System and method for solving large scale supply chain planning problems with integer constraints
A system and method is disclosed for solving supply chain planning problems. The system includes a database that stores data representing a planning problem of a supply chain network and a computer that accesses the planning problem of the supply chain network stored in the database and models the planning problem as a network of nodes and edges. The computer further generates a hierarchical linear programming solution of the planning problem and applies advanced heuristics to the generated hierarchical linear programming solution. The computer still further formulates a mixed integer program to generate an optimized global hierarchical solution and stores the generated optimized global hierarchical solution in the database.
1. A system, comprising:
a computer having a processor and a non-transitory computer readable medium, configured to generate a supply chain model wherein one or more buffers are represented by nodes and one or more material operations are represented by edges that connect the nodes, the computer further configured to:
prioritize and model one or more business objectives as a hierarchy of objective functions and solve the hierarchy of objective functions by variable fixing; and
obtain an integer feasible solution of the hierarchy of objective functions by:
sorting the one or more buffers from downstream to upstream;
calculating a time bucket-wise consumption and production profile for one or more time buckets from downstream time bucket to upstream;
processing a lot size and a resource setup;
checking for material availability from upstream to downstream for the one or more buffers;
determining a material and resource feasible integer solution; and
determining a global hierarchical solution; and
causing one or more of the supply chain entities to perform the one or more material operations to produce the one or more products, based on the global hierarchical solution that satisfies a demand of the one or more supply chain entities.
2. The system of claim 1 , wherein determining the global hierarchical solution comprises:
generating a model by:
fixing integer variables according to the material and resource feasible integer solution and solving for the topmost objective function;
converting hierarchical objective functions to constraints by adding slack and surplus variables;
introducing integer variables and integer constraints and calculating values for all the objective functions;
assigning one or more deviation-based normalization coefficients;
assigning one or more hierarchy-based objective coefficients;
grouping objective violation variables; and
assigning one or more intra-group objective coefficients; and
solving the model as a mixed integer problem.
3. The system of claim 2 , wherein assigning hierarchy-based objective coefficients comprises:
calculating one or more objective coefficients as decreasing exponents of a fixed base; and
each of the one or more objective coefficients are a multiplication of a hierarchy coefficient and a normalization coefficient.
4. The system of claim 3 , further comprising:
sources of materials comprising one or more of raw materials, inventory, work-in-progress, purchase orders and future procurements from one or more supply chain entities, the source of materials are represented as one or more nodes not having any upstream nodes;
customer orders for the one or more products are represented as one or more nodes not having any downstream nodes;
planned manufacturing operations are represented by one or more nodes having one or more upstream nodes and one or more downstream nodes; and
one or more inputs and one or more outputs are represented by edges.
5. The system of claim 4 , wherein:
an edge between two buffer nodes represents processing of material and an edge between different time buckets for the same buffer represents inventory carried forward.
6. The system of claim 5 , wherein the demand is one or more operational objectives of the one or more supply chain entities and comprises one or more of demand, safety stock limits, minimizing inventory, reducing backlog, obtaining a particular product mix, maintaining proportionality, reducing use of alternate items, and optimizing profit.
7. A computer-implemented method comprising:
generating a supply chain model of a supply chain network wherein one or more buffers are represented by nodes and one or more material operations are represented by edges that connect the nodes;
prioritizing and modeling one or more business objectives as a hierarchy of objective functions and solve the hierarchy of objective functions by variable fixing; and
obtaining an integer feasible solution of the hierarchy of objective functions by:
sorting the one or more buffers from downstream to upstream;
calculating a time bucket-wise consumption and production profile for one or more time buckets from downstream time bucket to upstream;
processing a lot size and a resource setup;
checking for material availability from upstream to downstream for the one or more buffers;
determining a material and resource feasible integer solution; and
determining a global hierarchical solution; and
causing one or more of the supply chain entities to perform the one or more material operations to produce the one or more products, based on the global hierarchical solution that satisfies a demand of the one or more supply chain entities.
8. The computer-implemented method of claim 7 , wherein determining the global hierarchical solution comprises:
generating a model by:
fixing integer variables according to the material and resource feasible integer solution and solving for the topmost objective function;
converting hierarchical objective functions to constraints by adding slack and surplus variables;
introducing integer variables and integer constraints and calculating values for all the objective functions;
assigning one or more deviation-based normalization coefficients;
assigning one or more hierarchy-based objective coefficients;
grouping objective violation variables; and
assigning one or more intra-group objective coefficients; and
solving the model as a mixed integer problem.
9. The computer-implemented method of claim 8 , wherein assigning hierarchy-based objective coefficients comprises:
calculating one or more objective coefficients as decreasing exponents of a fixed base; and
each of the one or more objective coefficients are a multiplication of a hierarchy coefficient and a normalization coefficient.
10. The computer-implemented method of claim 9 , further comprising:
representing as one or more nodes not having any upstream nodes, sources of materials comprising one or more of raw materials, inventory, work-in-progress, purchase orders and future procurements from one or more supply chain entities;
representing as one or more nodes not having any downstream nodes, customer orders for the one or more products;
representing as one or more nodes having one or more upstream nodes and one or more downstream nodes, planned manufacturing operations; and
representing as edges, one or more inputs and one or more outputs.
11. The computer-implemented method of claim 10 , wherein:
representing as an edge between two buffer nodes, processing of material; and
representing as an edge between different time buckets for the same buffer, inventory carried forward.
12. The computer-implemented method of claim 11 , wherein the demand is one or more operational objectives of the one or more supply chain entities and comprises one or more of demand, safety stock limits, minimizing inventory, reducing backlog, obtaining a particular product mix, maintaining proportionality, reducing use of alternate items, and optimizing profit.
13. A non-transitory computer-readable medium embodied with software, the software when executed using one or more computers is configured to:
generate a supply chain model of a supply chain network wherein one or more buffers are represented by nodes and one or more material operations are represented by edges that connect the nodes;
prioritize and model one or more business objectives as a hierarchy of objective functions and solve the hierarchy of objective functions by variable fixing; and
obtain an integer feasible solution of the hierarchy of objective functions by:
sorting the one or more buffers from downstream to upstream;
calculating a time bucket-wise consumption and production profile for one or more time buckets from downstream time bucket to upstream;
processing a lot size and a resource setup;
checking for material availability from upstream to downstream for the one or more buffers;
determining a material and resource feasible integer solution; and
determining a global hierarchical solution; and
cause one or more of the supply chain entities to perform the one or more material operations to produce the one or more products, based on the global hierarchical solution that satisfies a demand of the one or more supply chain entities.
14. The non-transitory computer-readable medium of claim 13 , wherein obtaining the integer feasible solution of the hierarchy of objective functions comprises:
sorting the one or more buffers from downstream to upstream;
calculating the time bucket-wise consumption and production profiles for the one or more time buckets from downstream time bucket to upstream;
processing a lot size and a resource setup;
checking for material availability from upstream to downstream for the one or more buffers;
determining a material and resource feasible integer solution; and
determining the global hierarchical solution.
15. The non-transitory computer-readable medium of claim 14 , wherein determining the global hierarchical solution comprises:
generating a model by:
fixing integer variables according to the material and resource feasible integer solution and solving for the topmost objective function;
converting hierarchical objective functions to constraints by adding slack and surplus variables;
introducing integer variables and integer constraints and calculating values for all the objective functions;
assigning one or more deviation-based normalization coefficients;
assigning one or more hierarchy-based objective coefficients;
grouping objective violation variables; and
assigning one or more intra-group objective coefficients; and
solving the model as a mixed integer problem.
16. The non-transitory computer-readable medium of claim 15 , wherein assigning hierarchy-based objective coefficients comprises:
calculating one or more objective coefficients as decreasing exponents of a fixed base; and
each of the one or more objective coefficients are a multiplication of a hierarchy coefficient and a normalization coefficient.
17. The non-transitory computer-readable medium of claim 16 , wherein the software is further configured to:
represent one or more nodes not having any upstream nodes, sources of materials comprising one or more of raw materials, inventory, work-in-progress, purchase orders and future procurements from one or more supply chain entities;
represent as one or more nodes not having any downstream nodes, customer orders for the one or more products;
represent as one or more nodes having one or more upstream nodes and one or more downstream nodes, planned manufacturing operations; and
represent as edges, one or more inputs and one or more outputs.
18. The non-transitory computer-readable medium of claim 17 , wherein the software is further configured to:
represent as an edge between two buffer nodes, processing of material; and
represent as an edge between different time buckets for the same buffer, inventory carried forward.