Using Lagrangean Techniques to Solve Hierarchical Production Planning Problems

This paper proposes and tests a procedure 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...

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Bibliographic Details
Published in:Management science Vol. 28; no. 3; pp. 260 - 275
Main Author: Graves, Stephen C
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.03.1982
Institute of Management Sciences
Institute for Operations Research and the Management Sciences
Series:Management Science
Subjects:
Aggregation
Batch processing
Capital costs
Carrying costs
Costs
Decision making
Decomposition
Feedback
Heuristics
hierarchical production planning
Hierarchies
Integer programming
Iterative solutions
Linear programming
MRP systems: lot-sizing
Operations research
Overtime
Overtime costs
Planning
Problem sets
Problem solving
Production
Production capacity
Production costs
Production planning
Relaxation
Scheduling
Studies
Techniques
ISSN:0025-1909, 1526-5501
Online Access:Get full text
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Summary:This paper proposes and tests a procedure 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 iteration, 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%. In addition, these best feasible solutions dominate the corresponding solutions obtained by a hierarchical procedure.
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ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.28.3.260