impacts of the shape of the demand distribution on procurement risk mitigation april 29, 2011 poms...
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![Page 1: Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation April 29, 2011 POMS 22nd Annual Conference Anssi Käki and Ahti Salo School](https://reader035.vdocuments.us/reader035/viewer/2022062511/5518c0bc550346a61f8b5571/html5/thumbnails/1.jpg)
Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation
April 29, 2011POMS 22nd Annual Conference
Anssi Käki and Ahti SaloSchool of Science, Aalto University, Finland
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Motivation
• Growing mismatches between demand and supply expose companies to serious operational risks. (Hendricks & Singhal 2005)
• Strategies for mitigating procurement risks can be evaluated with stochastic models.
• Yet, these models are not used in practice. (Kouvelis et al. 2006, Tang 2006)
• We show that the models’ results of can be very sensitive to assumptions about uncertainties.
• Thus, the uncertainties must be well understood when deploying models.
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Motivation
• How many components are needed, if demand planners state that ”our demand forecast is 10 000, with a variation of 5 000 items”?
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
0.5
1
1.5
2
2.5
3
3.5x 10
-4
Demand
f(x)
Probability mass functions
D1
D2
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Contents
• We study the capacity reservation option model of Cachon & Larivere (2003).
• We illustrate how the optimal procurement strategy depends on the shape of demand distribution.
• Our results suggest that inaccurate assumptions about uncertainties may lead to non-optimal behaviour.
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Capacity reservation option
• A component is procured from a single supplier.• The demand for the component is uncertain.• In the one-period model, at t=0 the manufacturer can:
– Make firm commitments m – Reserve capacity o.
• The component demand d is realized; the manufacturer then decides how much to execute e, restricted by the reserved capacity o. Thus, the total order is m+e ≤ m+o.
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Capacity reservation option
• Expected sales for capacity K
• Manufacturer’s profit for revenue r and prices wm, wo, we
• We set wm = $1.0, wo = $0.2, we = $0.9 and r = $2.0.
• Optimal strategy can be derived via maximization of (m,o)
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Example with bimodal demand
Product one: the expected sales is 10 000 and sales from 8 000 to 13 000 cover around 50% of probability mass.
Product two: one monopolistic customer accounts for approximately 2/3 of sales. The remaining sales comes from small customers. Expected sales is, again, 10 000.
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
1
2
3
x 10-4
f(x)
Demand
Probability mass functions
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Demand
F(x
)
Cumulative probability functions
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
1
2
3
x 10-4
Demand
f(x)
Probability mass functions
D1
D2
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Demand
F(x
)
Cumulative probability functions
D1
D2
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Example with bimodal demand
• Optimal strategies can be determined with numeric integration.
• Even if the optimal profits are identical, strategies differ significantly.
Demand m* o* m*+o* *
Product one
5 910 7 190 13 100 $8 250
Product two
4 440 10 810 15 250 $8 250
Difference +33% -33% -14% 0%
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
DemandF
(x)
Cumulative probability functions
D1
D2
*1m*
2m
*2
*2 om
*1
*1 om
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Two products and a common component
• A common component of two products with dependencies:❶ Substitute products, such as comparable devices for the same market area.
Demands are likely to be negatively dependent.
❷ Differentiated products for different market segments. There are no demand dependencies.
❸ Complementary products, such as a one device launched separately for two different market areas. Demands are likely to be positively dependent.
❸❷❶
Example samples from joint distributions of two product demands
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Two products and a common component
• The optimal strategies and corresponding profits determined with a stochastic optimization model
• For complementary products, the distribution is wider and has heavier right-tail. The option is utilized more.
• Still, the demand fulfilled is on average 3% less it is optimal to prepare for the ”fat-tail”, but the resulting expected profit is lower.
Product type m* o* m*+o* *
Substitute 15 460 8 130 23 590 $18 180
Differentiated 13 880 10 620 24 500 $17 430
Complementary 12 970 12 460 25 430 $16 940
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Practical implications
0 5000 10000 15000 200000%
25%
50%
75%
100%
Fixed orders (m)
Pro
fit v
s. O
ptim
al p
rofit
Profit without option
Product one (unimodal)Product two (bimodal)
• How many components are needed, if demand planners state that the demand forecast is 10 000 5 000 items?
• If there is no flexibility (such as the capacity reservation option), the profit can be significantly less.
![Page 12: Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation April 29, 2011 POMS 22nd Annual Conference Anssi Käki and Ahti Salo School](https://reader035.vdocuments.us/reader035/viewer/2022062511/5518c0bc550346a61f8b5571/html5/thumbnails/12.jpg)
0
10000
200000
10000
20000
-25%
0%
25%
50%
75%
100%
Firm commitments
Profit with option, bimodal product demand
Option reservations
Pro
fit v
s. O
ptim
al p
rofit
Practical implications
• If there is a flexible alternative (the option in our case), the profit can still drop remarkably.
For example, setting arbitrarily m=8 000, o=4 000 would yield 23% less profits compared to the optimal.
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Conclusions
• When evaluating/implementing procurement approaches, careful analysis of uncertainties is essential.
• We have illustrated how the optimal procurement strategy is dependent on:– Demand distribution width and ”fat-tails”– Demand distribution modality– Demand-dependencies between two products that share a
common component.
• Our future work will discuss how copula-based scenarios can be used to address more complex uncertainties, such as several products and uncertainty in supply.
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Thank you!
Cachon, G. P. and Lariviere, M. A. (2001). Contracting to assure supply: How to share demand forecasts in a supply chain. Management Science, 47(5):629-646.
Hendricks, K. B. and Singhal, V. R. (2005). Association between supply chain glitches and operating performance. Management Science, 51(5):695-711.
Kouvelis, P., Chambers, C., and Wang, H. (2006). Supply chain management research and Production and Operations Management: Review, trends, and opportunities. Production and Operations Management, 15(3):449-469.
Käki, A. and Salo, A. (2011). Impacts of the Shape of the Demand Distribution on Procurement Risk Mitigation. Proceedings of 22nd Annual POMS Conference. Available at: http://www.pomsmeetings.org/ConfPapers/020/020-0741.pdf
Tang, C. S. (2006). Review: Perspectives in supply chain risk management. International Journal of Production Economics, 103:451-488.
References