Determining order lead time for a supply chain using a probability distribution of order lead time

1. A computer-implemented method of determining a probability distribution to represent order lead time, comprising:

generating, using a computer, a plurality of probability distributions of order lead time options, each probability distribution of order lead time option associated with one of a plurality of categories;

identifying, using the computer, a category that corresponds to a supply chain comprising a plurality of nodes, the plurality of nodes comprising a starting node and an ending node that supplies a customer, the supply chain designating a path from the starting node to the ending node;

dividing, using the computer, the path into a plurality of order lead time segments;

selecting, using the computer, a probability distribution of order lead time option associated with the identified category as a probability distribution of order lead time of the supply chain, the probability distribution of order lead time describing order lead time at an ending node demand of the ending node; and

determining a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of ending node demand associated with an order lead time segment.

2. The method of claim 1 , further comprising:

associating the plurality of order lead time segments with the probability distribution of order lead time, each order lead time segment being associated with a corresponding order lead time range of the probability distribution of order lead time and wherein each demand percentage further describing a percentage of a total ending node demand associated with the corresponding order lead time segment.

3. The method of claim 1 , further comprising:

determining a demand percentage that corresponds with each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of a total ending node demand associated with the corresponding order lead time segment; and

calculating an inventory at each node of the plurality of nodes according to the demand percentages of the plurality of nodes.

4. The method of claim 1 , further comprising:

establishing a minimum offered lead time; and

modifying the probability distribution of order lead time to reflect the minimum offered lead time.

5. The method of claim 1 , further comprising:

establishing a minimum offered lead time;

identifying a most upstream stocking location in the supply chain such that the cumulative lead time from the stocking location to the ending node is less than the minimum offered lead time;

computing the expected percentage of demand at the ending node, using the order lead time distribution for which order lead time will be greater than the minimum offered lead time;

decrementing the demand at the ending node by this computed percentage; and

calculating a safety stock at the ending node using the decremented demand.

6. The method of claim 1 , further comprising:

establishing a maximum offered lead time; and

modifying the probability distribution of order lead time to reflect the maximum offered lead time.

7. The method of claim 1 , further comprising:

establishing a maximum offered lead time;

identifying a portion of ending node demand corresponding to an order lead time range greater than the maximum offered lead time; and

shifting the portion of ending node demand to the maximum offered lead time in order to modify the probability distribution of order lead time to reflect the maximum offered lead time.

8. The method of claim 1 , further comprising:

establishing a predicted change of ending node demand; and

modifying the probability distribution of order lead time to reflect the predicted change of ending node demand.

9. The method of claim 1 , further comprising generating the probability distribution of order lead time from an order lead time profile.

10. The method of claim 1 , wherein the plurality of categories categorize at least one of a plurality of customers, a plurality of products, a plurality of locations, and any combination of the preceding.

11. A system of determining a probability distribution to represent order lead time, comprising:

a database configured to store a plurality of probability distributions of order lead time options, each probability distribution of order lead time option associated with one of a plurality of categories; and

a computer system coupled with the database and configured to:

identify a category that corresponds to a supply chain comprising a plurality of nodes, the plurality of nodes comprising a starting node and an ending node that supplies a customer, the supply chain designating a path from the starting node to the ending node;

divide the path into a plurality of order lead time segments;

select a probability distribution of order lead time option associated with the identified category as a probability distribution of order lead time of the supply chain, the probability distribution of order lead time describing ending node demand of the ending node versus order lead time; and

determine a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of ending node demand associated with an order lead time segment.

12. The system of claim 11 , the computer system further configured to:

associate the plurality of order lead time segments with the probability of order lead time, each order lead time segment being associated with a corresponding order lead time range of the probability distribution of order lead time and wherein each demand percentage further describing a percentage of a total ending node demand associated with the corresponding order lead time segment.

13. The system of claim 11 , the computer system further configured to:

determine a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of a total ending node demand associated with the corresponding order lead time segment; and

calculate an inventory at each node of the plurality of nodes according to the demand percentages of the plurality of nodes.

14. The system of claim 11 , the computer system further configured to:

establish a minimum offered lead time; and

modify the probability distribution of order lead time to reflect the minimum offered lead time.

15. The system of claim 11 , the computer system further configured to:

establish a minimum offered lead time;

identify a portion of ending node demand corresponding to an order lead time range less than the minimum offered lead time; and

shift the portion of ending node demand to the minimum offered lead time in order to modify the probability distribution of order lead time to reflect the minimum offered lead time.

16. The system of claim 11 , the computer system further configured to:

establish a maximum offered lead time; and

modify the probability distribution of order lead time to reflect the maximum offered lead time.

17. The system of claim 11 , the computer system further configured to:

establish a maximum offered lead time;

identify a portion of ending node demand corresponding to an order lead time range greater than the maximum offered lead time; and

shift the portion of ending node demand to the maximum offered lead time in order to modify the probability distribution of order lead time to reflect the maximum offered lead time.

18. The system of claim 11 , the computer system further configured to:

establish a predicted change of ending node demand; and

modify the probability distribution of order lead time to reflect the predicted change of ending node demand.

19. The system of claim 11 , the computer system further configured to generate the probability distribution of order lead time from an order lead time profile.

20. The system of claim 11 , wherein the plurality of categories categorize at least one of a plurality of customers, a plurality of products, a plurality of locations, and any combination of the preceding.

21. A non-transitory computer-readable medium embodied with software for determining a probability distribution to represent order lead time, the software when executed using a computer is configured to:

generate a plurality of probability distributions of order lead time options, each probability distribution of order lead time option associated with one of a plurality of categories;

identify a category that corresponds to a supply chain comprising a plurality of nodes, the plurality of nodes comprising a starting node and an ending node that supplies a customer, the supply chain designating a path from the starting node to the ending node;

divide the path into a plurality of order lead time segments;

select a probability distribution of order lead time option associated with the identified category as a probability distribution of order lead time of the supply chain, the probability distribution of order lead time describing ending node demand of the ending node versus order lead time; and

determine a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of ending node demand associated with an order lead time segment.

22. The computer-readable medium of claim 21 , further configured to:

associate the plurality of order lead time segments with the probability distribution of order lead time, each order lead time segment being associated with a corresponding order lead time range of the probability distribution of order lead time and wherein each demand percentage further describing a percentage of a total ending node demand associated with the corresponding order lead time segment.

23. The computer-readable medium of claim 21 , further configured to:

determine a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of a total ending node demand associated with the corresponding order lead time segment; and

calculate an inventory at each node of the plurality of nodes according to the demand percentages of the plurality of nodes.

24. The computer-readable medium of claim 21 , further configured to:

establish a minimum offered lead time; and

modify the probability distribution of order lead time to reflect the minimum offered lead time.

25. The computer-readable medium of claim 17 , further configured to:

establish a minimum offered lead time;

identify a portion of ending node demand corresponding to an order lead time range less than the minimum offered lead time; and

shift the portion of ending node demand to the minimum offered lead time in order to modify the probability distribution of order lead time to reflect the minimum offered lead time.

26. The computer-readable medium of claim 21 , further configured to:

establish a maximum offered lead time; and

modify the probability distribution of order lead time to reflect the maximum offered lead time.

27. The computer-readable medium of claim 21 , further configured to:

establish a maximum offered lead time;

identify a portion of ending node demand corresponding to an order lead time range greater than the maximum offered lead time; and

shift the portion of ending node demand to the maximum offered lead time in order to modify the probability distribution of order lead time to reflect the maximum offered lead time.

28. The computer-readable medium of claim 21 , further configured to:

establish a predicted change of ending node demand; and

modify the probability distribution of order lead time to reflect the predicted change of ending node demand.

29. The computer-readable medium of claim 21 , further configured to generate the probability distribution of order lead time from an order lead time profile.

30. The computer-readable medium of claim 21 , wherein the plurality of categories categorize at least one of a plurality of customers, a plurality of products, a plurality of locations, and any combination of the preceding.

31. A system of determining a probability distribution to represent order lead time, comprising:

means for generating a plurality of probability distributions of order lead time options, each probability distribution of order lead time option associated with one of a plurality of categories;

means for identifying a category that corresponds to a supply chain comprising a plurality of nodes, the plurality of nodes comprising a starting node and an ending node that supplies a customer, the supply chain designating a path from the starting node to the ending node; and

means for selecting a probability distribution of order lead time option associated with the identified category as a probability distribution of order lead time of the supply chain, the probability distribution of order lead time describing ending node demand of the ending node versus order lead time; and

means for determining a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of ending node demand associated with an order lead time segment.

32. A method of determining a probability distribution to represent order lead time, comprising:

generating a plurality of probability distributions of order lead time options, each probability distribution of order lead time option associated with one of a plurality of categories;

identifying a category that corresponds to a supply chain comprising a plurality of nodes, the plurality of nodes comprising a starting node and an ending node that supplies a customer, the supply chain designating a path from the starting node to the ending node;

selecting a probability distribution of order lead time option associated with the identified category as a probability distribution of order lead time of the supply chain, the probability distribution of order lead time describing ending node demand of the ending node versus order lead time;

establishing a minimum offered lead time;

identifying a first portion of ending node demand corresponding to an order lead time range less than the minimum offered lead time;

shifting the first portion of ending node demand to the minimum offered lead time in order to modify the probability distribution of order lead time to reflect the minimum offered lead time;

establishing a maximum offered lead time;

identifying a second portion of ending node demand corresponding to an order lead time range greater than the maximum offered lead time;

shifting the second portion of ending node demand to the maximum offered lead time in order to modify the probability distribution of order lead time to reflect the maximum offered lead time;

establishing a predicted change of ending node demand;

modifying the probability distribution of order lead time to reflect the predicted change of ending node demand;

dividing the path into a plurality of order lead time segments;

associating the plurality of order lead time segments with the probability distribution of order lead time, each order lead time segment being associated with a corresponding order lead time range of the probability distribution of order lead time;

determining a demand percentage of each order lead time segment in accordance with the probability distribution of order lead time, each demand percentage describing a percentage of a total ending node demand associated with the corresponding order lead time segment; and

calculating an inventory at each node of the plurality of nodes according to the demand percentages of the plurality of nodes.