Journal ArticleDOI
Decomposition Principle for Linear Programs
George B. Dantzig,Philip Wolfe +1 more
TLDR
A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.Abstract:
A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations. The coordinating program generates at each cycle new objective forms for each part, and each part generates in turn from its optimal basic feasible solutions new activities columns for the interconnecting program. Viewed as an instance of a “generalized programming problem” whose columns are drawn freely from given convex sets, such a problem can be studied by an appropriate generalization of the duality theorem for linear programming, which permits a sharp distinction to be made between those constraints that pertain only to a part of the problem and those that connect its parts. This leads to a generalization of the Simplex Algorithm, for which the decomposition procedure becomes a special case. Besides holding promise for the efficient computation of large-scale systems, the principle yields a certain rationale for the “decentralized decision process” in the theory of the firm. Formally the prices generated by the coordinating program cause the manager of each part to look for a “pure” sub-program analogue of pure strategy in game theory, which he proposes to the coordinator as best he can do. The coordinator finds the optimum “mix” of pure sub-programs using new proposals and earlier ones consistent with over-all demands and supply, and thereby generates new prices that again generates new proposals by each of the parts, etc. The iterative process is finite.read more
Citations
More filters
Journal ArticleDOI
Large-scale network distribution of pooled empty freight cars over time, with limited substitution and equitable benefits
TL;DR: In this paper, a set of models and procedures for finding the optimal distribution of empty freight cars owned by the railroads participating in a pooling agreement is described, where a distinction is drawn between a system focus, in which the emphasis is on minimizing total cost, and a company focus, where the benefits of the agreement to the individual railroads are emphasized.
Journal ArticleDOI
Pricing interprocess streams using slack auctions
Rinaldo A. Jose,Lyle H. Ungar +1 more
TL;DR: It is claimed that the correct way of finding slack resources is to define slack resources over the process streams and price them using slack auctions, and it can be shown that the plant divisions' solutions are globally optimal when slack auctions terminate properly.
Journal ArticleDOI
Dynamic location of modular manufacturing facilities with relocation of individual modules
Andrew Allman,Qi Zhang +1 more
TL;DR: This work presents a generic mixed-integer linear programming (MILP) framework for determining optimal location and relocation of mobile production modules given time-varying demands, and introduces a new metric, the value of module mobility, to quantify the economic benefits of mobileproduction modules.
Journal ArticleDOI
Waste material recycling and exchanging decisions for industrial symbiosis network optimization
TL;DR: The results show that the proposed Mixed-Inter Programming optimization method and Epsilon-constraint technology are sufficient to obtain the solutions of industrial symbiosis optimization.
Journal ArticleDOI
Critical essay on the methodology of multiobjective analysis
TL;DR: While there are already many methods for multiobjective analysis, this field would gain from further methodological reflection, encompassing various approaches to multiobjectives optimization and decision making.