We study the multi-product production planning problem. This problem consists of determining the quantity of product to manufacture over a number of time periods in order to minimize a cost function that is the sum of the inventory holding costs and backlogging of finished goods. The solution must satisfy capacity constraints of the resources and result in non-negative work-in-process inventory. Since this problem can become unmanaageably large and should account for random events that disrupt production over the time horizon, we use a parameterized hierarchical production management system. In this approach, we aggregate the time units, the machines, and the part types in order to reduce the size of the problem. After computing a solution for this aggregated problem, we solve the subproblems that correspond to the production of each group of machines in the first aggregate time period. Parameters in each subproblem divide the part family demand among the part types. In addition, we exploit the parallelism of this hierarchical approach by using parallel computation to solve the independent subproblems simultaneously. Thus, we develop a much-needed system that facilitates effective and efficient production planning for complex manufacturing systems.
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