Abstract: A system and method are disclosed including a computer that receives a formulation of a multi-objective linear programming planning problem, the formulation including at least one variable fixed at an upper bound or a lower bound. The computer also solves the formulation for a higher-order objective and fixes the upper bound or the lower bound of at least one variable to preserve a solution of the formulation for the higher-order objective. The computer also replaces at least one variable in the formulation with a value of the upper bound or the lower bound, when the upper bound of at least one variable is fixed at the lower bound or the lower bound of at least one variable is fixed at the upper bound, and checks whether replacing at least one variable with the value of the upper bound or the lower bound divides the formulation into two independent components.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method are disclosed including a computer that receives a formulation of a multi-objective linear programming planning problem, the formulation including at least one variable fixed at an upper bound or a lower bound. The computer also solves the formulation for a higher-order objective and fixes the upper bound or the lower bound of at least one variable to preserve a solution of the formulation for the higher-order objective. The computer also replaces at least one variable in the formulation with a value of the upper bound or the lower bound, when the upper bound of at least one variable is fixed at the lower bound or the lower bound of at least one variable is fixed at the upper bound, and checks whether replacing at least one variable with the value of the upper bound or the lower bound divides the formulation into two independent components.

Abstract: A system and method for a risk management visualization system comprises a computer having a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process, and display a visualization of a risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method for a risk management visualization system comprises a computer having a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process, and display a visualization of a risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method for efficiently determining the fair-share bands of a supply chain planning problem modeled as a multi-objective hierarchical linear programming problem include a processor and memory and are configured to model a supply chain planning problem as a multi-objective hierarchal linear programming problem, assign weights at each band of a fixed number of at least two bands, determine a direction of improved band values from a value of a Key Process Indicator (KPI) calculated from an expected demand and short quantities, wherein the expected demand and short quantities are calculated from the multi-objective hierarchical linear programming problem using a sample generated by Gibbs sampling of a conditional Gaussian Bayesian Network, and generate a supply chain plan.

Abstract: A system and method for efficiently determining the fair-share bands of a supply chain planning problem modeled as a multi-objective hierarchical linear programming problem include a processor and memory and are configured to model a supply chain planning problem as a multi-objective hierarchal linear programming problem, assign weights at each band of a fixed number of at least two bands, determine a direction of improved band values from a value of a Key Process Indicator (KPI) calculated from an expected demand and short quantities, wherein the expected demand and short quantities are calculated from the multi-objective hierarchical linear programming problem using a sample generated by Gibbs sampling of a conditional Gaussian Bayesian Network, and generate a supply chain plan.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: 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.

Abstract: A system and method are disclosed for solving a supply chain planning problem modeled as a linear programming (LP) problem. Embodiments include receiving a matrix formulation of at least a portion of the LP problem representing a supply chain planning problem for a supply chain network, generating an image based on the matrix formulation to identify connected components, partitioning the matrix formulation based, at least in part, on the connected components constraint into at least two partitions, formulating an LP subproblem from each of the at least two partitions, and solving the LP subproblems to generate a global solution to the supply chain planning problem.

Abstract: A system and method for a risk management visualization system having a computer comprising a processor and memory and configured to model a supply chain network as a supply chain planning problem, one or more key process indicators (KPIs) of the supply chain planning problem is based, at least in part, on the one or more input variables, model an impact on the one or more KPIs from each of the one or more input variables at a selected confidence interval using a Bayesian optimization process comprising an exploration phase and a learning phase, and display a visualization of the risk profile for the one or more KPIs, the visualization indicating a probability that an actual KPI value differs from a predicted KPI value.

Abstract: 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.

Abstract: A system and method are disclosed for solving a supply chain planning problem modeled as a linear programming (LP) problem. Embodiments include receiving a matrix formulation of at least a portion of the LP problem representing a supply chain planning problem for a supply chain network, generating an image based on the matrix formulation to identify connected components, partitioning the matrix formulation based, at least in part, on the connected components constraint into at least two partitions, formulating an LP subproblem from each of the at least two partitions, and solving the LP subproblems to generate a global solution to the supply chain planning problem.

Abstract: A system and method for efficiently determining the fair-share bands of a supply chain planning problem modeled as a multi-objective hierarchical linear programming problem include a processor and memory and are configured to model a supply chain planning problem as a multi-objective hierarchal linear programming problem, assign weights at each band of a fixed number of at least two bands, determine a direction of improved band values from a value of a Key Process Indicator (KPI) calculated from an expected demand and short quantities, wherein the expected demand and short quantities are calculated from the multi-objective hierarchical linear programming problem using a sample generated by Gibbs sampling of a conditional Gaussian Bayesian Network, and generate a supply chain plan.

Abstract: A system and method for efficiently determining the fair-share bands of a supply chain planning problem modeled as a multi-objective hierarchical linear programming problem include a processor and memory and are configured to model a supply chain planning problem as a multi-objective hierarchal linear programming problem, assign weights at each band of a fixed number of at least two bands, determine a direction of improved band values from a value of a Key Process Indicator (KPI) calculated from an expected demand and short quantities, wherein the expected demand and short quantities are calculated from the multi-objective hierarchical linear programming problem using a sample generated by Gibbs sampling of a conditional Gaussian Bayesian Network, and generate a supply chain plan.

Abstract: A system and method are disclosed for solving a supply chain planning problem modeled as a linear programming (LP) problem. Embodiments further include receiving a multi-period matrix formulation of a least a portion of an LP supply chain master planning problem representing a supply chain planning problem for a supply chain network and having a planning horizon divided into time buckets separated by time-bucket boundaries, mapping constraints of the LP supply chain master planning problem and variables of the LP supply chain master planning problem to the time buckets, calculating a quantity of cross-over variables for the constraints and the time buckets, selecting one or more decomposition boundaries from the time-bucket boundaries, and formulating at least two time-based decomposed subproblems by decomposing the LP supply chain master planning problem at the one or more decomposition boundaries.