1Game Theory and Contracting Analysis for Price and Lead-time OptimizationISyE 6230 – Economic Decision Analysis II Pelin Pekgün03/13/2008H. Milton StewartH. Milton StewartSchool of Industrial and Systems EngineeringSchool of Industrial and Systems EngineeringCoordination of Marketing and Production for Price and Lead-time DecisionsbyPelin PekgünPaul Griffin and Pınar KeskinocakH. Milton StewartH. Milton StewartSchool of Industrial and Systems EngineeringSchool of Industrial and Systems EngineeringThis research is partially supported by NSF Career Award DMI-009384422IntroductionIntroductionCommon Incentives:Maximize RevenueMaximize VolumeMARKETING PRODUCTIONCommon Incentives:Minimize CostIncrease Operational Efficiency3Losing Sight of the Common ObjectiveI'm glad that the holeis not on our side!Source: Mumin Kurtulus34Karl Kempf - Intel Fellow and Director of Decision Technologies in Intel’s Technologyand Manufacturing Group:“I have lost count of the number of times the sales and marketing guys have made a price move on a particular product only to find 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)”5Nell 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 profitable business into the hotel.”46Research QuestionsResearch QuestionsWhat are the inefficiencies that result from the decentralization of price and lead-time decisions?Pricing → Marketing DepartmentLeadtime → Production DepartmentHow to align the incentives of production and marketing with the firm’s overall objectives? Optimal decisions and overall profitability?market characteristicsdecision-making sequences capacity7Literature ReviewLiterature ReviewDue date management literatureSteady-state, price and lead-time sensitive demand, uniform delivery time guarantees:Palaka, Erlebacher and Kropp (1998), So and Song (1998), Boyaci and Ray (2003), Ray and Jewkes (2004)All assume a centralized decision maker!Marketing/operations interfaceEliashberg and Steinberg (1993), Li and Atkins (2002), Chatterjee, Slotnick and Sobel (2002), Ho and Zheng(2004), Balasubramanian and Bhardwaj (2004), Golbasi and Wu (2005)First work to consider price and leadtimedecisions within the marketing/operations interface58Constant capacityM/M/1 queue with mean production rate (capacity), μand mean arrival rate, λ~D(p,L)Linear demand function:Model AssumptionsModel AssumptionsNo inventory holding or lateness penalty costs, only linear production costs (m)Service level constraint: (Percentage of orders filled on time: s)1-e-(μ-λ)L≥ s ⇔ (μ-λ)L ≥ k, where k = ln(1/1-s) Positive Demand Assumption: D(m,k/μ)=a-bm-ck/μ> 0D(p,L)=a-bp-cLQuoted priceQuoted lead-timeMarket potentialPrice sensitivityLead-time sensitivity9Centralized Setting ( Centralized Setting ( C C ))Optimal Solution:Special case of (Palaka et al., 1998) for the fixed capacity case with no WIP holding and no lateness penalty costs.pCUnit production costProblem: Maximize profits subject to the service level constraint0; 0max ( ) s.t. ( - )CCCCCCLCCacLmbLkλμλπλμλ≤≤ ≥−−=−≥****2***(2 )( )()/CCCCCCCkLamb ckpa cLbμλλμλ μλ=−−− − ==−−610Decentralized Setting ( Decentralized Setting ( PP) ) Production is the Stackelberg leader and marketing is the follower1. Production quotes lead-time s.t. service level constraint2. Marketing quotes the best price in response to the lead-timeBackward inductionMarketing:Problem: Maximize firm revenueOptimal decisionsas a function of lead-time :Production:Problem: Maximize firm profit s.t. service level constraintr : Incentive for production11Decentralized Setting ( Decentralized Setting ( P P ) ) --SolutionSolutionMaximize a convex function over a closed intervalOptimal solution lies in the boundaries)(28)2(2***21*PPPPPLcckaayLλλμμ=+−+−==Optimal solution:For a nontrivial optimal solution with positive profit, we need:price)(min m2capacity)(min 2**0≥−=⇔−+=>bcLapmbackbmPPμμ712Decentralized Setting ( Decentralized Setting ( MM))Production:Marketing:Problem: Solution: Problem: Solution: Marketing is the Stackelberg leader and production is the follower1. Marketing quotes price maximizing its revenue2. Production quotes the best lead-time in response to priceBackwards induction13Comparison of Decision Comparison of Decision --Making SequencesMaking SequencesOptimal decisions: where P: Production - Stackelberg Game (Prod-Stac)M : Marketing - Stackelberg Game (Mar-Stac)Optimality equations for demand: The optimal demand rate under the decentralized setting is independent of m and b regardless of the decision-making sequence!************ )( )( )( )(PMCPMCPMCPMCivLppiiiLLLiiiπππλλλ≥>≥>≤<≤<ckμ)λ)(μλackμ)μλ)(μλackμ)λ)(μλmba*M*M*P*P*C*C=−−=−−=−−−222(2(2(814Comparison of DecisionComparison of Decision--Making SequencesMaking SequencesDecentralized settingFirm better off if marketing is the leader, especially under tight capacity. Deviation from the centralized profit increases as the price sensitivity of the customers or the unit production cost gets higher When production is the leader, high capacity is required for approaching centralized profit.Higher capacity does not necessarily lead to higher profits for a decentralized firm.0 20 40 600102030405060a=50,b=4,c=4,m=5,s=0.95Capacity, μProfit, πC PM800 20 40 60 80050100150200a=50,b=2,c=4,m=5,s=0.95Capacity, μProfit, πC PM0 20 40 60 8005101520a=50,b=6,c=4,m=5,s=0.95Capacity, μProfit, πC PM15Comparison of Decision Comparison of Decision --Making SequencesMaking SequencesSensitivity of the optimal decisions to the problem parameters916Price vs. capacityPrice vs. capacityUnder C and M, higher prices are charged within a tight capacity interval to quote lower lead-times. As capacity increases, the firm decreases its prices to attract more customers.17Price vs. LeadPrice vs. Lead--time Sensitivity & Service Leveltime Sensitivity &