Pricing for Environmental Compliance in the Auto Industry | ISYE 6230, Study notes of Systems Engineering

Download Pricing for Environmental Compliance in the Auto Industry | ISYE 6230 and more Study notes Systems Engineering in PDF only on Docsity! Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 1 Pricing for Environmental Compliance in the Auto Industry Summer 2003 Julie L. Swann Regulations • Vehicles contribute to the environment • California Air Resource Board – 10% of all vehicles sold will be partial or full Zero- Emissions Vehicles (ZEV) • European Union – C02 emissions will be reduced by 25% between 1995 and 2008 • United States Congress – Minimum Corporate Average Fuel Economy (CAFE) standards Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 2 CAFE Background • Purpose • CAFE Target Values – 27.5 mpg for car, 20.7 mpg for truck – Truck rising to 22.2 by 2007 • Penalties • Debits/Credits Manufacturer’s Solution • Improve fuel efficiency of current vehicles • Develop electric and hybrid vehicles • Research alternative fuel sources • Problem: – Technologies fail – Standards change – Market demand shifts – Consumer preferences run counter to environmental standards Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 5 Current Decision Making Process • Steps – Determine volume needed to meet CAFE – Achieve volume through incentives • Goal: Comply with CAFE regulations • Missing Pieces – Demand/price relation not fully known – Testing calculation considered after the fact – Profit absent Model Formulation • Maximize Profitability • subject to: – CAFE target – Capacity – Testing Rules – Demand Curves – Min/Max Price and Volume • Variables: Volume/Price Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 6 Mathematical Model Variables: Vi Volume of vehicle i Pi Price of vehicle i Sets: I Set of all vehicles (each representing a configuration) E Set of all vehicle engines T Set of all vehicle transmissions A Set of all vehicle assembly types Input Parameters: Ti Test value for vehicle I: 1 indicates vehicle is tested, 0 otherwise Mi MPG of vehicle I Beta i Demand intercept for vehicle i alphai Demand multiplier for vehicle i Aik Vector of attributes; one value for each vehicle and each attribute (1..k) ce Capacity of engine e ct Capacity of transmission t ca Capacity of assembly type a M CAFE target value Ki Production cost for vehicle i maximize Profit ∑ ∈ − Ii iii KPV )(* subject to: CAFE constraint: ∑∑ ≤ ∈ i Ii i ii V Mm TV 1* Engine Capacity: ∑ = ≤ eAi ei iE cV : ∀ e ∈ E Transmission Capacity: ∑ = ≤ tAi ti iT cV : ∀ t ∈ T Assembly Capacity: a aAi i iA cV∑ = ≤ : ∀ a ∈ A Calc. Volume: iiii PV βα += ∀ i ∈ I Min/Max: ul iii vVv ≤≤ ∀ i ∈ I ul iii pPp ≤≤ ∀ i ∈ I + Testing Constraints Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 7 Visual CAFE • Tool for pricing and production decisions • Tracks top volume configurations • Allows user to adjust volume or price • Calculates profitability and CAFE compliance • Offers “Excel Solver” to optimize profitability of all vehicles simultaneously Optimal Pricing Estimated Profitability under CAFE $- $1,000 $2,000 $3,000 $4,000 $5,000 $6,000 $7,000 $8,000 $9,000 $10,000 20.5 20.9 21.3 21.7 22.1 22.5 22.9 CAFE Target P ro fi t ( 10 00 K ) Optimal Current Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 10 Discrete Choice Demand Models • Based on choice of customer from options • Model utility (or preference) • Uses product characteristics and importance of attribute • Estimate parameters and use to generate elasticities iii VU ε+= ikikiiiii xxxV βββ +++= ...2211 Logit Models • Assumes Weibull distribution for error terms (McFadden 1973) • Red Bus/Blue Bus (Independence of Irrelevant Alternatives) • Nested Multinomial Logit Model • Auto Applications (Berry et al 1998) Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 11 Segmented Choice Logit Model • Segments: for each pair of vehicles (i,j), customers choose i, j, or drop out of market • Input: diversion choices, own elasticities, base price and volume, and market elasticity • Output: parameters for utility functions for each segment Single Segment Example ) 1 (),( i buythat number ++ == ji i xx x jii ee eNPPQ ) 1 (),( j buythat number ++ == ji j xx x jij ee e NPPQ • Utilities and probability of a choice • Given prices and number in a segment, ∑ ∈ = Cj x x j i e e i )chosen is Pr(    −= −= jjjj iiii Px Px αβ αβ Julie L. Swann Using Flexible Pricing to Improve Supply Chain Performance 12 Single Segment Example • Elasticity definitions and previous equations • Given an overall price level of δ within a segment, 1 )1( ++ + = ∂ ∂ −= ji j xx x ii i i i i i ee eP Q P P Q E α 1 )1( ++ + = ∂ ∂ −= ji i xx x jj j j j j j ee eP Q P P Q E α iiiii PU εδαβ +−= )( Single Segment Example • Total demand and total elasticity for the segment are: • More algebra gives us: • 5 unknowns: N, Βi, Βj, αi, αj; 5 boxed equations ) 1 ( ++ + =+= ji ji xx xx jiT ee ee NQQQ 1=∂ ∂ −= δ δ δ T T T Q Q E )1)(( +++ + = jiji ji xxxx x jj x ii T eeee ePeP E αα