Economic Decision Analy
Economic Decision Analy ISYE 6230
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Date Created: 11/02/15
Georgia l Tech l H Milton Stewart School of Industrial and Systems Engineering 7 Game Theory and I Contracting Analysis for Price and Leadtime l I Optimization ISyE 6230 Economic Decision Analysis Pelin Pekgun 02202007 Georgia ll Tech E H Milton Stewart School of Industrial and Systems Engineering Coordination of I Marketing and Production for Price L and Leadtime Decisions by Pelin Pengn Paul Griffin and Pinar Keskinocak This research is partially supported by NSF CareerAward DMI0093844 I I Introduction quotMARKETING PRODUCTION Common Incentives Common Incentives l1 Maximize Revenue I Minimize Cost l1 Maximize Volume I Increase Operational Ef ciency Losing Sight of the Common Objective I39m glad that the hole is not on our side Source Mumin Kurtulus 39 i l 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 historicall y 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 l l l Research Questions o 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 9 Optimal decisions and overall profitability I market characteristics I decisionmaking sequences I capacity 39 1 Literature Review a Due date management literature Steadystate price and leadtime sensitive demand uniform deliveLv 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 39L 1 Model Assumptions a Constant capacity MM1 queue with mean production rate capacity u and mean arrival rate lDpL Linear demand function DmLiabpCL Leadtime sensitivity QUOted pm Price sensitivity QUOted leadimeMarket potential 9 No inventory holding or lateness penalty costs only linear production costs m a Service level constraint Percentage of orders filled on time s 18 01397 2 s ltgt u lL 2 k where k ln11s a Positive Demand Assumption Dmkuabmckpgt 0 39 1 Centralized Setting C Problem Maximize profits subject to the service level constraint max 715C m Woks OSlcSIt CZO b Unit production st 41ch z k pC Cost Optimal Solution L L I Ac 6121 mbul2 cku p a Z cLZb Special case of Paaka et al 1998 for the xed capacity case With no WIP holding and no lateness penalty costs I Decentralized Setting P Production is the Slackelberg 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 Q Backward induction Market 9 Mn Problem Maximize rm revenue Plug W 17p 7017 39Lpl p o imaI unrieinne null 39PLi a e writ 7 UL gig xutmm as afunction of e leadtim Produc n 7Lrl Problem Maximize rm pro t m L v i st service level constraint Fr 39 quotV r r r 39 Incentive for producllon s H 7 AltLl1 k 39 I Decentralized Setting P Solution Maximize a convex function over a closed interval Optimal solution lies in the boundaries For a nontrivial optimal solution with positive pro t we need ck u gt no bm 7 mm capacity arzmb A a 1 1 arcL P 42quot mln nce PF 25 p a72u a 211280k Optimal solution lp Yip A 120 Decentralized Settin M Marketing is the Stackelberg leader and production is the ollower 1 Marketing quotes price maximizing its revenue 2 Production quotes the best leadtime in response to price ckwards induction Production m Problem It in um amid quotiw rim in 7 m 7 by 7 L r Li l Solution p m o hp it i I hp ti 1 46 quotJ 7 I 3 1pui V n V I il 7 lip 7 or 11 n Solution m7lzdirwm72bp 7m4 p39 uaxp fniup 39 39 Wu 7 up 701 Ha M 7 2m 7 39 Comparison of Decision Making Sequences 0 Optimal decisions In a 9x 11LCltLVI 1 mp gtp4 21 mag gt75 27 where P Production Stackelberg Game ProdStac M Marketing Stackelberg Game MarStac Optimality equations for demand km27279017 akt a72m7ycky a 7 2714 7 M ck t The optimal demand rate under the decentralized setting is independent of m and b regardless of the decisionmaking sequencel 39 I Companson of DecisionMaking Sequences sse meme s O H H 5 H 1 2 up w an Decenzrsnzed semng r Fmquot bener all M marketing Is the leader especral under ugh capacrn Dewanon mm the cennshzed pror moreases as the We sensmwzy oMe customers or Me unupmducnon cos gezs mgner x When produdron Is the leader mgn cspscny rs reqwed my sppmsemng cemrshzedpmm Higher capacrn does no necessaryy lead 0 mgner prams m s deeennsnzed Mm n I Companson of Decision Making Sequences a Sensmy uHhe upwwa demsmnsm me pysmem pavemetevs Price vs capacity Optimal price p customers t 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 39 11 Price vs Leadtime Sensitivity amp Service Level High Capacity Low Capacity Medium Capacity Decrease Increase Decrease Decrease C u amb3 amb3 lt u lt amb u 2 amb M ugaS a3ltulta p211 the customers un er leader 2 Capacity levels are de ned only by the production cost and price sensitivity of Q Higher capacity does not necessarily lead to charging higher for better service c Under medium capacity profits may increase in c on When marketing is the 39 13 Coordination Mechanisms Transfer price contract with bonus payments e For each unit produced marketing paysw to production a Bonus payment as a fraction of the total revenues generated 05 Marketing s share of revenue 1x2 Production s share of revenue a General model Ogalglandogangal Marketing s problem 1mm in mpx 7 u39la 7 bp 7 CL 3 Production s problem 1233 f39 7 quotM w 7 Inllu 7 lip 7 Li 51 it 7 u 7 bp 7 KL nL g l I 19 1 quot Coordination Mechanisms Solution 9 The minimum fraction of a The minimum transfer revenue that should be price39 offered to production wlum 1quotlti39 0 517411 7 7 i gyml1 J 7 17 1 Positive margin for production 0217 u39 7 m 5 U Production Stackelberg u 7 2 7 mm u 7 2 7 winmi M LF LP r l rL39 tl39h 7 r 7 a 24 J Marketing Stackelberg finlt 7 a 7 2A3 7 nibmm 7 A3112 51W L irirrfpgt u A 149 1 Coordination Mechanisms Solution In order to achieve coordination A A Unique transfer price that coordinates production and marketing wquot u ProductionStackelberg MarketingStackelberg n 739 aquot r u aim ll Higher transfer price for ProductionStackelberg WI gt mm 1F ll Fraction of pro ts realized by marketing rrrm39 mm 39rr p mu riilllll am 7 gm My 7 mm m 3 mm Special Cases Revenue Sharing Contract 0 g a g 1 a2 1 a Coordination l Transfer Priceonly Contract at 1 0120 Coordination l Revenue Sharing Contract with no Transfer Price w0 Coordination X I Robustness of Contracts P a Percent profit loss when price sensitivity or leadtime sensitivity is misestimated Price sensitivity b Leadtime sensitivity c 9 Underestimating p 39 9 lb Lower profit loss as compared to sensitivity b leads to higher price sensitivi P39Ofit loss than OVer ID Medium capacities result in highest estimating profit loss 39 Capacity Decision 0 K unit capacity cost a Minimum cost incurred per unit of demand mK Centralized Setting 770 7 5LC AC Cb mlc K c n 6 7 Acne 2 k Ml max 101 LC YHCgtZO m4 inn 4 H M arketin g r 4 A Capacityamp Marketing Capacity Price 00 Leadtime 39 u Comparison of Settings with Capacity Decision a Optimal capacity under all settings Optimal generated demand plus an adjustment amount to meet the service level f j H L 0 Optimal leadtime under P and C are equal and satisfy c2L3 7 00 7 m KbL2 21m 0 e Under P more demand is generated and higher capacity is required Positive profit may not be generated for high capacity cost Minimum average cost per unit 1 If It rm ix quot3 u A 7 AL 017pz 771Ibquot2 gt I I1Inlquoti u t O prsarsprevea mm pmm Ms 12m I n quotComparison of Settings with Capacity Decision s Proms ProdeStac lt Marsmac lt Centrahzed o Optrrnar Capacrty MareSIac lt Centrahzed ltProdeSIac As Krgcreases p rncreaseswmre pp decreases Marketmg e Stacke berg prom approachea me centrahzed prom Dormnance The rm suH prerers Marketmgestacketberg under decentrahzed settmg especrauy at mgher capacrty costs 39 Conclusuons a Decentralized setting I Lower prices longer leadtimes higher demand lower profits regardless of a dominant function within the firm Leadtime and price independent of changes in price sensitivity and unit production cost respectively 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 e Coordination achieved with transfer price contract with bonus payments 6 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 ll Tech M H Milton Stewart School of Industrial and Systems Engineering Centralized vs I decentralized competition for price and leadtime l I sensitive demand 7 by Pelin Pekgiin Paul M Griffin and Pinar Keskinocak This research is supported in part by NSF grants DMl0093844 and DMI 0113881 l as Research Questions a Can decentralization be more profitable than centralization under competition If yes when l Both firms are centralized CC I Only one firm is centralized CD or DC I Both firms are decentralized DD o What is the impact of different market and firm characteristics on the price and lead time competition in the market I 29 LL iteratu re Review Centralized firms l 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 l Price andor waiting time as independent factors in customer dem Allen and Federgruen 2004ab Linear model with general waiting time distribution I So 2000 Loglog model constant market size Li and Lee 1994 Ho and Zheng 2004 Besbes and Zeevi 2005 Utility model constant e 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 Bernstein and Federgruen 2004 2006 Price and ll rate multiperiod t First work to consider price and leadtime competition within a comparative centralized decentralized framework in steadystate 39 g 30 Model Assumptions 4 Constant capacity 4 MM1 queue MM 4 Linear production costs m7 4 Service level constraint 1 Percentage of orders filled on time 87 1 MquotiL i gt 87 if 7 A0197 2 6239 Where 7432 ln11 39 g 31 Model Assumptions 4 Linear demand function A2 az bz pi CiL7Ll ijpjszLj j 3 17 i 12 X Cross lead Base market Own price Own leadtime 5ng time 39 H I quot 39 sensitivit potentlal senSItIVIty senSItIVIty sensitivity y Total market size A1 A2 a1a2bl 21P1b2 612P2 01 721L1 C2 712L2 4 Parameters b gt j7 Cigtj 73172 39 g I 32 Firm iProblem Best response if Centralized Setting pic 8i 7 AiOLiC 2 k7 Decentralized Setting 1 Marketing leader production follower m Marketing s Problem maxpiDZmi piDAiD I Production s Problem max pp miD LiDpz DZO Z Z S39t39 Hi AiDLiDpiD 2 k i I 33 Firm iProblem Best response 439 Given pjLj define 14239 ai 5139ij quotliij Generated demand becomes A7 Az bill CiLz 4 Optimal solution for both settings is given by the monopolistic firm results in Pekgun et al 2006 Observation Optimal prices leadtimes generated demand and the optimal profit under both centralized and decentralized settings increase in pjLj and in ij ij 17 1IiZT Duopow Both rms simultaneously announce price and lead time decisions to the market Equilibrium is reached when none of the rms has an incentive to deviate from its decisions In a decentralized rm Marketing sets the price Production sets the leadtime Price and leadtime quotes are announced to the market Demand is realized v been 6 3 scenarios CC CD amp DC DD lterative procedure converges to the unique Nash equilibrium solution for the duopoly under all decision making scenarios 6 39 Duopow 4 Identical firms I Under CC and DD symmetric solution for firm 1amp2 l UnderCD ja 100 24 24 771 151 5095 1175 11 3 Firm 1 C Firm 2 D 3 108001 110998 2 40393 35532 Observation Under a hybrid scenario the centralized rm does not always generate higher pro ts Duopoly Comparison of Scenarios Mfg Z Percentage of customers firm j loses through price competition 3 CC12 gt CD12DC12 gt DD12 2 ij12 ij 7 gt Percentage of customers firm j loses through leadtime competition I Identical firms 3 62 OR 36 Observation When price competition is more intense than leadtime competition a centralized decision making strategy is dominant Duopoly Comparison of Scenarios Firm 1 PComp lt LTComp 4 When 2 I 3012 gt CD12 Firm 2 PComp gt LTComp gtm and C2 1621 2 721 3 Q 191 and D012 gtDD12 37 12 1 lt C1 I i rm 2 p re fe rs C Firm 1 prefers Observation The rm with a competitive advantage over the quoted prices can bene t from a decentralized strategy in which case the competitor will prefer a centralized strategy 312 712 Firm 1 Firm 2 2 1 QC1gt DC1gt QD1gt DD1 39 1 QC1gt CC1gtQD1gtCD1 D22 gt C92 DD2gt CD2 19 1 33 Effect of Capacity Identical Firms Profit 3 37 w 1 1800 1600 1400 1200 1000 5 15 25 35 45 55 65 75 85 95 p I Higher capacity does not always result in higher pro ts under competition even if it comes for free A centralized strategy dominates under high capacity Effect of Capacity 1 v 39 p2 25 F39 m 1 Firm 2 ll39 Profit Change over CC Profit Change over cc Osmwsmmum 5 15 25 35 45 55 65 75 85 95 5 25 45 65 85 105 1 1 l Dominant Strategy is centralization for both rms High capacity rm bene ts more if competitor is decentralized Firm 1 Firm 2 20 1 Effect ofCapacity 3 3 v 3 9 2 25 FIrm 1 Irm Profit Change over cc Profit Change over CC CD1 39 DD1 05 04 CD2 0339 cc2 02 01 0 1 20 40 60 80 0 I When intensity of price competition increases both rms prefer a decentralized strategy until increasing capacity becomes a disadvantage 25 40 D D 40 80 C D gt80 C C 1 L Effect of Production Cost Identical Firms Profit Change over CC ADD 15 m 20 25 30 3 1 39y 397 it 20 m In CD C bene ts while D loses from an increase in unit production cost I The gap increases as the production cost increases Effect of Production Cost Identical Firms Profit Change over CC U 5 10 15 20 25 30 m 5 2 2 n 39 H 20 1 Even when the operating costs are high rms may bene t from D when the intensity of price competition is high Conclusions 9 Competition on the basis of quoted price and leadtime in a common market e A decentralized decision making strategy I may be preferable when price competition is less intense than leadtime competition I may result in high loss of pro ts under high capacity high flexibility I may still be preferable under high production costs when the intensity of price competition is high but less effective than leadtime competition 22