| Abstract: | The methodology takes a sufficiently long time horizon and breaks the problem into two subproblems. The first subproblem is the long range planning model and the second the short run production scheduling model. The long range model is essentially a resource constrained model and has a linear programming formulation with a profit maximization objective function. The long range plan fixes the discretionary marketing variables, such as the selection of product line, and the timing and extent of promotional sales. It estimates manpower requirements and establishes the raw material procurement plans. Lagrange multipliers obtained in the long range model are then used in the short run production scheduling model. The scheduling algorithm, having a Lagrangian function for an objective, is the solution to an unconstrained maximization problem. This then reduces to one of sequential allocation of production facilities to products. The algorithm is being applied on a problem with five production lines, 126 products, 26 time periods and 32 raw material constraints. |
