Domain-aware decomposition for supply chain master planning using linear programming
A system and method are disclosed for solving a supply chain planning problem modeled as a linear programming (LP) problem. Embodiments include receiving an LP problem representing a supply chain planning problem for a supply chain network comprising material buffers and resource buffers, partitioning the supply chain network at a complicating node into at least two supply chains sharing the complicating node, formulating a decomposed subproblem for each of the supply chains, calculating an effective dual based, at least in part, on a mathematical difference of at least two dual values calculated by solving the functional-based decomposed subproblems, and generating a globally-optimal LP solution to the LP problem using subgradient descent with the effective dual.
1. A system of solving a supply chain planning problem modeled as a linear programming (LP) problem, comprising:
a computer, comprising a processor and memory, the computer configured to:
receive an LP problem representing a supply chain planning problem for a supply chain network, the supply chain network comprising material buffers and resource buffers;
partition the supply chain network at a complicating node into at least two supply chains sharing the complicating node;
formulate a decomposed subproblem for each of the at least two supply chains;
generate a globally-optimal LP solution to the LP problem using subgradient descent with an effective dual by:
calculate the effective dual based, at least in part, on a mathematical difference of at least two dual values, each of the at least two dual values calculated by solving the functional-based decomposed subproblems;
combine solutions for the solved functional-based decomposed subproblems; and
repeating the calculate and combine steps until a stopping criteria is met indicating a threshold of infeasibility or a threshold suboptimality; and
generate a globally-optimal LP solution to the LP problem based on the stopping criteria indicating optimality of the combined solutions.
2. The system of claim 1 , wherein the computer is further configured to:
generate a supply chain graph by modeling the material buffers and resource buffers as nodes and consumption, production, or loading as weights on edges connecting the nodes; and
search for balanced supply chains using a maxflow.mincut technique.
3. The system of claim 2 , wherein the computer is further configured to:
in response to not detecting balanced supply chains using the maxflow.mincut technique, traverse the material buffers and resource buffers to locate the complicating node.
4. The system of claim 3 , wherein traverse the material buffers and resource buffers to locate the complicating node comprises moving from upstream nodes to downstream nodes in response to determining the supply chain network is divergent.
5. The system of claim 3 , wherein traverse the material buffers and resource buffers to locate the complicating node comprises moving from downstream nodes to upstream nodes in response to determining the supply chain network is convergent.
6. The system of claim 3 , wherein traverse the material buffers and resource buffers to locate the complicating node comprises moving from most connected nodes to least connected nodes.
7. The system of claim 3 , wherein the computer is further configured to:
update a learning rate and a value of the complicating node based, at least in part, on the calculated effective dual; and
solve the functional-based decomposed subproblems based, at least in part, on the updated learning rate and the updated value of the complicating node.
8. A computer-implemented method, comprising:
receiving an LP problem representing a supply chain planning problem for a supply chain network, the supply chain network comprising material buffers and resource buffers;
partitioning the supply chain network at a complicating node into at least two supply chains sharing the complicating node;
formulating a decomposed subproblem for each of the at least two supply chains;
generating a globally-optimal LP solution to the LP problem using subgradient descent with an effective dual by:
calculating the effective dual based, at least in part, on a mathematical difference of at least two dual values, each of the at least two dual values calculated by solving the functional-based decomposed subproblems;
combining solutions for the solved functional-based decomposed subproblems; and
repeating the calculating and combining steps until a stopping criteria is met indicating a threshold of infeasibility or a threshold suboptimality; and
generating a globally-optimal LP solution to the LP problem based on the stopping criteria indicating optimality of the combined solutions.
9. The method of claim 8 , further comprising:
generating a supply chain graph by modeling the material buffers and resource buffers as nodes and consumption, production, or loading as weights on edges connecting the nodes; and
searching for balanced supply chains using a maxflow.mincut technique.
10. The method of claim 9 , further comprising:
in response to not detecting balanced supply chains using the maxflow.mincut technique, traversing the material buffers and resource buffers to locate the complicating node.
11. The method of claim 10 , wherein traversing the material buffers and resource buffers to locate the complicating node comprises moving from upstream nodes to downstream nodes in response to determining the supply chain network is divergent.
12. The method of claim 10 , wherein traversing the material buffers and resource buffers to locate the complicating node comprises moving from downstream nodes to upstream nodes in response to determining the supply chain network is convergent.
13. The method of claim 10 , wherein traversing the material buffers and resource buffers to locate the complicating node comprises moving from most connected nodes to least connected nodes.
14. The method of claim 10 , further comprising:
updating a learning rate and a value of the complicating node based, at least in part, on the calculated effective dual; and
solving the functional-based decomposed subproblems based, at least in part, on the updated learning rate and the updated value of the complicating node.
15. A non-transitory computer-readable medium embodied with software, the software when executed:
receives an LP problem representing a supply chain planning problem for a supply chain network, the supply chain network comprising material buffers and resource buffers;
partitions the supply chain network at a complicating node into at least two supply chains sharing the complicating node;
formulates a decomposed subproblem for each of the at least two supply chains;
generates a globally-optimal LP solution to the LP problem using subgradient descent with an effective dual by:
calculates an effective dual based, at least in part, on a mathematical difference of at least two dual values, each of the at least two dual values calculated by solving the functional-based decomposed subproblems;
combines solutions for the solved functional-based decomposed subproblems; and
repeating the calculates and combines steps until a stopping criteria is met indicating a threshold of infeasibility or a threshold suboptimality; and
generates a globally-optimal LP solution to the LP problem based on the stopping criteria indicating optimality of the combined solutions.
16. The non-transitory computer-readable medium of claim 15 , wherein the software when executed further:
generates a supply chain graph by modeling the material buffers and resource buffers as nodes and consumption, production, or loading as weights on edges connecting the nodes; and
searches for balanced supply chains using a maxflow.mincut technique.
17. The non-transitory computer-readable medium of claim 16 , wherein the software when executed further:
in response to not detecting balanced supply chains using the maxflow.mincut technique, traverses the material buffers and resource buffers to locate the complicating node.
18. The non-transitory computer-readable medium of claim 17 , wherein traverses the material buffers and resource buffers to locate the complicating node comprises moving from upstream nodes to downstream nodes in response to determining the supply chain network is divergent.
19. The non-transitory computer-readable medium of claim 17 , wherein traverses the material buffers and resource buffers to locate the complicating node comprises moving from downstream nodes to upstream nodes in response to determining the supply chain network is convergent.
20. The non-transitory computer-readable medium of claim 17 , wherein traverses the material buffers and resource buffers to locate the complicating node comprises moving from most connected nodes to least connected nodes.