Method of selecting an optimum mix of resources to maximize an outcome while minimizing risk

• US 6,591,232 B1
• Filed: 08/31/1999
• Issued: 07/08/2003
• Est. Priority Date: 06/08/1999
• Status: Expired due to Fees

• Current Assignee: Sikorsky Aircraft Corporation (Martin Marietta Corporation)
• Original Assignee: Sikorsky Aircraft Corporation (Martin Marietta Corporation)
• Inventors: Kassapoglou, Christos
• Primary Examiner(s): Broda, Samuel
• Assistant Examiner(s): PHAN, THAI Q
• Application Number:
  US09/386,667
• Time in Patent Office: 1,407 Days
• Field of Search: 703/2, 703/7, 700/95, 700/96, 700/97, 700/99, 705/6, 705/7, 705/8, 705/9, 705/36
• US Class Current: 703/2
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G06Q 10/0635 Risk analysis of enterprise or organisation activities

Abstract

A method of selecting the optimum mix of resources for achieving an outcome while minimizing risk is presented. In one embodiment, the method is applied to selecting the optimum mix of manufacturing technologies and amount of use of each technology for fabricating a helicopter fuselage structure in order to minimize the recurring cost and keep the risk below a pre-selected value. The method involves selecting a plurality of resources which can be used to achieve the desired outcome. Determining an associated outcome for each resource. Establishing at least one target risk level for the desired outcome. Calculating an associated outcome and risk for a plurality of combinations of the resources at a plurality of percentage applications of each resource. Then determining an optimum mix of resources and percentage of application of each resource which maximizes the outcome while maintaining the risk below the at least one target risk level. The method can also be tailored to provide resource mixes which achieve a desired outcome over time.

Claims

1. A method of determining the optimum mixture of resources for achieving an outcome while maintaining the risk associated with achieving the outcome below a threshold, the method comprising the steps of:

selecting a plurality of resources which can be used to achieve a desired outcome;

determining an associated outcome for each resource;

establishing at least one target risk level for the desired outcome;

calculating an associated outcome and risk for a plurality of combinations of the resources at a plurality of percentage applications of each resource; and

determining an optimum mix of resources and percentage of application of each resource which maximizes the outcome while maintaining the risk below the at least one target risk level.

2. The method of claim 1 wherein the step of determining the associated outcome for each resource involves determining a mean and variance of distribution for the associated outcome.

3. The method of claim 1 further comprising the step of determining the maximum applicability of each resource, and wherein the step of determining the optimum mix of resources also involves maintaining use of each resource in the mix below the maximum applicability of that resource.

4. The method of claim 3 further comprising the step of determining the applicability of each resource from zero to its associated maximum applicability as a function of time.

5. The method of claim 1 further comprising the step of determining a range of probabilities that the outcome associated with the optimum mix will exceed a predetermined value for the same risk level.

6. The method of claim 5 further comprising the step of selecting a target optimum mix for a desired probability.

7. The method of claim 1 further comprising the steps of:

determining the required investment associated with using each resource and the applicability level of the resource as a function of time; and

determining the mix of resources which results in the lowest overall investment, and the mix of resources which results in the maximum outcome for each time period.

8. The method of claim 7 wherein the mix of resources which results in the maximum outcome for each time period is the mix which results in the maximum cost savings for the time period.

9. The method of claim 7 further comprising the steps of:

determining intermediate strategies between lowest investment strategy and the maximum outcome for each time period;

calculating an investment cost for each intermediate strategy;

determining the lowest cost to achieve an intermediate strategy;

ranking of strategies as a function of investment and associated outcome; and

selecting the desired strategy.

10. The method of claim 1 wherein the resources selected are manufacturing technologies for fabricating a helicopter fuselage and wherein the associated outcome is a cost savings associated with fabricating a portion of the helicopter fuselage using the manufacturing technology, and wherein the step of determining the associated cost savings for each manufacturing technology involves determining a mean and variance of cost savings over a baseline.

11. The method of claim 10 further comprising the step of determining the maximum applicability of each manufacturing technology, and wherein the step of determining the optimum mix of resources involves determining the optimum mix of manufacturing technologies to achieve the maximum cost savings while maintaining the risk associated with that optimum mix below the target level, and wherein the amount that each technology is used in the optimum mix is below the maximum applicability for that manufacturing technology.

12. A method of determining the optimum mixture of manufacturing technologies for fabricating at least one component of an aircraft which achieves a desirable cost savings at a desirable level of risk, the method comprising the steps of:

selecting a plurality of manufacturing technologies which are capable of producing the at least one component;

determining a cost associated with manufacturing the at least one component using each manufacturing technology;

establishing at least one target risk level for the component cost savings;

calculating an associated cost savings and risk for a plurality of combinations of manufacturing technologies and for varying amounts of application of each manufacturing technology; and

determining an optimum mix of manufacturing technologies and amount that each manufacturing technology is used which maximizes the cost savings while maintaining the risk below the at least one target risk level.

13. The method of claim 12 wherein the step of determining the cost associated with manufacturing the at least one component using each manufacturing technology involves determining a mean and variance of cost savings over a baseline.

14. The method of claim 12 further comprising the step of determining the maximum amount of the at least one component that each technology can fabricate, and wherein the step of determining the optimum mix of manufacturing technologies involves maintaining use of each manufacturing technology in the mix below the maximum amount for that manufacturing technology.

15. The method of claim 14 further comprising the step of determining the applicability of each manufacturing technology from zero to its associated maximum applicability as a function of time.

16. The method of claim 12 further comprising the step of determining a range of probabilities that the cost savings associated with the optimum mix will exceed a set value.

17. The method of claim 16 further comprising the step of selecting a target optimum mix for a desired probability.

18. The method of claim 12 further comprising the steps of:

determining the required investment associated with using each manufacturing technology and the applicability level of the manufacturing technology as a function of time; and

determining the mix of manufacturing technologies which results in the lowest overall investment, and the mix of manufacturing technologies which results in the maximum cost savings for each time period.

19. The method of claim 18 further comprising the steps of:

determining intermediate strategies for a series of time periods between lowest investment strategy and the maximum cost savings;

calculating an investment cost for each intermediate strategy at each time period;

determining the lowest cost to any intermediate strategy for each time period;

ranking of strategies as a function of investment and cost savings; and

selecting the desired strategy.

20. The method of claim 12 wherein the at least one component is a plurality of components and wherein the step of calculating an associated cost savings and risk is according to the following formula $C_s^{\left(i\right)}=\sum _{}^{}$

j=1N

xij

sij

 



(i=1,…



 



M)

subject to;

$\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>x_{\mathrm{ij}}^2<br><br>{\mathrm{\sigma <br><br>}}_{\mathrm{ij}}^2\le <br><br>{\mathrm{\alpha <br><br>}}^2,\text{\hspace{1em}<br><br>}<br><br>\left(i=1,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M\right)$ 

0≦

x_ij≦

1 $\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>x_{\mathrm{ij}}=1,\text{\hspace{1em}<br><br>}<br><br>\left(i=1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M\right),\text{\hspace{1em}<br><br>}<br><br>\mathrm{and}<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\alpha <br><br>}}^2=v/\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>d_i^2$

where i denotes the associated component, j denoted the manufacturing technology associated with producing component i, s_ij denotes the mean of the cost savings realized by applying the manufacturing technology j to the component i, x_ij denotes the percentage of component i that is manufactured using technology j, N is the total number of manufacturing technologies that are being considered to produce each component i, M is the total number of components, v is the target variance, α

² denotes the cost savings variance for all components, σ

_ij² denotes the variance of cost savings realized by applying technology j to component i, and d_i is the cost fraction of the entire aircraft that component i accounts for.

21. The method of claim 20 wherein the step of determining the optimum mix of manufacturing technologies and amount of each manufacturing technology is according to the following formula $C_s=\sum _{}^{}$

i=1M

di

∑

j=1N

xij

sij

where C_s is the cost savings and is maximized subject to the following equations $\underset{i=1}{\overset{M}{\sum <br><br>}}<br><br>d_i^2<br><br>\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>x_{\mathrm{ij}}^2<br><br>s_{\mathrm{ij}}^2\le <br><br>v$ 

0≦

x_ij≦

1,

and $\underset{j=1}{\overset{N}{\sum <br><br>}}<br><br>x_{\mathrm{ij}}=1,\text{\hspace{1em}<br><br>}<br><br>\left(i=1,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>M\right).$

22. A method of determining the optimum mixture of resources for achieving a maximum outcome while maintaining the risk associated with achieving the outcome below a threshold, the method comprising the steps of:

selecting a plurality of resources which can be used to achieve the desired outcome;

determining an associated mean and variance of distribution for each manufacturing technology;

establishing at least one target risk level for the outcome;

determining the maximum applicability of each resource as a function of time;

calculating an associated outcome and risk for a plurality of resource mixes and for varying amounts of usage for each resource;

determining an optimum mix of resources with an associated amount that each resource is used in the mix, where the optimum mix maximizes the outcome while maintaining the risk associated with the mix below the at least one target risk level and maintaining use of each resource in the mix below the maximum applicability of that resource;

determining a range of probabilities that the outcome associated with the optimum mix will exceed a predetermined value for the at least one target risk level;

selecting a target optimum mix based on a desired probability;

determining the required investment associated with using each resource and the applicability level of the resource as a function of time;

determining the mix of resources which results in the lowest overall investment, and the mix of resources which results in the maximum outcome for each time period;

determining intermediate resource mixes between the resource mix generating the lowest investment and the resource mix generating the maximum outcome;

calculating an investment cost for each intermediate resource mix;

determining the lowest cost to achieve an intermediate resource mix;

ranking the resource mixes as a function of investment and outcome; and

selecting a desired resource mix.

23. The method of claim 22 wherein the resources selected are manufacturing technologies for fabricating a portion of a helicopter fuselage and wherein the associated outcome is a cost savings associated with fabricating the portion of the helicopter fuselage using the manufacturing technology, and wherein the step of determining the associated cost savings for each manufacturing technology involves determining a mean and variance of cost savings over a baseline.