Distribution-Independent Inventory Approach under Multiple Service Level Targets

1 . A system, comprising:

a supply chain entity comprising an inventory having one or more items; and

an inventory planner comprising a server and configured to:

model a supply chain planning problem as a Markov decision process (MDP);

solve the MDP;

generate a number of inventory policies for each item of the one or more items based, at least in part, on a global target;

select a first inventory policy of the generated inventory policies for each item of the one or more items wherein the average weighted target of the one or more items is at least equal to the global target; and

comparing the first inventory policy for at least one item and a current inventory level of the corresponding item to determine the difference between the current inventory level of the corresponding item and an inventory reorder point of the inventory policy; and

responsive to the difference between the current inventory level and the inventory reorder point of the inventory policy of the corresponding item, sending, by the inventory planner to automated machinery, instructions to cause the automated machinery to retrieve an amount of at least one item equal to an inventory target quantity minus the difference between the current inventory level and the inventory reorder point from a first location and to move the amount of the corresponding item to an inventory location of the corresponding item.

2 . The system of claim 1 , wherein the inventory planner uses a column generation technique to creates new inventory policies to improve a chosen objective function while meeting the global target.

3 . The system of claim 2 , wherein the inventory planner selects the inventory policy for each item of the one or more items by:

associating a total cost and service level with each inventory policy,

associating a weight with each item;

selecting inventory policies that minimize the total cost of all inventory policies that meet the global service level targets based, at least in part, on the weight associated with each item.

4 . The system of claim 3 , wherein the inventory planner generates one or more additional inventory policies for the one or more items using a policy generation model comprising a probabilistic flow linear programming formulation.

5 . The system of claim 4 , wherein the cost comprises one or more of inventory cost, order cost, and stockout cost.

6 . The system of claim 5 , wherein the weight is based, at least in part, on the expected demand of the item of the one or more items or a dual value for a target constraint.

7 . The system of claim 6 , wherein the number of inventory policies generated is based, at least in part, on a cost of an item, a target service level, or a predetermined total number of inventory policies.

8 . A method, comprising:

modeling a supply chain planning problem of a supply chain entity comprising an inventory having one or more items as a MDP;

solving the MDP;

generating a number of inventory policies for each item of the one or more items based, at least in part, on a global target;

selecting a first inventory policy of the generated inventory policies for each item of the one or more items wherein the average weighted target of the one or more items is at least equal to the global target;

comparing the first inventory policy for at least one item and a current inventory level of the corresponding item to determine the difference between the current inventory level of and an inventory reorder point of the inventory policy; and

responsive to the difference between the current inventory level and the inventory reorder point of the inventory policy of the corresponding item, sending to automated machinery instructions to cause the automated machinery to retrieve an amount of the corresponding item equal to an inventory target quantity minus the difference between the current inventory level and the inventory reorder point from a location and to move the amount of the item to a different inventory location.

9 . The method of claim 8 , further comprising:

creates new inventory policies using a column generation technique to improve a chosen objective function while meeting the global target.

10 . The method of claim 9 , wherein selecting the inventory policy for each item of the one or more items comprises:

associating a total cost and service level with each inventory policy,

associating a weight with each item;

selecting inventory policies that minimize the total cost of all inventory policies that meet the global service level targets based, at least in part, on the weight associated with each item.

11 . The method of claim 10 , further comprising:

generating one or more additional inventory policies for the one or more items using a policy generation model comprising a probabilistic flow linear programming formulation.

12 . The method of claim 11 , wherein the cost comprises one or more of inventory cost, order cost, and stockout cost.

13 . The method of claim 12 , wherein the weight is based, at least in part, on the expected demand of the item of the one or more items or a dual value for a target constraint.

14 . The method of claim 13 , wherein the number of inventory policies generated is based, at least in part, on a cost of an item, a target service level, or a predetermined total number of inventory policies.

15 . A non-transitory computer-readable medium embodied with software, the software when executed is configured to:

model a supply chain planning problem of a supply chain entity comprising an inventory having one or more items as a MDP;

solve the MDP;

generate a number of inventory policies for each item of the one or more items based, at least in part, on a global target;

select a first inventory policy of the generated inventory policies for each item of the one or more items wherein the average weighted target of the one or more items is at least equal to the global target;

compare the first inventory policy for at least one item and a current inventory level of the corresponding item to determine the difference between the current inventory level of the item and an inventory reorder point of the inventory policy; and

responsive to the difference between the current inventory level and the inventory reorder point of the inventory policy of the corresponding item, send to automated machinery instructions to cause the automated machinery to retrieve an amount of the item equal to an inventory target quantity minus the difference between the current inventory level and the inventory reorder point from a first location and to move the amount of the item to an inventory location of the corresponding item.

16 . The non-transitory computer-readable medium of claim 15 , wherein the software when executed is further configured to:

create new inventory policies using a column generation technique to improve a chosen objective function while meeting the global target.

17 . The non-transitory computer-readable medium of claim 16 , wherein the inventory policy for each item of the one or more items is selected by:

associating a total cost and service level with each inventory policy,

associating a weight with each item;

selecting inventory policies that minimize the total cost of all inventory policies that meet the global service level targets based, at least in part, on the weight associated with each item.

18 . The non-transitory computer-readable medium of claim 17 , wherein the software when executed is further configured to:

generate one or more additional inventory policies for the one or more items using a policy generation model comprising a probabilistic flow linear programming formulation.

19 . The non-transitory computer-readable medium of claim 18 , wherein the cost comprises one or more of inventory cost, order cost, and stockout cost.

20 . The non-transitory computer-readable medium of claim 19 , wherein the weight is based, at least in part, on the expected demand of the item of the one or more items or a dual value for a target constraint.