more profit than the ase in eentralize FPSC Similarly, Beause of ϕδtm( B α αδtm( B α π π s s (α B ( α B ϕ δtm( B α ϕ α (α B ( α B, ( α B ( α B αm(α B (α B, αm(α B ϕ ( α B Hene, π π 0 That is the supplier uner ost- an revenue- sharing ontrat s s an earn more profit than the ase in eentralize FPSC Theorem iniates that when the ost-sharing oeffiient ϕ is equal to the revenue-sharing oeffiient ϕ, an they are all in the range of αm(α B (α B,, the FPSC an be oorinate by the ( α B ( α B fresh-keeping ost- an revenue-sharing ontrat an that a win-win situation between

26 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems the fresh prout retailer an supplier an be ahieve A omparison of the FPSC profits shows that all parties inur higher profits in the ost- an revenue-sharing ontrat in omparison to the eentralize ase Consequently, the retailer an the supplier have enough motivation to aept ost- an revenue- sharing ontrat We now isuss how the ost- an revenue- sharing ontrat an be implemente in pratie The supplier an the retailer first agree on ost- an revenue- sharing ontrat ( ϕ, ϕ, w, the supplier an observe the optimal retail prie an the optimal fresh-keeping effort whih etermine by retailer As for Q, the supplier an onut a hek of the orering quantity when the ontrat is reahe The wholesale prie an then be etermine by w ( ϕ Aoring to the ontrat, the fresh-keeping ost sharing proportion of supplier is ϕ, the retailer s proportion is ( ϕ ; the revenue sharing proportion of supplier is ϕ, the retailer s proportion is ( ϕ ; where ϕ ϕ, they are in the range of αm(α B (α B, ( α B ( α B Corollary Uner the fresh-keeping ost- an revenue-sharing ontrat ( ϕ, ϕ, w, if onsumers sensitivity to the prie of prout α is greater, the FPSC will be iffiult to oorinate However if onsumers sensitivity to the freshness of prout β is greater, the FPSC will be easy to oorinate Proof Aoring to Theorem ϕ αm(α B (α B [, ], enoting as ( α B ( α B ϕ [ ϕmin, ϕmax ] Taking the first erivative of ϕ min with respet to α, we get

27 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems ϕ α mb > 0; that is, ϕ min is positively relate to α Taking the first ( α B min erivative of that is ϕmax (α B mb ϕ max with respet to α, we get < 0 ; α ( α B ϕ max is negatively orrelate to α Therefore, the range of ϕ is ereasing with an inreasing α when ϕ [ ϕmin, ϕmax ] In other wors, the revenue-sharing oeffiient of the fresh prout supplier is negatively orrelate with onsumers sensitivity to prie, making the supplier unwilling to aept the ontrat an the FPSC iffiult to oorinate Similarly, ϕ β α mb < 0 β( α B min ϕ max αm(α B B > 0, β β ( α B Therefore, the range of ϕ is inreasing with the inreasing min max β when ϕ [ ϕ, ϕ ] In other wors, the revenue-sharing oeffiient of the fresh prout supplier is positively relate to onsumers sensitivity to freshness, making the supplier willing to aept the ontrat an the FPSC easy to oorinate From Theorem an Corollary, we know that it is neessary to hoose the proper onitions when negotiating a ontrat The total FPSC profit is positively relate with onsumers sensitivity to prout prie an negatively orrelate with onsumers sensitivity to prout freshness Numerial analysis In the above setions, we theoretially isuss how to oorinate the FPSC uner a ontrat situation an a non-ontrat ontrat situation an then explore the ifferenes between the entralize FPSC an the eentralize FPSC To illustrate the theoretial results, we present some numerial examples in this setion The

28 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems parameters are summarize in Table Insert Table Parameters Using the parameters in Table, we apply them into previously analyse senarios Insert Figure Optimal eisions uner ifferent preferenes without a ontrat The results in Figure verify Theorems an an Proposition They show the optimal retail prie an the optimal fresh-keeping effort between the entralize FPSC an the eentralize FPSC Figure & iniate that the optimal fresh-keeping effort in a entralize supply hain is higher than that in a eentralize supply hain Figure & illustrate that that the optimal retail prie in a entralize supply hain is lower than that in a eentralize supply hain Figure & emonstrate that the optimal total profit in a entralize supply hain is greater than that in a eentralize supply hain In sum, the optimal eisions in the entralize FPSC are better than those in the eentralize FPSC Insert Figure Optimal eisions an profits uner the fresh-keeping ost-sharing ontrat From Figure, we an see that the optimal fresh-keeping effort uner the fresh-keeping ost-sharing ontrat is the same as that foun in the entralize FPSC (Figure & However, the retailer prie is higher than that in the entralize FPSC (Figure & ; an the total profit is lower (Figure & Therefore, the FPSC annot be oorinate via a fresh-keeping ost-sharing ontrat Insert Figure Optimal eisions an profits uner the fresh-keeping ost- an revenue-sharing ontrat Figure reveals the optimal eisions an profits uner the fresh-keeping ost- an revenue-sharing ontrat These finings onfirm Theorems an By omparing

29 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems the results in Figure & with Figure &, an Figure & with Figure &, it beomes lear that the optimal fresh-keeping effort an retail prie uner the fresh-keeping ost- an revenue-sharing ontrat ahieve the level of the entralize FPSC; the iniviual profit is higher than those in other two senarios Moreover, from Figure &, it an be seen that the total profit is the same as that in the entralize supply hain Insert Figure The effets of onsumers sensitivity to prie an freshness on profit Base on Corollary, we an illustrate the effets of onsumers sensitivity to prie an freshness on profit, whih is epite in Figure We know that the optimal profit that uner the fresh-keeping ost- an revenue-sharing ontrat ahieve the level of the entralize FPSC From Figure, it is lear that the FPSC profit inreases with the inreasing of onsumers sensitivity to prout freshness, an it ereases with the inreasing of onsumers sensitivity to prout prie Our analysis thus reveals that from the prout s fresh-keeping perspetive, ost- an revenue- sharing ontrat offere by the retailer or obtaine through negotiation leas to a higher fresh-keeping effort in FPSC, brings more profit to both supplier an retailer The results explain the reason why supplier an retailer woul prefer ost- an revenue- sharing ontrat uner fresh-keeping effort, an woul ooperate with supply hain partners in orer to benefit from the fresh-keeping initiatives Conlusion an future researh One of the speifi hallenges in foo supply hain is that freshness of foo is one of the keys for ustomers purhasing eision This leas to two important questions: first, how muh effort an resoures are neee among FPSC members in orer to

30 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems keep the prout refresh Seon, how to motivate an oorinate PFSC members through ontrat mehanism This paper strives to answer these questions In this paper, we have examine the oorination of FPSC with a fresh-keeping effort We fous on the oorination of the FPSC through ifferent ontrats when the fresh-keeping effort is onsiere in the moel Two ases are onsiere: a fresh-keeping ost-sharing ontrat an a fresh-keeping ost- an revenue-sharing ontrat In eah ase, we etermine the optimal retail prie, the optimal wholesale prie an the optimal fresh-keeping effort The result suggests that the fresh-keeping ost- an revenue-sharing ontrat is more effetive for oorinating the FPSC We fin that, in negotiating the ontrat, it is neessary to arefully onsier the onitions to maximize total profit without sarifying iniviual profit It is worth noting that the profit of the FPSC is negatively orrelate with onsumers sensitivity to prout prie, while it is positively relate to onsumers sensitivity to prout freshness There are several topis that merit further researh In this paper, we assume that the fresh-keeping ost is pai by the fresh prout retailer in a entralize supply hain A natural extension is to examine a setting in whih the fresh-keeping ost is pai by the fresh prout supplier Sine, in this researh, the onsumer arrival rate at any time is assume to be onstant, another interesting possibility is to examine a situation in whih the rate is stohasti Finally, we will exten our moel to onsier how to oorinate the FPSC through ost- an revenue-sharing ontrats when two retailers ompete by stuying the oorination mehanisms of the FPSC when one

31 Inustrial Management & Data Systems Page 0 of Inustrial Management & Data Systems retailer has the priority to make its eision first Referene Akay, Y, Natarajan, HP an Xu, SH (00, Joint ynami priing of multiple perishable prouts uner onsumer hoie, Management Siene, Vol No, pp Avinaav, T, Herbon, A an Spiegel, U (0, Optimal inventory poliy for a perishable item with eman funtion sensitive to prie an time, International Journal of Proution Eonomis, Vol No, pp Blakburn, J an Suer, G (00, Supply Chain Strategies for Perishable Prouts : The Case of Fresh Proue, Proution an Operations Management, Vol No, pp Cahon, GP an Kök, AG (00, Implementation of the newsvenor moel with learane priing: How to (an how not to estimate a salvage value, Manufaturing & Servie Operations Management, Vol No, pp 0 Cahon, GP an Lariviere, MA (00, Supply hain oorination with revenue-sharing ontrats: strengths an limitations, Management siene, Vol No, pp 0 Cai, X, Chen, J, Xiao, Y an Xu, X (00, Optimization an Coorination of Fresh Prout Supply Chains with Freshness Keeping Effort, Proution an Operations Management, Vol No, pp Cai, X, Chen, J, Xiao, Y, Xu, X an Yu, G (0, Fresh-prout supply hain management with logistis outsouring, Omega, Vol No, pp Chen, J an Bell, PC (0, Coorinating a eentralize supply hain with ustomer returns an prie-epenent stohasti eman using a buybak poliy, European Journal of Operational Researh, Vol No, pp 00 Chew, EP, Lee, C, Liu, R, Hong, K an Zhang, A (0, Optimal ynami priing an orering eisions for perishable prouts, International Journal of Proution Eonomis, Vol, pp Dan, B, Xu, G an Liu, C (0, Priing poliies in a ual-hannel supply hain with retail servies, International Journal of Proution Eonomis, Vol No, pp 0 Dong, L, Kouvelis, P an Tian, Z (00, Dynami priing an inventory ontrol of substitute prouts, Manufaturing & Servie Operations Management, Vol No, pp Dye, C-Y (00, Joint priing an orering poliy for a eteriorating inventory with partial baklogging, Omega, Vol No, pp Feng, Q an Lu, LX (0, Supply hain ontrating uner ompetition: bilateral bargaining vs Stakelberg, Proution an Operations Management, Vol No, pp Ferguson, ME an Koenigsberg, O (00, How shoul a firm manage eteriorating inventory?, Proution an Operations Management, Vol No, pp 0 Gallego, G an Hu, M (0, Dynami priing of perishable assets uner ompetition,

32 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Management Siene, Vol No, pp Halim, KA, Giri, BC an Chauhuri, KS (00, Fuzzy eonomi orer quantity moel for perishable items with stohasti eman, partial baklogging an fuzzy eterioration rate, International Journal of Operational Researh, Vol No -, pp He, Y an Zhao, X (0, Coorination in multi-ehelon supply hain uner supply an eman unertainty, International Journal of Proution Eonomis, Vol No, pp 0 Herbon, A, Levner, E an Cheng, TCE (0, Perishable inventory management with ynami priing using time-temperature iniators linke to automati eteting evies, International Journal of Proution Eonomis, Vol, pp Jiang, W an Chen, X (0, Optimal strategies for manufaturer with strategi ustomer behavior uner arbon emissions-sensitive ranom eman, Inustrial Management & Data Systems, Vol No, pp Kanhanasuntorn, K an Tehanitisawa, A (00, An approximate perioi moel for fixe-life perishable prouts in a two-ehelon inventory istribution system, International Journal of Proution Eonomis, Vol 00 No, pp 0 Ketzenberg, M an Ferguson, ME (00, Managing Slow Moving Perishables in the Groery Inustry, Proution an Operations Management, Vol No, pp Krishnan, H, Kapusinski, R an Butz, DA (00, Coorinating ontrats for eentralize supply hains with retailer promotional effort, Management siene, Vol No, pp Lau, AHL, Lau, H-S an Wang, J-C (00, How a ominant retailer might esign a purhase ontrat for a newsvenor-type prout with prie-sensitive eman, European Journal of Operational Researh, Vol 0 No, pp Lee, CKM, Lin, D an Pasari, R (0, Strategi prourement from forwar ontrat an spot market, Inustrial Management & Data Systems, Vol No, pp Li, S, Zhang, J an Tang, W (0, Joint ynami priing an inventory ontrol poliy for a stohasti inventory system with perishable prouts, International Journal of Proution Researh, Vol No 0, pp Li, Y, Lim, A an Rorigues, B (00, Note-priing an inventory ontrol for a perishable prout, Manufaturing & Servie Operations Management, Vol No, pp Loree, EJ an Uzohukwu, BM (00, Proution planning for a eteriorating item with stohasti eman an onsumer hoie, International Journal of Proution Eonomis, Vol No, pp Ma, P, Wang, H an Shang, J (0a, Contrat esign for two-stage supply hain oorination: Integrating manufaturer-quality an retailer-marketing efforts, International Journal of Proution Eonomis, Vol No, pp Ma, P, Wang, H an Shang, J (0b, Supply hain hannel strategies with quality an marketing effort-epenent eman, International Journal of Proution Eonomis, Vol No, pp

33 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Nakanala, D, Lau, H an Zhang, J (0, Cost-optimization moelling for fresh foo quality an transportation, Inustrial Management & Data Systems, Vol No, pp Pasternak, BA (00, Optimal priing an return poliies for perishable ommoities, Marketing siene, Vol No, pp Rong, A, Akkerman, R an Grunow, M (0, An optimization approah for managing fresh foo quality throughout the supply hain, International Journal of Proution Eonomis, Vol No, pp Sainathan, A (0, Priing an replenishment of ompeting perishable prout variants uner ynami eman substitution, Proution an Operations Management, Vol No, pp Sana, SS an Chauhuri, KS (00, A eterministi EOQ moel with elays in payments an prie-isount offers, European Journal of Operational Researh, Vol No, pp Shang, W an Yang, L (0, Contrat negotiation an risk preferenes in ual-hannel supply hain oorination, International Journal of Proution Researh, No ahea-of-print, pp 0 Sommer, SC an Loh, CH (00, Inentive ontrats in projets with unforeseeable unertainty, Proution an Operations Management, Vol No, pp Wang, CX an Webster, S (00, Markown money ontrats for perishable goos with learane priing, European Journal of Operational Researh, Vol No, pp Wang, X an Li, D (0, A ynami prout quality evaluation base priing moel for perishable foo supply hains, Omega, Vol No, pp 0 Xiao, T, Shi, K an Yang, D (00, Coorination of a supply hain with onsumer return uner eman unertainty, International Journal of Proution Eonomis, Vol No, pp 0 Xiao, T an Xu, T (0, Coorinating prie an servie level eisions for a supply hain with eteriorating item uner venor manage inventory, International Journal of Proution Eonomis, Vol No, pp Xiao, T, Yang, D an Shen, H (0, Coorinating a supply hain with a quality assurane poliy via a revenue-sharing ontrat, International Journal of Proution Researh, Vol No, pp 0 Xin, C, Pang, Z an Limeng, P (0, Coorinating Inventory Control an Priing Strategies for Perishable Prouts, Operations Researh, Vol No May, pp 00 Xu, G, Dan, B, Zhang, X an Liu, C (0, Coorinating a ual-hannel supply hain with risk-averse uner a two-way revenue sharing ontrat, International Journal of Proution Eonomis, Vol, pp Xu, H, Liu, ZZ an Zhang, SH (0, A strategi analysis of ual-hannel supply hain esign with prie an elivery lea time onsierations, International Journal of Proution Eonomis, Vol No, pp Zhang, WG, Fu, J, Li, H an Xu, W (0, Coorination of supply hain with a revenue-sharing

34 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems ontrat uner eman isruptions when retailers ompete, International Journal of Proution Eonomis, Vol No, pp

35 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Table Parameters k m δ T 0 θ η

36 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Fresh-keeping ost-sharing ontrat ( w, ϕ Centralize FPSC Deentralize FPSC Contrat Comparison Figure Researh Framework for a FPSC Fresh-keeping ost- an revenue- sharing ontrat ( w, ϕ, ϕ

37 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Supplier etermines wholesale prie Retailer etermines quantity an effort Prout freshness observe Retailer etermines retailer prie Figure Relationships of Events uner Consieration Market eman satisfie

38 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Figure The effet of onsumers sensitivity to prie on fresh-keeping effort Figure The effet of onsumers sensitivity to freshness on fresh-keeping effort Figure The effet of onsumers sensitivity to prie on retail prie Figure The effet of onsumers sensitivity to freshness on retail prie Figure The effet of onsumers sensitivity to prie on profit Figure The effet of onsumers sensitivity to freshness on profit Figure Optimal eisions uner ifferent preferenes without a ontrat

39 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Figure The effet of onsumers sensitivity to prie on fresh-keeping effort Figure The effet of onsumers sensitivity to freshness on fresh-keeping effort Figure The effet of onsumers sensitivity to prie on retail prie Figure The effet of onsumers sensitivity to freshness on retail prie Figure The effet of onsumers sensitivity to prie on profit Figure The effet of onsumers sensitivity to freshness on profit Figure Optimal eisions an profits uner the fresh-keeping ost-sharing ontrat

40 Page of Inustrial Management & Data Systems Inustrial Management & Data Systems Figure The effet of onsumers sensitivity to prie on fresh-keeping effort Figure The effet of onsumers sensitivity to freshness on fresh-keeping effort Figure The effet of onsumers sensitivity to prie on retail prie Figure The effet of onsumers sensitivity to freshness on retail prie Figure The effet of onsumers sensitivity to prie on profit Figure The effet of onsumers sensitivity to freshness on profit Figure Optimal eisions an profits uner the fresh-keeping ost- an revenue-sharing ontrat

41 Inustrial Management & Data Systems Page of Inustrial Management & Data Systems Figure The effets of onsumers sensitivity to prie an freshness on profit