Abstract: A method includes forming a working mixed integer linear program (MILP) from a given MILP for job allocation to allocate people to jobs at least by choosing a subset of variables from the MILP. Only person/job combinations that are deemed most valuable are chosen for the subset. The working MILP includes the chosen subset of variables but no other variables from the given MILP. The working MILP is solved to determine a solution. Using the solution, a special linear program is formed and solved to determine a price of each constraint relative to the solution. Using the prices, variables that are not in the working MILP are evaluated to determine any variables that can contribute to an improved solution. The variables evaluated as contributing to an improved solution are added to the working MILP. The working MILP with the added variables is solved. Apparatus and program products are also disclosed.

Abstract: A method includes forming a working mixed integer linear program (MILP) from a given MILP for job allocation to allocate people to jobs at least by choosing a subset of variables from the MILP. Only person/job combinations that are deemed most valuable are chosen for the subset. The working MILP includes the chosen subset of variables but no other variables from the given MILP. The working MILP is solved to determine a solution. Using the solution, a special linear program is formed and solved to determine a price of each constraint relative to the solution. Using the prices, variables that are not in the working MILP are evaluated to determine any variables that can contribute to an improved solution. The variables evaluated as contributing to an improved solution are added to the working MILP. The working MILP with the added variables is solved. Apparatus and program products are also disclosed.

Abstract: A method includes forming a working mixed integer linear program (MILP) from a given MILP at least by choosing a subset of variables from the MILP, wherein the working MILP includes the chosen subset of variables but no other variables from the given MILP. The working MILP is solved to determine a solution. Using the solution, a special linear program is formed and solved to determine a price of each constraint relative to the solution. Using the prices, variables that are not in the working MILP are evaluated to determine any variables that can contribute to an improved solution. The variables evaluated as contributing to an improved solution are added to the working MILP. The working MILP with the added variables is solved. Apparatus and program products are also disclosed.

Abstract: A method includes forming a working mixed integer linear program (MILP) from a given MILP at least by choosing a subset of variables from the MILP, wherein the working MILP includes the chosen subset of variables but no other variables from the given MILP. The working MILP is solved to determine a solution. Using the solution, a special linear program is formed and solved to determine a price of each constraint relative to the solution. Using the prices, variables that are not in the working MILP are evaluated to determine any variables that can contribute to an improved solution. The variables evaluated as contributing to an improved solution are added to the working MILP. The working MILP with the added variables is solved. Apparatus and program products are also disclosed.

Abstract: One or more processors determine a financial target for a plurality of business accounts across a plurality of product brands that are included in a business account level of an organizational hierarchy of a business organization. The organizational hierarchy includes a plurality of levels. One or more processors determine respective financial targets and quotas for a plurality of nodes included in a level of the organizational hierarchy. One or more processors determine respective financial targets for combinations of business accounts and product brands. The determination of the financial targets is based on a statistical model that is fitted at a middle level of the organizational hierarchy, and a risk-based stochastic optimization that is used to set financial targets and quotas at one or more levels of the organizational hierarchy.