Generating a supply chain plan

• US 7,672,862 B1
• Filed: 12/04/2001
• Issued: 03/02/2010
• Est. Priority Date: 04/02/2001
• Status: Active Grant

• Current Assignee: Blue Yonder Group, Inc. (Panasonic Holdings Corporation)
• Original Assignee: i2 Technologies US Incorporated (Panasonic Holdings Corporation)
• Inventors: Michael, David, Abraham, Manoj, Venkatasubramanyan, Narayan, Sheikhzadeh, Mehdi
• Primary Examiner(s): Sterrett; Jonathan G.
• Assistant Examiner(s): CHOI, PETER H
• Application Number:
  US10/004,725
• Time in Patent Office: 3,010 Days
• Field of Search: 705/7, 705/8
• US Class Current: 705/7.22
• CPC Class Codes: G06Q 10/06312 Adjustment or analysis of established resource schedule, e.g. resource or task levelling, or dynamic rescheduling
• CPC Class Codes: G06Q 10/08 Logistics, e.g. warehousing, loading or distribution; Inventory or stock management

Abstract

Generating a supply chain plan includes accessing data describing a supply chain network having buffers. Each buffer is operable to store items and is associated with a corresponding time variable. The supply chain network is constrained by a constraint. A linear programming problem is generated for the supply chain network. The linear programming problem is approximated by discretizing the time variables of the buffers to yield discretized time variables and by relaxing the constraint to yield a relaxed constraint. An optimized supply chain plan is calculated for the approximated linear programming problem. The optimized supply chain plan describes a quantity of items at each buffer for at least one time value of the corresponding time variable. The optimized supply chain plan is adjusted to satisfy the constraint.

Claims

1. A computer-implemented method of generating a supply chain plan and using the supply chain plan to generate an order plan, comprising:

accessing, by a server, data in a database describing a supply chain network comprising a plurality of buffers, each buffer configured to store a plurality of items and associated with a corresponding time variable, the supply chain network constrained by one or more constraints selected from the group consisting of a lead time constraint, a lot size constraint and a capacity constraint;

generating, by the server, a linear programming problem for the supply chain network;

approximating, by the server, the linear programming problem by discretizing the corresponding time variables of the buffers to yield a plurality of discretized corresponding time variables and by relaxing the one or more constraints to yield a relaxed constraint;

calculating, by the server, an optimized supply chain plan for the approximated linear programming problem, the optimized supply chain plan describing a quantity of items at each buffer for at least one time value of the corresponding time variable and including a list of producers configured to supply the items to each buffer; and

adjusting, by the server, the optimized supply chain plan to satisfy the one or more constraints, wherein adjusting the optimized supply chain plan comprises;

repeating the following until a last upstream buffer is reached;

selecting a buffer;

sorting the list of producers in order of preference according to the optimized supply chain plan and the amount of items across a time horizon that each producer may be able to supply;

selecting a producer from the list;

determining whether the producer selected is capable of producing all, some, or none of the quantity of items at the buffer;

adjusting one of (a) the quantity of items at the selected buffer, and (b) at least one time value of the corresponding time variable of the selected buffer, to satisfy the one or more constraints; and

proceeding to a next upstream buffer; and

repeating the following until a last downstream buffer is reached;

selecting a buffer;

determining whether there is a remaining quantity of items to be produced;

deciding whether to delay delivery or delay planning to the next buffer based on the determining whether there is a remaining quantity of items to be produced and delaying planning of the remaining quantity until a next buffer or delay delivery in accordance with the decision;

determining whether there is a next downstream buffer;

planning production to either (a) supply the items to the selected buffer at the adjusted time value, or (b) supply the adjusted quantity of items to the selected buffer; and

proceeding to a next downstream buffer; and

generating, by the server, an order plan by planning production to supply the quantity of items to each buffer according to the list of producers associated with the buffer.

2. The method of claim 1, wherein adjusting the optimized supply chain plan comprises adjusting at least one time value of a corresponding time variable of at least one buffer to satisfy the lead time constraint.

3. The method of claim 1, wherein adjusting the optimized supply chain plan comprises adjusting at least one time value of a corresponding time variable of at least one buffer to satisfy a feasible time constraint.

4. The method of claim 1, wherein adjusting the optimized supply chain plan comprises adjusting a quantity of items of at least one buffer to satisfy the lot size constraint.

5. The method of claim 1, wherein adjusting the optimized supply chain plan comprises adjusting a quantity of items of at least one buffer to satisfy the capacity constraint.

6. The method of claim 1, wherein generating the order plan comprises repeating the following until a last upstream buffer is reached:

selecting a buffer that requires a quantity of items;

planning production to supply the quantity of items to the selected buffer using at least some of the producers from the list of producers associated with the buffer; and

proceeding to a next upstream buffer.

7. The method of claim 1, wherein generating the order plan comprises repeating the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer;

planning production to supply at least some of the items to the buffer using the producer;

determining a remaining quantity of items required by the buffer; and

proceeding to a next producer on the list.

8. The method of claim 1, wherein generating the order plan comprises repeating the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer;

planning production to supply at least some of the quantity of items to the buffer using the producer;

proceeding to a next producer on the list if there is a next producer; and

planning production regardless of the list if there is no next producer.

9. The method of claim 1, wherein generating the order plan comprises repeating the following if a quantity of items cannot be supplied to a buffer by a deadline, until the quantity of items for the buffer is planned:

selecting a producer from the list of producers associated with the buffer, the producers configured to supply the items to the buffer after the deadline;

planning production to supply at least some of the quantity of items to the buffer using the selected producer; and

proceeding to a next producer on the list.

10. The method of claim 1, wherein generating the order plan comprises repeating the following if a quantity of items cannot be supplied to a buffer by a deadline, until the quantity of items for the buffer is planned:

selecting a supply time according to the list of producers associated with the buffer, the producers configured to supply the items to the buffer at one or more supply times after the deadline;

planning production to supply at least some of the quantity of items to the buffer using a producer configured to supply the items at the selected supply time; and

proceeding to a next supply time.

11. The method of claim 1, further comprising planning production and removing the selected producer from the list if it is determined that the selected producer is capable of producing all of the quantity of items at the buffer.

12. The method of claim 1, further comprising determining whether there is a next producer if it is determined that the selected producer is capable of producing none of the quantity of items at the buffer.

13. The method of claim 1, further comprising planning partial production and updating the quantity of items at the buffer to reflect a partial quantity provided by the selected producer if it is determined that the selected producer is capable of producing some of the quantity of items at the buffer.

14. The method of claim 1, further comprising, if it is determined that the selected producer is capable of producing some or none of the quantity of items at the buffer, performing the acts comprising:

determining whether there is a next producer on the list; and

if it is determined that there is a next producer on the list, selecting the next producer.

15. The method of claim 1, further comprising, if it is determined that the selected producer is capable of producing some or none of the quantity of items at the buffer, performing the acts comprising:

determining whether there is a next producer on the list wherein;

if it is determined that there is a not a next producer on the list, performing the acts comprising;

generating a list of producers that is sorted in order of preference and chronological order;

selecting a producer from the list;

planning production to satisfy one or more constraints using the selected producer; and

determining whether all items have been produced wherein;

if it is determined that all items have been produced, determining whether there is a next buffer; and

if it is determined that less than all items have been produced, determining whether there is a next producer on the list and performing the acts comprising;

 

selecting the next producer and determining whether there is a next buffer if it is determined that there is a next producer; and

 

determining whether there is a next buffer if it is determined that there is not a next producer on the list.

16. The method of claim 1, further comprising:

generating a list of producers that is sorted in order of preference and chronological order, the list describing the producers and supply times at which the producers may provide items to the buffer;

selecting a supply time from the list;

planning production to satisfy one or more constraints using a producer capable of supplying items at the selected supply time; and

determining whether all items have been produced wherein;

if it is determined that all items have been produced, determining whether there is a next buffer; and

if it is determined that less than all items have been produced, determining whether there is a next supply time on the list wherein;

if it is determined that there is a next supply time on the list, selecting a next supply time and determining whether there is a next buffer; and

if it is determined that there is not a next supply time on the list, determining whether there is a next buffer.

17. The method of claim 1, further comprising:

generating the order plan regardless of supply chain recommendations; and

determining whether there is a next buffer.

18. A system of generating a supply chain plan and using the supply chain plan to generate an order plan, comprising:

a database configured to store data describing a supply chain network comprising a plurality of buffers, each buffer configured to store a plurality of items and associated with a corresponding time variable, the supply chain network constrained by a one or more constraints selected from the group consisting of a lead time constraint, a lot size constraint and a capacity constraint;

a linear programming optimizer coupled with the database and configured to;

generate a linear programming problem for the supply chain network;

approximate the linear programming problem by discretizing the corresponding time variables of the buffers to yield a plurality of discretized corresponding time variables and by relaxing the one or more constraints to yield a relaxed constraint; and

calculate an optimized supply chain plan for the approximated linear programming problem, the optimized supply chain plan describing a quantity of items at each buffer for at least one time value of the corresponding time variable and including a list of producers configured to supply the items to each buffer; and

a heuristic solver coupled with the database and configured to adjust the optimized supply chain plan to satisfy the one or more constraints, wherein the heuristic solver is configured to adjust the optimized supply chain plan by;

repeating the following until a last upstream buffer is reached;

selecting a buffer;

sorting the list of producers in order of preference according to the optimized supply chain plan and the amount of items across a time horizon that each producer may be able to supply;

selecting a producer from the list;

determining whether the producer selected is capable of producing all, some, or none of the quantity of items at the buffer;

adjusting one of (a) the quantity of items at the selected buffer, and (b) at least one time value of the corresponding time variable of the selected buffer to satisfy the one or more constraints; and

proceeding to a next upstream buffer; and

repeating the following until a last downstream buffer is reached;

selecting a buffer;

determining whether there is a remaining quantity of items to be produced;

deciding whether to delay delivery or delay planning to the next buffer based on the determining whether there is a remaining quantity of items to be produced and delaying planning of the remaining quantity until a next buffer or delay delivery in accordance with the decision;

determining whether there is a next downstream buffer;

planning production to either (a) supply the items to the selected buffer at the adjusted time value, or (b) supply the adjusted quantity of items to the selected buffer; and

proceeding to a next downstream buffer; and

an order planner coupled with the database and configured to generate an order plan by planning production to supply the quantity of items to each buffer according to the list of producers associated with the buffer.

19. The system of claim 18, wherein the heuristic solver is configured to adjust the optimized supply chain plan by adjusting at least one time value of a corresponding time variable of at least one buffer to satisfy the lead time constraint.

20. The system of claim 18, wherein the heuristic solver is configured to adjust the optimized supply chain plan by adjusting at least one time value of a corresponding time variable of at least one buffer to satisfy a feasible time constraint.

21. The system of claim 18, wherein the heuristic solver is configured to adjust the optimized supply chain plan by adjusting a quantity of items of at least one buffer to satisfy the lot size constraint.

22. The system of claim 18, wherein the heuristic solver is configured to adjust the optimized supply chain plan by adjusting a quantity of items of at least one buffer to satisfy the capacity constraint.

23. The system of claim 18, wherein the order planner is configured to repeat the following until a last upstream buffer is reached:

selecting a buffer that requires a quantity of items;

planning production to supply the quantity of items using at least some of the producers from the list of producers associated with the buffer; and

proceeding to a next upstream buffer.

24. The system of claim 18, wherein the order planner is configured to repeat the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer;

planning production to supply at least some of the items to the buffer using the producer;

determining a remaining quantity of items required by the buffer; and

proceeding to a next producer on the list.

25. The system of claim 18, wherein the order planner is configured to repeat the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer;

planning production to supply at least some of the quantity of items to the buffer using the producer;

proceeding to a next producer on the list if there is a next producer; and

planning production regardless of the list if there is no next producer.

26. The system of claim 18, wherein the order planner is configured generate the order plan by repeating the following if a quantity of items cannot be supplied to a buffer by a deadline, until the quantity of items for the buffer is planned:

selecting a producer from the list of producers associated with the buffer, the producers configured to supply the items to the buffer after the deadline;

planning production to supply at least some of the quantity of items to the buffer using the selected producer; and

proceeding to a next producer on the list.

27. The system of claim 18, wherein the order planner is configured to generate the order plan by repeating the following if a quantity of items cannot be supplied to a buffer by a deadline, until the quantity of items for the buffer is planned:

selecting a supply time according to the list of producers associated with the buffer, the producers configured to supply the items to the buffer at one or more supply times after the deadline;

planning production to supply at least some of the quantity of items to the buffer using the producer configured to supply the items at the selected supply time; and

proceeding to a next supply time.

28. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan by planning production and removing the selected producer from the list if it is determined that the selected producer is capable of producing all of the quantity of items at the buffer.

29. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan by determining whether there is a next producer if it is determined that the selected producer is capable of producing none of the quantity of items at the buffer.

30. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan by planning partial production and updating the quantity of items at the buffer to reflect a partial quantity provided by the selected producer if it is determined that the selected producer is capable of producing some of the quantity of items at the buffer.

31. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan if it is determined that the selected producer is capable of producing some or none of the quantity of items at the buffer, by performing the acts comprising:

determining whether there is a next producer on the list; and

if it is determined that there is a next producer on the list, selecting the next producer.

32. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan if it is determined that the selected producer is capable of producing some or none of the quantity of items at the buffer, by performing the acts comprising:

determining whether there is a next producer on the list wherein;

if it is determined that there is a not a next producer on the list, performing the acts comprising;

generating a list of producers that is sorted in order of preference and chronological order;

selecting a producer from the list;

planning production to satisfy one or more constraints using the selected producer; and

determining whether all items have been produced wherein;

if it is determined that all items have been produced, determining whether there is a next buffer; and

if it is determined that less than all items have been produced, determining whether there is a next producer on the list and performing the acts comprising;

 

selecting the next producer and determining whether there is a next buffer if it is determined that there is a next producer; and

 

determining whether there is a next buffer if it is determined that there is not a next producer on the list.

33. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan by:

generating a list of producers that is sorted in order of preference and chronological order, the list describing the producers and supply times at which the producers may provide items to the buffer;

selecting a supply time from the list;

planning production to satisfy one or more constraints using a producer capable of supplying items at the selected supply time; and

determining whether all items have been produced wherein;

if it is determined that all items have been produced, determining whether there is a next buffer; and

if it is determined that less than all items have been produced, determining whether there is a next supply time on the list wherein;

if it is determined that there is a next supply time on the list, selecting a next supply time and determining whether there is a next buffer; and

if it is determined that there is not a next supply time on the list, determining whether there is a next buffer.

34. The system of claim 18, wherein the heuristic solver is further configured to adjust the optimized supply chain plan by:

generating the order plan regardless of supply chain recommendations; and

determining whether there is a next buffer.

35. Logic for generating a supply chain plan and using the supply chain plan to generate an order plan, the logic encoded in a computer-readable medium and when executed by a computer configured to:

access data describing a supply chain network comprising a plurality of buffers, each buffer configured to store a plurality of items and associated with a corresponding time variable, the supply chain network constrained by a one or more constraints selected from the group consisting of a lead time constraint, a lot size constraint, and a capacity constraint;

generate a linear programming problem for the supply chain network;

approximate the linear programming problem by discretizing the corresponding time variables of the buffers to yield a plurality of discretized corresponding time variables and by relaxing the one or more constraints to yield a relaxed constraint;

calculate an optimized supply chain plan for the approximated linear programming problem, the optimized supply chain plan describing a quantity of items at each buffer for at least one time value of the corresponding time variable and including a list of producers configured to supply the items to each buffer; and

adjust the optimized supply chain plan to satisfy the one or more constraints, the logic configured to adjust the optimized supply chain plan by;

repeating the following until a last upstream buffer is reached;

selecting a buffer;

sorting the list of producers in order of preference according to the optimized supply chain plan and the amount of items across a time horizon that each producer may be able to supply;

selecting a producer from the list;

determining whether the producer selected is capable of producing all, some, or none of the quantity of items at the buffer;

adjusting one of (a) the quantity of items at the selected buffer, and (b) at least one time value of the corresponding time variable of the selected buffer, to satisfy the constraint; and

proceeding to a next upstream buffer; and

repeating the following until a last downstream buffer is reached;

selecting a buffer;

determining whether there is a remaining quantity of items to be produced;

deciding whether to delay delivery or delay planning to the next buffer based on the determining whether there is a remaining quantity of items to be produced and delaying planning of the remaining quantity until a next buffer or delay delivery in accordance with the decision;

determining whether there is a next downstream buffer;

planning production to either (a) supply the items to the selected buffer at the adjusted time value, or (b) supply the adjusted quantity of items to the selected buffer; and

proceeding to a next downstream buffer; and

generate an order plan by planning production to supply the quantity of items to each buffer according to the list of producers associated with the buffer.

36. The logic of claim 35, the logic configured to adjust the optimized supply chain plan by adjusting at least one time value of a corresponding time variable of at least one buffer to satisfy the lead time constraint.

37. The logic of claim 35, the logic configured to adjust the optimized supply chain plan by adjusting at least one time value of a corresponding time variable of at least one buffer to satisfy a feasible time constraint.

38. The logic of claim 35, the logic configured to adjust the optimized supply chain plan by adjusting a quantity of items of at least one buffer to satisfy the lot size constraint.

39. The logic of claim 35, the logic configured to adjust the optimized supply chain plan by adjusting a quantity of items of at least one buffer to satisfy the capacity constraint.

40. The logic of claim 35, the logic configured to generate the order plan by repeating the following until a last upstream buffer is reached:

selecting a buffer that requires a quantity of items;

planning production to supply the quantity of items to the selected buffer using at least some of the producers from the list of producers associated with the buffer; and

proceeding to a next upstream buffer.

41. The logic of claim 35, the logic configured to generate the order plan by repeating the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer;

planning production to supply at least some of the items to the buffer using the producer;

determining a remaining quantity of items required by the buffer; and

proceeding to a next producer on the list.

42. The logic of claim 35, the logic configured to generate the order plan by repeating the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer;

planning production to supply at least some of the quantity of items to the buffer using the producer;

proceeding to a next producer on the list if there is a next producer; and

planning production regardless of the list if there is no next producer.

43. The logic of claim 35, the logic configured to generate the order plan by repeating the following if a quantity of items cannot be supplied to a buffer by a deadline, until the quantity of items for the buffer is planned:

selecting a producer from the list of producers associated with the buffer, the producers configured to supply the items to the buffer after the deadline;

planning production to supply at least some of the quantity of items to the buffer using the selected producer; and

proceeding to a next producer on the list.

44. The logic of claim 35, the logic configured to generate the order plan by repeating the following if a quantity of items cannot be supplied to a buffer by a deadline, until the quantity of items for the buffer is planned:

selecting a supply time according to the list of producers associated with the buffer, the producers configured to supply the items to the buffer at one or more supply times after the deadline;

planning production to supply at least some of the quantity of items to the buffer using a producer configured to supply the items at the selected supply time; and

proceeding to a next supply time.

45. The logic of claim 35, further configured to adjust the optimized supply chain plan by planning production and removing the selected producer from the list if it is determined that the selected producer is capable of producing all of the quantity of items at the buffer.

46. The logic of claim 35, further configured to adjust the optimized supply chain plan by determining whether there is a next producer if it is determined that the selected producer is capable of producing none of the quantity of items at the buffer.

47. The logic of claim 35, further configured to adjust the optimized supply chain plan by planning partial production and updating the quantity of items at the buffer to reflect a partial quantity provided by the selected producer if it is determined that the selected producer is capable of producing some of the quantity of items at the buffer.

48. The logic of claim 35, further configured to adjust the optimized supply chain plan if it is determined that the selected producer is capable of producing some or none of the quantity of items at the buffer, by performing the acts comprising:

determining whether there is a next producer on the list; and

if it is determined that there is a next producer on the list, selecting the next producer.

49. The logic of claim 35, further configured to adjust the optimized supply chain plan if it is determined that the selected producer is capable of producing some or none of the quantity of items at the buffer, by performing the acts comprising:

determining whether there is a next producer on the list wherein;

if it is determined that there is a not a next producer on the list, performing the acts comprising;

generating a list of producers that is sorted in order of preference and chronological order;

selecting a producer from the list;

planning production to satisfy one or more constraints using the selected producer; and

determining whether all items have been produced wherein;

if it is determined that all items have been produced, determining whether there is a next buffer; and

if it is determined that less than all items have been produced, determining whether there is a next producer on the list and performing the acts comprising;

 

selecting the next producer and determining whether there is a next buffer if it is determined that there is a next producer; and

 

determining whether there is a next buffer if it is determined that there is not a next producer on the list.

50. The logic of claim 35, further configured to adjust the optimized supply chain plan by:

generating a list of producers that is sorted in order of preference and chronological order, the list describing the producers and supply times at which the producers may provide items to the buffer;

selecting a supply time from the list;

planning production to satisfy one or more constraints using a producer capable of supplying items at the selected supply time; and

determining whether all items have been produced wherein;

if it is determined that all items have been produced, determining whether there is a next buffer; and

if it is determined that less than all items have been produced, determining whether there is a next supply time on the list wherein;

if it is determined that there is a next supply time on the list, selecting a next supply time and determining whether there is a next buffer; and

if it is determined that there is not a next supply time on the list, determining whether there is a next buffer.

51. The logic of claim 35, further configured to adjust the optimized supply chain plan by:

generating the order plan regardless of supply chain recommendations; and

determining whether there is a next buffer.

52. A system for generating a supply chain plan and using the supply chain plan to generate an order plan, comprising:

means for accessing data describing a supply chain network comprising a plurality of buffers, each buffer configured to store a plurality of items and associated with a corresponding time variable, the supply chain network constrained by a one or more constraints selected from the group consisting of a lead time constraint, a lot size constraint, and a capacity constraint;

means for generating a linear programming problem for the supply chain network;

means for approximating the linear programming problem by discretizing the corresponding time variables of the buffers to yield a plurality of discretized corresponding time variables and by relaxing the one or more constraints to yield a relaxed constraint;

means for calculating an optimized supply chain plan for the approximated linear programming problem, the optimized supply chain plan describing a quantity of items at each buffer for at least one time value of the corresponding time variable and including a list of producers configured to supply the items to each buffer; and

means for adjusting the optimized supply chain plan to satisfy the one or more constraints, wherein adjusting the optimized supply chain plan comprises;

repeating the following until a last upstream buffer is reached;

selecting a buffer;

sorting the list of producers in order of preference according to the optimized supply chain plan and the amount of items across a time horizon that each producer may be able to supply;

selecting a producer from the list;

determining whether the producer selected is capable of producing all, some, or none of the quantity of items at the buffer;

adjusting one of (a) the quantity of items at the selected buffer, and (b) at least one time value of the corresponding time variable of the selected buffer, to satisfy the constraint; and

proceeding to a next upstream buffer; and

repeating the following until a last downstream buffer is reached;

selecting a buffer;

determining whether there is a remaining quantity of items to be produced;

deciding whether to delay delivery or delay planning to the next buffer based on the determining whether there is a remaining quantity of items to be produced and delaying planning of the remaining quantity until a next buffer or delay delivery in accordance with the decision;

determining whether there is a next downstream buffer;

planning production to either (a) supply the items to the selected buffer at the adjusted time value, or (b) supply the adjusted quantity of items to the selected buffer; and

proceeding to a next downstream buffer; and

means for generating an order plan by planning production to supply the quantity of items to each buffer according to the list of producers associated with the buffer.

53. A computer-implemented method of generating a supply chain plan and using the supply chain plan to generate an order plan, comprising:

accessing, by a server, data in a database describing a supply chain network comprising a plurality of buffers, each buffer configured to store a plurality of items and associated with a corresponding time variable, the supply chain network constrained by a plurality of one or more constraints selected from the group consisting of a lead time constraint, a lot size constraint, and a capacity constraint;

generating, by the server, a linear programming problem for the supply chain network;

approximating, by the server, the linear programming problem by discretizing the corresponding time variables of the buffers to yield a plurality of discretized corresponding time variables and by relaxing the one or more constraints to yield a plurality of relaxed constraints;

calculating, by the server, an optimized supply chain plan for the approximated linear programming problem, the optimized supply chain plan describing a quantity of items at each buffer for at least one time value of the corresponding time variable and including a list of producers configured to supply the items to each buffer;

generating, by the server, an order plan by planning production to supply the quantity of items to each buffer according to the list of producers associated with the buffer; and

adjusting, by the server, the optimized supply chain plan to satisfy the one or more constraints, by repeating the following until a last upstream buffer is reached;

selecting a buffer, adjusting at least one time value of the corresponding time variable of the selected buffer to satisfy the lead time constraint, adjusting the quantity of items at the selected buffer to satisfy the lot size constraint, and proceeding to a next upstream buffer; and

repeating the following until a last downstream buffer is reached;

selecting a buffer, planning production to supply the adjusted quantity of items to the selected buffer at the adjusted time value, and proceeding to a next downstream buffer.

54. The method of claim 53, wherein generating the order plan comprises repeating the following until production to supply a quantity of items to a buffer is planned:

selecting a producer from the list of producers associated with the buffer, planning production to supply at least some of the items to the buffer using the producer, determining a remaining quantity of items required by the buffer, and proceeding to a next producer on the list.