Radiotherapy Treatment Design Using Mathematical Programming Models
Article Abstract:
Radiotherapy is a major treatment tool in cancer. Current radiotherapy techniques use a two-dimensional approach that involves considerable trial and error. The present paper presents a treatment design approach that relies on mathematical optimization to reduce the trial and error involved and ultimately facilitates a three-dimensional treatment design. Models are presented that illustrate the application of mathematical programming to radiology treatment design. The new and standard approaches are compared in a lung cancer case study. Graphs and diagrams illustrate the technique.
Publication Name: Operations Research
Subject: Petroleum, energy and mining industries
ISSN: 0030-364X
Year: 1985
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Mathematical Pitfalls in the One Machine Multiproduct Economic Lot Scheduling Problem
Article Abstract:
A group of products sharing the same piece of production equipment is considered. It is shown that two mathematical problem formulations in the literature are ill-posed. In both cases, the infimum of the cost function occurs at a boundary point that is not feasible.
Publication Name: Operations Research
Subject: Petroleum, energy and mining industries
ISSN: 0030-364X
Year: 1983
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The Solution of the Chemical Equilibrium Programming Problem with Generalized Benders Decomposition
Article Abstract:
An algorithm for solving the chemical equilibrium problem is derived. It parallels Geoffrion's development of the Generalized Benders Decomposition Algorithm. Computational results are discussed.
Publication Name: Operations Research
Subject: Petroleum, energy and mining industries
ISSN: 0030-364X
Year: 1984
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