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DESIGN AND OPERATION OF A MULTICOMMODITY PRODUCTION-DISTRIBUTION SYSTEM USING PRIMAL GOAL DECOMPOSITION

MANAGEMENT SCIENCE 1987年第11期33卷 1469-1480页

作者： BROWN, GG GRAVES, GW HONCZARENKO, MD UNIV CALIF LOS ANGELES GRAD SCH MANAGEMENT LOS ANGELES CA 90024 USA NABISCO BRANDS INC E HANOVER NJ 07936 USA

An optimization-based decision support system has been developed and used by NABISCO to manage complex problems involving facility selection, equipment location and utilization, and manufacture and distribution of products such as the familiar Ritz Crackers, Oreo Cookies, Fig Newtons, etc. (all product names trademarks of NABISCO). A mixed-integer, multi-commodity model is presented for the problems at hand, and a new class of goal decompositions is introduced to yield pure network subproblems for each commodity; the associated master problems have several notable properties which contribute to the effectiveness of the algorithm. Excellent quality solutions for problems with more than 40,000 variables (including several hundred binary variables with fixed charges) and in excess of 20,000 constraints require only 0.6 megabytes region and less than one compute minute on a time-shared IBM 3033 computer; average problems (with fewer binary variables) require only a second or two. The solution method has more to recommend it than sheer efficiency: new insights are given for the fundamental convergence properties of formal decomposition techniques. Several applications of this powerful interactive tool are discussed.

关键词： programming: large-scale systems programming: integer applications facilities/equipment planning

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MATHEMATICAL-programming APPROACHES TO CAPACITY-CONSTRAINED MRP systems - REVIEW, FORMULATION AND PROBLEM REDUCTION

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MANAGEMENT SCIENCE 1983年第10期29卷 1126-1141页

作者： BILLINGTON, PJ MCCLAIN, JO THOMAS, LJ CORNELL UNIV GRAD SCH BUSINESS & PUBL ADMITHACANY 14853

This paper introduces a line of research on capacity-constrained multi-stage production scheduling problems. The first section introduces the problem area as it arises from a failure of MRP systems. Then a review of the literature and an analysis of the type of problems that exist are presented in §2. Section 3 outlines linear and mixed integer-linear programming formulations. These formulations compute the required production lead times according to the demands on available capacity, thereby reducing in-process inventory compared to the usual practice in MRP. A discussion of how to use the LP version is included. However, the size of the problems in practice implies that more efficient solution techniques must be found. The final topic of this paper, Product Structure Compression, is introduced as a method to reduce the size of the problem without losing optimality.

关键词： inventory/production: material requirements planning programming: large-scale systems programming: integer applications

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