The introduction of feedback into a hierarchical production planning system
Massachusetts Institute of Technology, Operations Research Center, 1980 - Business & Economics - 52 pages
This paper proposes and tests a framework for decomposing a large scale production planning problem, modeled as a mixed-integer linear program. We interpret this decomposition in the context of Hax and Meal's hierarchical framework for production planning. The procedure decomposes the production planning problem into two subproblems which correspond to the aggregate planning subproblem and a disaggregation subproblem in the Hax-Meal framework. The linking mechanism for these two subproblems is an inventory consistency relationship which is priced out by a set of Lagrange multipliers. The best values for the multipliers are found by an iterative procedure which may be interpreted as a feedback mechanism in the Hax-Meal framework. At each iterative, the procedure finds both a lower bound on the optimal value to the production planning problem and a feasible solution from which an upper bound is obtained. Our computational tests show that the best feasible solution found from this procedure is very close to optimal. For thirty-six test problems the percentage deviation from optimality never exceeds 4.4%, and the average percentage deviation is 2.2%. Twenty-seven of the test problems are mixed-integer linear programs with 240 zero-one variables, while nine test problems have 480 zero-one variables. (Author).
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240 zero-one variables aggregate planning subproblem aggregation scheme aq pxnon available regular best feasible solution bound for problem computational experience difference between best dual problem families aggregated family demand family disaggregation subproblem family setup costs forty families fourth problem set framework for decomposing given Hax and Meal Hax-Meal framework heuristic hierarchical approach initial inventory inventory holding costs iterative procedure jeT(i Lagrangean relaxation Lasdon and Terjung lower bound Massachusetts mixed-integer linear program moderate seasonality monolithic approach nine problems number of families objective function obtain Operations Research optimal solution value overtime costs Percentage difference period planning and scheduling planning horizon problem size problem to PPS product types production planning problem random draw relaxation to PPS Resource Utilization scheduling problem SECURITY CLASSIFICATION set of multipliers solution and lower solution to PPS subgradient procedure Terjung 12 three problem sets Type 1 Type Type demand type i family uniform distribution upper bound