Valuing Lead Time. Valuing Lead Time. Prof. Suzanne de Treville. 13th Annual QRM Conference 1/24

Transcription

1 Valuing Lead Time Prof. Suzanne de Treville 13th Annual QRM Conference 1/24

2 How compelling is a 30% offshore cost differential? Comparing production to order to production to forecast with a long lead time Extended supply chain (offshoring) High utilization Large lot sizes Trading off lower-cost production for increased supply-chain risk Today s focus: quantifying the cost of the supply-demand mismatches that arise from increased exposure to demand volatility that comes from an increased lead time 2/24

3 OpLab at the University of Lausanne QRM Lead-time reduction Organizational implications of short lead times Real-options theory to quantify/price demand-volatility exposure Revenue-management opportunities that arise from short lead time Extreme value theory to include unusual events into supply-chain planning Working together with GSK Vaccines, Nissan Europe, Nestlé Switzerland 3/24

4 The context: A decision maker is placing an order for delivery on a given date A fashion item to be delivered for the spring season (high demand volatility, low residual value) A long-shelf-life product with moderate demand volatility and a 20% inventory-holding cost If it is possible to delay placing the order until right before delivery then full demand information will be available Placing the order far before the delivery date causes exposure to demand risk 4/24

5 Option-like Payoff Structure f(d) (P C)D (P C)Q CQ P Q D CQ 5/24

6 Traditional inventory theory: Lead time is taken as given The impact of lead time on forecast quality is not considered A demand density is assumed for the given lead time (typically a normal, uniform, or empirical distribution) We use the newsvendor model to balance overstock and understock costs service level that maximizes profits Managers have been observed to not have intuition about the demand density Normal-distribution assumption a low coefficient of variation (typically 30% or less) is assumed 6/24

7 Taking a financial-engineering perspective: Build our analysis around the demand forecast-evolution process rather than a given demand density Managers turn out to have excellent intuition about key elements of the forecast-evolution process This allows us to estimate how demand volatility and mismatch costs evolve in lead time Lead time becomes a decision variable 7/24

8 How does the forecast evolve? Four possibilities: No forecast evolution Constant information arrivals (constant instantaneous volatility) Brownian motion (normal marginal density) Geometric Brownian motion (lognormal marginal density) Clustered information arrivals (stochastic instantaneous volatility, lognormal marginal density) Jumps (affect the skewness and kurtosis of the marginal demand density) 8/24

9 Estimating volatility: Example from L Oréal Switzerland Consider a product with substantial supply-demand mismatches. Think about a demand value that is in the middle (50% chance demand will be higher or lower) Now think about an extreme value of demand. How many times higher will that extreme value be than the middle value? Answer: 2 How often would you expect that extreme? 2 weeks per year σ = ln(2)/φ 1 (1 2/50) 40% If price is normalized to 100, what would be the make-to-order cost and salvage value? 44, 10 9/24

10 Forecast evolution: Geometric Brownian motion Demand forecast Relative lead time 10/24

11 Marginal lognormal density for a relative lead time of t For a full relative lead time t = 1, log [D] N ( µ, σ 2) Let s break an order quantity Q = e µ+zσ into the product of median demand e µ and a multiplicative safety stock e zσ The actual-to-median ratio AM log [AM] N ( 0, σ 2) For lead times 0 t 1, log [AM] N ( 0, tσ 2) 11/24

12 How compelling is a 30% offshore cost reduction? We expect demand to be 3X the median 1 week out of 10 Demand distribution lognormal with a volatility of 0.86 (coefficient of variation of 1.04) for the full relative lead time (t = 1) Expected price $100, short-lead-time cost $44, long-lead-time cost $31, and salvage value $20 The newsvendor profit-maximizing order quantity is at the quantile that satisfies: = 0.70 (short lead time) = 0.86 (long lead time) 12/24

13 Lognormal demand density varying relative lead time /24 The relative lead time (service level) varies from 0.05 (0.7) to 0.3 (0.75) to 1.0 (0.863).

14 The cost-differential frontier What cost reduction is required to compensate for the increase in demand volatility exposure caused by lead time? Assumption: optimal conditions for the long-lead-time option (profit-maximizing order quantity, no supply risk, constant information arrival). What then happens as: Volatility increases? Residual value decreases? The order quantity exceeds that which maximizes profit? Relative lead time from 0 to 1 14/24

15 Case: Major global pharmaceutical producer Filling and packaging lead time averages 10 months (can be considerably longer) Most business in the form of tenders, usually awarded 2-4 months before delivery (type of jump) Probability of winning a tender 50% when production begins Short shelf life and minimal salvage value Two sources of demand uncertainty: Tenders and volatility 15/24

16 Assumptions Focus on the actual-to-forecast ratio Constant instantaneous volatility of 20% Markov jump term to capture tender loss ( jump to default model) Default intensity λ The probability of losing the tender given that we have not lost it so far is 1 e λ (RLT 0.2) for RLT 0.2, 0 for RLT < 0.2 We vary λ from 0 (no tender-loss risk) to /24

17 Cost Differential Frontier (%) λ = 0.8 λ = 0.5 λ = 0.2 No tender loss risk /24 Relative lead time

18 Result Brought lead time to the attention of top management Identified 2 key bottlenecks that were the primary cause of long lead time Cost of an 80% reduction in lead time estimated at less than 1 mm Covered many times over by the reduction in mismatch costs 18/24

19 Summary Pricing supply-chain mismatch costs motivates lead-time reduction Forecast evolution Constant information arrival flow Clustered information arrival flow Jumps Implications of forecast evolution for sustainability The break-even cost differential often increases at a decreasing rate Incremental lead-time reduction may be of limited value Fill rate vs profit-maximizing service level 19/24

20 Reshoring opportunities: Foundation: high volatility/high profit margin products with a short shelf life capacity buffer to be filled with standard products (revenue management) Allocate the cost of the capacity buffer to the high vola/high margin products Thus, revenue from the standard products only needs to cover variable cost Making these products completely competitive with low-cost suppliers (even if subsidized) QRM: reducing lead times for high vola/high margin products is surprisingly easy and cost effective 20/24

21 Wikipedia: 21/24

22 Sigma Coefficient Peak weekly demand of variation as a multiple of median demand Assumes 50 weeks a year z = Φ 1 ( ) = 2.05 The expected peak is e zσ 22/24

23 Computing the fill rate for a lognormal distribution log [D] N ( µ, σ 2) σ2 zσ For given z and σ: Fill rate = Φ(z σ) + e 2 (1 Φ(z)) 23/24

24 The impact of lead time on the actual-to-forecast distribution 24/24 Without forecast evolution, the demand distribution for a given period is the same irrespective of the time between order commitment and demand, hence the traditional inventory-theory assumption that if period demand follows a normal distribution N (µ, σ 2 ), then aggregated demand over 5 periods will follow a normal distribution N (5µ, 5σ 2 ) Vs. 1 period s demand in 5 periods under (constant instantaneous volatility) forecast evolution; not combining 5 days demand: The variance is linear in lead time five-fold increase in lead time N (µ, 5σ 2 ) The same applies when it is the log of the actual-to-forecast ratio that is normally distributed