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Economic Decision Analy

by: Maryse Thiel

Economic Decision Analy ISYE 6230

Maryse Thiel

GPA 3.82

Paul Griffin

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Paul Griffin
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This 0 page Class Notes was uploaded by Maryse Thiel on Monday November 2, 2015. The Class Notes belongs to ISYE 6230 at Georgia Institute of Technology - Main Campus taught by Paul Griffin in Fall. Since its upload, it has received 8 views. For similar materials see /class/234199/isye-6230-georgia-institute-of-technology-main-campus in Industrial Engineering at Georgia Institute of Technology - Main Campus.

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Date Created: 11/02/15
Geo ia 1a H Milton Stewart School of Industrial and Systems Engineering Game Theory and Contracting Analysis for Price and Leadtime O timization ISyE 6230 Economic Decision Analysis Pelin PngUn 03132008 e i H Milton Stewart School of Industrial and Systems Engineering Coordination of Marketing and Production for Price and Leadtime Decisions by Pelin Pengn Paul Griffin and Plnar Keskinocak This research is partially supported by NSF Career Award DMI0093844 39i 2 Introduction Common Incentives Common Incentives I Maximize Revenue l Minimize Cost I Maximize Volume I Increase Operational Ef ciency Losing Sight of the Common Objective L i39m glad that the hole I is not on our side Source Mumin Kurtulus 39 1 Karl Kempf Intel Fellow and Director of Decision Technologies in Intel s Technology and Manufacturing Group have lost count of the number of times the sales and marketing guys have made a price move on a particular product only to nd that manufacturing capacity fungibility is not What they expected and to capture the increased demand for the target product required cannibalization of a number of other products it is not uncommon for this kind of problem to have a 100M negative impact overall prior discussion could have minimized the impact Nell Williams Marriott s VP of Global Revenue Management Organization Salespeople have historically been compensated on volume and not profit and that s part of the reason Why they are at odds With revenue managers The Whole hotel Wins When both disciplines work together towards the same goal and that is bringing the most pro table business into the hotel Research Questions e What are the inefficiencies that result from the decentralization of price and leadtime decisions I Pricing gt Marketing Department I Leadtime gt Production Department a How to align the incentives of production and marketing with the firm s overall objectives e Optimal decisions and overall profitability I market characteristics I decisionmaking sequences I capacity Literature Review a Due date management literature Steadystate price and leadtime sensitive demand uniform delivery time guarantees I Palaka Erlebacher and Kropp 1998 So and Song 1998 Boyaci and Ray 2003 Ray and Jewkes 2004 All assume a centralized decision maker a Marketingoperations interface I Eliashberg and Steinberg 1993 Li and Atkins 2002 Chatterjee Slotnick and Sobel 2002 Ho and Zheng2004 Balasubramanian and Bhardwaj 2004 Golbasi and Wu 2005 a First work to consider priCe and leadtime decisions Within the marketingoperations interface 39 1 Model Assumptions a Constant capacity a MM1 queue with mean production rate capacity u and mean arrival rate lDpL 3 Linear demand function DpLa bp CL Leadtime sensitivity QUOted PFIC Price sensitivity QUOted leadmmeMarket potential w No inventory holding or lateness penalty costs only linear production costs m a Service level constraint Percentage of orders filled on time s I e39W39M 2 s lt3 1 JJL 2 k where k ln11s a Positive Demand Assumption Dmkpa bm ckpgt 0 Centralized Setting C Problem Maximize profits subject to the service level constraint a CLO 1C max 7239s m tC O c u CZO b Unit production st yACLC 2k 7C cost Optimal Solution k Lo 2 I Ac 6121 mb12 cklt p lta 2 cLgtb Special case of Paaka et al 1998 for the xed capacity case With no WIP holding and no lateness penalty costs 39 Decentralized Setting P Production is the Stackelberg leader and marketing is the follower 1 Production quotes leadtime st service level constraint 2 Marketing quotes the best price in response to the leadtime O Backward induction Marks 9 m Problem Maximize rm revenue 1119 WP ppln hp 39 Lp 4 Optima dnritinns l u a Ln as afunctlon of pFlLy Lu rm md Apllpl a bpeanJ a La leadtime Produc n NLILFI Problem Maximize lirm pro t m wax u M 77711 le3 st service level constraint ngLP 39 lncenllveforproducllon H M ILL71L I J U Decentralized Setting P Solution Maximize a convex function over a closed interval Optimal solution lies in the boundaries For a nontrivial optimal solution m with positive pro t we need ck u gt M bm rnln capacity a r 2mb v a 1 1n e quot 39 pp 2 m mm price Optimal solution 1 124 4 Decentralized Settin Marketing is the Stackelberg leader and production is the follower 1 Marketing quotes price maximizing its revenue 2 Production quotes the best leadtime in response to price I Backwards induction a Production Problem 1 imllnrlqiquot 41 yr lurluerMrdullL I u r b l l Amiga pt l Marketing Problem Solution anyquot i u p maxim ml 6P 39 I U Comparison of Deci ion Making Sequences amp Optimal decisions 1 1 06M g4 11LCltLVI 1 111pgtpw 21 mm gt7r 27 where P Production Stackelberg Game ProdStac M Marketing Stackelberg Game MarStac v Optimality equations for demand aambali mai f ch aaMZXitaAZMHkn enmity sky c The optimal demand rate under the decentralized setting is independent of m and b regardless of the decisionmaking sequence I quotComparison of DecisionMakin Sequences b2 4 mi 5 95 I 39 I 39g j 39 M M Cap wy 5 03mm L 5 Capagnw U U Dfecenjtralizedsetting 6 Firm better off if marketing is the leader especially under tight capacity Deviation from the centralized pro t increases as the price sensitivity of the customers or the unit production cost gets higher 0 When production is the leader high capacity is required for approaching centralized profit a Higher capacity does not necessarily lead to higher profits for a decentralized firm I 15 1 a Comparison of Decision Making Sequences 9 Sensitivity of the optimal decisions to the problem parameters 39 1 quot Price vs capacity 8 6 Under C and M higher prices are Charged Within a tight capacity interval to quote lower leadtimes As capacity increases the rm decreases its prices to attract more customers 39 1 t 11 Prlce vs Leadtlme SenSItIVIty amp SerVIce Level Low Capacity Medium Capacity High Capacity Decrease Increase Decrease Decrease C u amb3 amb3 ltu lt a mb u 2 amb M u aS a3ltulta uza 0 Capacity levels are defined only by the production cost and price sensitivity of the customers under C G Higher capacity does not necessarily lead to charging higher for better service 0 Under medium capacity profits may increase in c or s When marketing is the leader 39 1 quot Coordination Mechanisms Transfer price contract with bonus pavments For each unit produced marketing pays w to production Bonus payment as a fraction of the total revenues generated or Marketing s share of revenue or Production s share of revenue General model 0g 0511 and 0s 05231 01 Marketing s problem max of 7 nip 7 1139a 7 24 7 3in Mm Production s problem lt max 7 7 127 z7m Lxgu 39 I 1 75p 7amp1 ml lli 1lt L L L l Coordination Mechanisms Solution 9 The minimum fraction of revenue that should be offered to production a The minimum transfer price Wm n lt w lt n u 7 A yin ini 39lg ngguiml I 1 7 7 1 7 02 i 17 01 Positive margin for production 21539 w 7 m g 0 Production Stackelberg L 7 u 7 2o 7 u bul u 7 2y 7 u bnilquot m quot n 14 w u 7 L ml n 7 Pr 2h 2m AP 2 2u39 Marketing Stackelberg far 81 a i 2A wbm u A 2 a 61w L 7 141701 7A 7cLb Profit Loss Robustness of Contracts P 4 Percent profit loss when price sensitivity sensitivity is misestimated Price sensitivit b of 39 1 20 Coordination Mechanisms Solution o In orderto achieve coordination A A o Unique transfer price that coordinates production and marketing w l ProductionStackelberg MarketingStackelberg i 2E C f 2 11 1 1 to cum I Highertransfer price for ProductionStackelberg w gt mm 3910 l Fraction of profits realized by marketing MR t i r i gtl v r Tip G 1pc ltfpClt c i 11C39iiiC alrrc uip gt aim 2 Hip uiL JAE 2 111 nz alrrz 1r rm Special Cases Revenue Sharing Contract 0 s or s 1 a2 1 061 Coordination xi Transfer Priceonly Contract a1 1 a2 0 Coordination i Revenue Sharing Contract with no Transfer Price w0 Coordination X 39 21 or leadtime Leadtime sensitivity c a50b4cO4m5s095 a50b04c4m5s095 so 70 02 60 in 8 015 50 A E 40 9 n 01 30 o 20 005 2 4 6 8 10 Estimate of Price Sensitivity b Est 4 6 8 10 imate of Leadtime Sensitivity c 12 ID Underestimating price sensitivity b leads to higher profit loss than over estimating price sensitivity pro t loss ID Lower pro t loss as compared to It Medium capacities result in highest Capacity Decision e K unit capacity cost Minimum cost incurred per unit ofdemand mK Centralized Setting Ca 5LC AC cb m c Klc 51 yo i c c 2k Ilaill inn 1 max cch HOBO 39 2 Comparison of Settings with Capacity Decision e Optimal capacity under all settings Optimal generated demand plus an adjustment amount to meet the service level k 2 L Optimal leadtime under P and C are equal and satisfy CZLS 7 Ca 7 m KbL2 2chb 0 a Under P more demand is generated and higher capacity is required Positive profit may not be generated for high capacity cost Minimum averag cost per unit 171Pm 02 gt u A 7 A3 p 7 up m Kb2 gt o n 7 n quot1 NEW gt 0 39 2 Comparison of Settings with Capacity Decision M P is displayed until pro t hits zero 39 p 1 25 Comparison of Settings with Capacity Decision e Pro ts ProdStac lt MarStac lt Centralized o Optimal Capacity MarStac lt Centralized lt ProdStac s As Kincreases gtllt gtllt I PM increases while pp decreases I Marketing Stackelberg pro t approaches the centralized pro t e Dominance The rm still prefers MarketingStackelberg under decentralized setting especially at higher capacity costs I J Conclusions Decentralized setting I Lower prices longer leadtimes higher demand lower profits regardless of a dominant function within the firm I Leadtime and price independent of changes in price sensitivity and unit production cost respectively I Suboptimal performance by the revenue based incentive mechanism for marketing and communication failure I Misalignment of incentives mitigated through having marketing as the leader as in Li and Atkins 2002 9 Coordination achieved with transfer price contract with bonus payments a Under coordination I Higher capacity does not necessarily lead to charging higher for better service I Estimation errors in price sensitivity much costlier than those in leadtime sensitivity Georgia Tech H Milton Stewart School of Industrial and S stems En ineerin Centralized vs decentralized competition for price and leadtime sensitive demand by Pelin Pekgiin Paul M Griffin and PInar Keskinocak This research is supported in part by NSF grants DMl0093844 and DMI 0113881 Research Questions a Can decentralization be more profitable than centralization under competition If yes when I Both firms are centralized C C I Only one firm is centralized CD or D C l Both firms are decentralized DD oWhat is the impact of different market and firm characteristics on the price and lead time competition in the market II 7 29 Literature Review a Centralized firms Price and waiting time aggregated into a full pricequot Loch 1991 Armony and Haviv 2003 Chen and Wan 2003 Lederer and Li 1997 Cachon and Harker 2002 I Price andor waiting time as independent factors in customer demand Allen and Federgruen 2004ab Linear model with general waiting time distribution So 2000 Loglog model constant market size Li and Lee 1994 Ho and Zheng 2004 Besbes and Zeevi 2005 Utility model constant market size Tsay and Agrawal 2000 Boyaci and Ray 2003 Linear model market size independent of cross effects Decentralized firms Bhardwaj 2001 Mishra and Prasad 2005 Price and salesperson effort level Parlar and Weng 2006 Price and production quantity single period Balasubramanian and Bhardwaj 2004 Price and quality deterministic linear model constant market size McGuire and Staelin 1983 Price deterministic model Boyaci and Gallego 2004 Inventory and ll rate queuing with generic leadtime distrbution l Bernstein and Federgruen 2004 2006 Price and ll rate multiperiod 6 First work to consider price and leadtime competition within a quot quot 39 39 quot quot 39 in steadystate 39I an Model Assumptions a Constant capacity o MM1 queue Aim 9 Linear production costs m1 Service level constraint8 1 7 e W WI 2 m ML 2 k where AIn11 a o Linear demand function A71 11 7 bipa 101 ijpj yiij j 3 7 i i 17 2 B miiiet Own price Own leadtime 07 58 potential sensitivity sensitivity pnce Cross lead tim sensitivity sensmwty I 31 gt Model Assumptions o Total market size o Parameters L i nv n39 w Njh l 2 m J bi gt ip Ci gt Wm I o Positive demand assumption AiZGi biW CikiMigt0 jZS i 22172 quot Game Structure sum rms slmullanenusly mouse an organizational structure Organizalmnal strumures become common knuwzedge sel Marketing rm selecs a Bruce and men a non Mamean rst mu selecls selects a price and on 2 arms arm a men WINCth 4m lemme selects a resume rur nmn acts a lead for rm l Bum mms simultaneously announus their market and must demand is re Dnce and leadrhme decisions lame llzed 1 a Firm iProblem o Centralized Setting X ma 7121mL20 I l All39Ll39 2 Iquot o Decentralized Setting I Marketing lead I Marketing s Problem m a x I Production s Problem max RAKE020 silt Best response 1 7 nilAW er production follower 02ml plDAiD Pin ml ugt H Am 4101 19 3 I 39 1 Firm i Problem Best response v v 0 Given pjLj define Ai ai 5139ij M39ij Generated demand becomes M Ai bipi CiLi Optimal solution for both settings is given by the monopolistic firm results in Pekgun et al 2008 Observation Optimal pn39ces leadtimes generated demand and the optimal pro t under both centralized and decentralized settings increase in pj7Lj and in ija iij Duopoly 0 O G 6 Both firms simultaneously announce price and leadtime decisions to the market Equilibrium is reached when none of the firms has an incentive to deviate from its decisions Iterative procedure I Game is played starting at an initial solution until the subgame perfect Nash equilibrium is reached Iterative procedure converges to the unigue Nash equilibrium solution for the duopoly under an 338 39 Stage 1 Strategic Decisions Identical Firms 36 4 Four possible outcomes of Stage 1 2 Ca O D 2 D DaD o Under C C and DD symmetric solution for both firms 4r Under DD longer leadtimes lower prices larger demand than under C C 4 Under a hybrid scenario the C firm quotes higher prices and lower lead times than the D firm 37 1 Stage 1 Strategic Decisions Identical Firms a Under C D EXn1nn kl nl m1u1 0001 71 1 w MN u r o r no 4 a v44 H 4 llllllllll llllllll 10998 M 40393 35532 Observation Under a hybrid scenario the centralized rm does not always generate higher pro ts 39 1 Stage 1 Strategic Decisions Identical Firms v Percentage of customers firm j loses through leadtime competition Percentage of customers firm j loses through price competition C1C12 gt CiD12 D1C12 gt DiD12 Observation When price competition is more intense than leadtime competition a centralized organizational structure is dominant 38 39 I Effect of Capacity Identical Firms Profit 5 3 1 1 1800 1600 1400 1200 1000 33 00 400 CD1 J co2 200 5 15 25 35 45 55 65 75 85 95 u I Higher capacity does not always result in higher profits under competition even if it comes for free IA centralized structure dominates under high capacity 39 20 40 Effect of Production Cost Identical Firms low7 Profit Change over CC U 5 10 15 20 25 30 m 33 1 39y 2 39 it 20 I In CD quot0 bene ts while D loses from an increase in unit production cost I The gap increases as the production cost increases I 41 Effect of Production Cost Identical Firms high Profit Change over CC 0 5 10 15 20 25 30 m 5 22 v 39 u 20 I Even when the operating costs are high rms may bene t from D when the intensity of price competition is high 21 Stage 1 Strategic Decisions Nonidentical Firms If gtm ij12 i7 j L Percentage of customers firm j loses through leadtime competition V Percentage of customers firm j loses through price competition 3 C C12 gt 0 D12aD C12 gt D D12 Observation When price competition is more intense than leadtime competition a centralized organizational structure is dominant Stage 1 trategic Decisions Nonidentical Firms Firm 2 PComp gt LTComp Firm 1 PComp lt LTComp When gtm an QltM b2 C2 51 C1 l CC12 gt CD12 and D012 gtDD12 Firm 2 prefers C Firm 1 prefers c gt DC1gtQD gtDD 9 gt cc gt 032 co QC c cc gt90 gtco Observation The rm with a competitive advantage over the quoted prices can benefit from a decentralized structure in which case the competitor will prefer a entralized stucture I Effect of Capacity Nonidentical Firms low Firm 1 s3 1 v 239 2 25 Profit Change over CC Firm 2 Profit Change over CC Ogmwbmmuoo lDominant Structure is centralizatiOn for both rms High capacity rm bene ts more if competitor is decentralized Firm 1 Firm 2 I Effect of Capacity Nonidentical Firms high 5 Firm 1 lt3 3 7 39 1I2 25 Firm 2 Profit Change over cc Profit Change over CC CD1 39DD1 A I When intensity Of price competition increases both rms prefer a decentralized structure until increasing capacity becomes a disadvantage M1 Firm 1 Firm 2 25 40 D D 40 80 C D gt80 C C o 23


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