IEEM 341 Supply Chain Management Week 11 Risk-Pooling Dr. Lu 11-1
Impact of Aggregation on Safety Inventory Risk-pooling effect Models of aggregation Information centralization Specialization Product substitution Component commonality Postponement Improved forecast Quick response 11-2
Risk-Pooling var D i 2, i 1, 2,..., k E D i u, i 1, 2,..., k var k i 1 D i n 2 k var i 1 k i 1 D i E D i n nu 1 n u u var D i E D i u 11-3
Safety Stock Level W/O aggregation : ss z CSL k L With Aggregation : ss z CSL k L z CSL k L z CSL F S 1 CSL 11-4
Impact of Aggregation (Example 11.7) Car Dealer : 4 dealership locations (disaggregated) D = 25 cars; σ D= 5 cars; L = 2 weeks; desired CSL=0.90 What would the effect be on safety stock if the 4 outlets are consolidated into 1 large outlet (aggregated)? At each disaggregated outlet: For L = 2 weeks, σ L = 7.07 cars ss = F -1 s (CSL) x σ L = F -1 s (0.9) x 7.07 = 9.06 Each outlet must carry 9 cars as safety stock inventory, so safety inventory for the 4 outlets in total is (4)(9) = 36 cars 11-5
Impact of Aggregation (Example 11.7) One outlet (aggregated option): Expected demand per period for the aggregate demand = D 1 + D 2 + D 3 + D 4 = 25+25+25+25 = 100 cars/wk σ C = Sqrt(5 2 + 5 2 + 5 2 + 5 2 ) = 10 σ LC = σ DC Sqrt(L) = (10)Sqrt(2) = (10)(1.414) = 14.14 ss = F -1 s (CSL) x σ C L = F -1 s (0.9) x 14.14 =18.12 or about 18 cars 11-6
var Risk-Pooling var D i i 2, i 1, 2,..., k k i 1 E D i u i, i 1, 2,..., k D i k i 1 k i 1 i 2 2 i j i 2 2 i j k When ij 0, var i 1 D i cov D i, D j ij i j k i 1 i 2 k i 1 i 2 k i 1 i 11-7
Safety Inventory W and W/O Aggregation k W/O aggregation : ss z CSL L i 1 i k With Aggregation : ss z CSL L i 1 i 2 2 i j ij i j k Independent : ss z CSL L i 1 i 2 k z CSL L i 1 i z CSL F S 1 CSL 11-8
Table 11.3 Benefits of aggregation can be affected by: coefficient of variation of demand (higher cv yields greater reduction in safety inventory from centralization) If ρ does not equal 0 (demand is not completely independent), the impact of aggregation is not as great (Table 11.3) value of item (high value items provide more benefits from centralization) ρ 0 Safety inventory w/o aggregation 36.24 Safety stock with aggreation 18.12 0.2 0.4 36.24 36.24 22.92 26.88 0.6 36.24 30.32 0.8 36.24 33.41 1.0t 36.24 36.24 11-9
Discussion of Risk Pooling In case of independent stocking locations, we have square root law By aggregation, the safety stock can be reduced by square root of n Many e-commerce retailers attempt to take advantage of aggregation (Amazon) Aggregation has two major disadvantages: Increase in response time to customer order Increase in transportation cost to customer Some e-commerce firms (such as Amazon) have reduced aggregation to mitigate these disadvantages 11-10
Information Centralization Virtual aggregation Information system that allows access to current inventory records in all warehouses from each warehouse Most orders are filled from closest warehouse In case of a stockout, another warehouse can fill the order Better responsiveness, lower transportation cost, higher product availability with reduced safety inventory Examples: McMaster-Carr, Gap, Wal-Mart 11-11
Specialization Stock all items in each location or stock different items at different locations? Different products may have different demands in different locations (e.g., snow shovels) Centralize slow-moving products which typically have a high coefficient of variation (why) to achieve largest benefit of aggregation Leave fast-moving, low-value products closer to customers to provide faster service and save delivery cost 11-12
Value of Aggregation at Grainger (Table 11.4) Motors Cleaner Mean demand 20 1,000 SD of demand 40 100 Disaggregate cv 2 0.1 Value/Unit $500 $30 Disaggregate ss $105,600,000 $15,792,000 Aggregate cv 0.05 0.0025 Aggregate ss $2,632,000 $394,770 Holding Cost $25,742,000 $3,849,308 Saving Saving / Unit $7.74 $0.046 11-13
Product Substitution Substitution: use of one product to satisfy the demand for another product Manufacturer-driven one-way substitution Customer-driven two-way substitution If the cost difference is small, one should carry more higher-value components to substitute the shortage of lower-value product Joint management of inventories across substitutable products 11-14
Component Commonality Using common components in a variety of different products Can be an effective approach to exploit aggregation and reduce component inventories 11-15
Example 11.9 Evaluate the safety stock requirement for the following example. Suppose Dell is to produce 27 different PCs with three distinct components: processor, memory and hard drive. Monthly demands for each computer is independent and normally distributed variable with mean 5000, and standard deviation 3000. Suppose Dell is targeting 95% CSL Case 1: if Dell designs specific components for each PC resulting 3*27=81 components Common components: 3 processors, 3 memory and 3 hard drives to create 27 kinds of computers 11-16
Example 11.9: Value of Component Commonality 450000 400000 350000 300000 250000 200000 150000 100000 50000 0 1 2 3 4 5 6 7 8 9 SS 11-17
Postponement The ability of a supply chain to delay product differentiation or customization until closer to the time the product is sold Goal is to have common components in the supply chain for most of the push phase and move product differentiation as close to the pull phase as possible Examples: Dell, Benetton 11-18
Postponement Delay of product differentiation until closer to the time of the sale of the product All activities prior to product differentiation require aggregate forecasts more accurate than individual product forecasts Individual product forecasts are needed close to the time of sale demand is known with better accuracy (lower uncertainty) Results in a better match of supply and demand Higher profits, better match of supply and demand 11-19
Value of Postponement: Benetton For each color Mean demand = 1,000; SD = 500 For each garment Sale price = $50 Salvage value = $10 Production cost using Option 1 (long lead time) = $20 Production cost using Option 2 (uncolored thread) = $22 What is the value of postponement? Expected profit increases from $94,576 to $98,092 11-20
Value of Postponement with Dominant Product Color with dominant demand: Mean = 3,100, SD = 800 Other three colors: Mean = 300, SD = 200 Expected profit without postponement = $102,205 Expected profit with postponement = $99,872 11-21
Tailored Postponement: Benetton Produce Q 1 units for each color using Option 1 and Q A units (aggregate) using Option 2 Results: Q 1 = 800 Q A = 1,550 Profit = $104,603 Tailored postponement allows a firm to increase profits by postponing differentiation only for products with the most uncertain demand; products with more predictable demand are produced at lower cost without postponement 11-22
Tailored Sourcing A firm uses a combination of two supply sources One is lower cost but is unable to deal with uncertainty well The other is more flexible, and can therefore deal with uncertainty, but is higher cost The two sources must focus on different capabilities Depends on being able to have one source that faces very low uncertainty and can therefore reduce costs Increase profits, better match supply and demand 11-23
Tailored Sourcing Sourcing alternatives Low cost, long lead time supplier» Cost = $245, Lead time = 9 weeks High cost, short lead time supplier» Cost = $250, Lead time = 1 week 11-24
Tailored Sourcing Strategies Fraction of demand from Annual Profit overseas supplier 0% $37,250 50% $51,613 60% $53,027 100% $48,875 11-25
Tailored Sourcing: Multiple Sourcing Sites Characteristic Primary Site Secondary Site Manufacturing High Cost Flexibility High (Volume/Mix) Responsiveness High Low Low Low 11-26
Managerial Levers to Improve Supply Chain Profitability Obvious actions Increase salvage value of each unit Decrease the margin lost from a stockout Postponement Tailored sourcing Improved forecasting Quick response 11-27
Improved Forecasts Improved forecasts result in reduced uncertainty Less uncertainty (lower σ R ) results in either: Lower levels of safety inventory (and costs) for the same level of product availability, or Higher product availability for the same level of safety inventory, or Both lower levels of safety inventory and higher levels of product availability 11-28
Impact of Improving Forecasts (Example) Demand: Normally distributed with a mean of R = 350 and standard deviation of σ R = 100 Purchase price = $100 Retail price = $250 Disposal value = $85 Holding cost for season = $5 How many units should be ordered as σ R changes? 11-29
Impact of Improving Forecasts σ R O* Expected Expected Expected Overstock Understock Profit 150 526 186.7 8.6 $47,469 120 491 149.3 6.9 $48,476 90 456 112.0 5.2 $49,482 60 420 74.7 3.5 $50,488 30 385 37.3 1.7 $51,494 0 350 0 0 $52,500 11-30
Quick Response Set of actions taken by managers to reduce lead time Reduced lead time results in improved forecasts Typical example of quick response is multiple orders in one season for retail items (such as fashion clothing) For example, a buyer can usually make very accurate forecasts after the first week or two in a season Multiple orders are only possible if the lead time is reduced otherwise there wouldn t be enough time to get the later orders before the season ends Benefits: Lower order quantities less inventory, same product availability Less overstock Higher profits 11-31
Quick Response: Multiple Orders Per Season Ordering shawls at a department store Selling season = 14 weeks Cost per handbag = $40 Sale price = $150 Disposal price = $30 Holding cost = $2 per week Expected weekly demand = 20 SD of weekly demand = 15 11-32
Service Level Impact of Quick Response Single Order Order Size Ending Invent. Expect. Profit Initial Order Two Orders in Season OUL for 2 nd Order Average Total Order Ending Invent. Expect. Profit 0.96 378 97 $23,624 209 209 349 69 $26,590 0.94 367 86 $24,034 201 201 342 60 $27,085 0.91 355 73 $24,617 193 193 332 52 $27,154 0.87 343 66 $24,386 184 184 319 43 $26,944 0.81 329 55 $24,609 174 174 313 36 $27,413 0.75 317 41 $25,205 166 166 302 32 $26,916 11-33
Service Level Forecast Improves for Second Order (SD=3 Instead of 15) Single Order Order Size Ending Invent. Expect. Profit Initial Order Two Orders in Season OUL for 2 nd Order Average Total Order Ending Invent. Expect. Profit 0.96 378 96 $23,707 209 153 292 19 $27,007 0.94 367 84 $24,303 201 152 293 18 $27,371 0.91 355 76 $24,154 193 150 288 17 $26,946 0.87 343 63 $24,807 184 148 288 14 $27,583 0.81 329 52 $24,998 174 146 283 14 $27,162 0.75 317 44 $24,887 166 145 282 14 $27,268 11-34
Summary Risk pooling effect is discussed to reduce the safety inventory Several application is discussed, information centralized, substitution, common components, postponement, tailored sourcing Improved forecast Quick response 11-35