1The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 1Georgia Institute of TechnologySystems and Industrial Engineering DepartmentPaper PresentationThe Role of Production Lead Time and Demand Uncertainty in Marketing Durable GoodsBy: Aly Samy MegahedApril, 2008The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 2AgendaAgenda• Introduction• Literature Review• Model• Analysis and Results• Conclusions2The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 3Introduction and Literature ReviewThe Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 4Introduction and Motivation Consider a firm planning to introduce a new product in the market.  Given the production lead time, the production decision may be based on the expectations about the market demand.  E.g. Shrek 2 DVDs, Chinese cell phone and iPods. That might lead to excess inventory or excess shortage. Those goods might also be durable.3The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 5Introduction (Cont’d) In the traditional literature, production lead times in uncertain environments were neglected. Although they might crucial (determining capacities, infra structure, ...etc). Also, having durable goods was not studied in deep details. Although having them leads to a new market competition between new and used items. In this paper, the authors are dealing with both issues in an uncertain environment.The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 6Literature Review According to the authors: “Most of the literature do not consider both demand uncertainty and production lead time”. Some researchers as Van Mieghem and Dada (1999), and Ferguson and Koenigsberg (2007) studied similar problems. But according to the authors, they addressed more features as the existence of resale markets, and the ability to lease or sell the good to consumers. Kekre and Srinivasan 1990 and Kulp et al. 2004 addressed marketing issues, but the authors seem to develop a more integrative view of the firm.4ModelThe Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 8Model Overview and AssumptionsPeriod 1 Period 2Q1 Producedq1new+Q2 Producedq1usedq2newInv.Qiis quantity produced in period i.qinis amount of new products sold in period i. q2uis amount of used products sold in period 2.==+5The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 9Model Overview and Assumptions (Cont’d)Firm chooses level of production (Q1)Firm chooses quantity to market q1newFirm chooses Q2and then q2newDemand UncertaintyDemand certainty Demand certainty}Period 1Period 2Stage 1 Stage 2Stage 3Lead TimeThe Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 10Modeling Durability Products sold in Period 1 can be resold by the subsequent owner in the secondhand market in Period 2. Durability is captured through the parameter δ, 0<δ<1. If δ=1, the product does not deteriorate. If δ=0, the product is nondurable. In case of selling, used units compete against new units that the manufacturer sells. While, in the case of leasing, the old and new products still compete but the firm has control over both prices.6The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 11Modeling Demand System and Uncertainty Assume that customers’ valuation of owning new product per period is φ, φ ~U [0, α].Now, the following inverse demand system exists:r1new= α-q1new(new product in 1st period)r2new= α-q2new-δq2ued(new product in 2nd period)r2used = δ(α-q2new-q2used) (used product in 2nd period)Where rimis the product’s one period price in period i, for either used (u) or new (n) products. To model uncertainty, α can either be αHwith probability θ or αL with probability 1-θ.The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 12Using Backward Induction In order to derive a subgame-perfect equilibrium, the game is solved by backward induction.7The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 13Model ReviewFirm chooses level of production (Q1)Firm chooses quantity to market q1newFirm chooses Q2and then q2newDemand UncertaintyDemand certainty Demand certainty}Period 1Period 2Stage 1 Stage 2Stage 3Lead TimeThe Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 14Using Backward Induction (Cont’d) Start from Stage 3 in Period 2:  Required:Optimal production quantity (Q2*). Subject to:Q2>0αNo uncertainty in this stage.Inv.Inventory known from previous stageα8The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 15Using Backward Induction (Cont’d) Thus, the firm maximizes profit in Stage 3 (period 2):π3= r2new q2new–c Q2-k =(r2new–c) Q2+r2new Inv. - k (Since I+Q2=q2n)= (r2new–c)Q2+r2new(Q1-q1new)-kWhere k is the setup cost per production,C is the production cost per unit. Therefore best response Q2*can be obtained, as a function of Q1, q1newand q2new.The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 16Model ReviewFirm chooses level of production (Q1)Firm chooses quantity to market q1newFirm chooses Q2and then q2newDemand UncertaintyDemand certainty Demand certainty}Period 1Period 2Stage 1 Stage 2Stage 3Lead Time9The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 17Using Backward Induction (Cont’d) Now, move to stage 2 (period 1): Required:Optimal selling quantity (q1new*). Subject to:q1new<Q1αNo uncertainty in this stage.Obtained from previous step.Q2*The Role of Production Lead Time and Demand Uncertainty in Marketing Durable Goods 18Using Backward Induction (Cont’d) Thus, the firm maximizes profit in Stage 2 (period 1):π2= (r1new+ρr2used)q1new-h Inv.=(α-q1new+ ρδ(α-Q2*-I-q1new))q1new-h Inv.Where h is the holding cost per unit per period.And ρ is the discounted factor for used products. Therefore best response q2new*can be obtained, as a function of Q1and q1n.10The Role of