Ashford, Robert W. (1981) Multi time period stochastic programming for medium term production planning. PhD thesis, University of Warwick.

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Abstract

Exact solutions to stochastic, capacitated, multi-commodity, multi-stage production/inventory models are in general computationally intractable. The practical application of such models is therefore inhibited. In this thesis a general stochastic, capacitated, multi- commodity, multi-stage production/inventory model with linear cost structure is proposed. Under convexity conditions it is a stochastic linear program. A good computationally efficient approximate solution technique is developed and some numerical results reported.

It is important to assess the merit of approximate techniques and this is done statistically by replicative simulation. But the accuracy of this method improves only as the square root of the number of simulation trials made, so it is important to eliminate any unnecessary variability in each trial. It is proposed that this be done by the use of control statistics. Several novel control statistics are developed, the most powerful being a martingale control statistic constructed independently for each trial from information provided by the approximate technique being tested.

Results are reported of testing the approximate solution technique developed for the general model, ordinary linear programming ignoring all the stochastic elements in the problem, and two other approximate techniques, by replicative simulation. These suggest that the penalty incurred by ignoring the stochastic nature of the problem is significant, but that first order deviations from optimal decisions may lead only to second order penalties. This is a desirable feature of the stochastic models, for it indicates that approximate solution techniques to stochastic programs may be more reliable than would be supposed from the approximations made.

Item Type:	Thesis (PhD)
Subjects:	H Social Sciences > HD Industries. Land use. Labor
Library of Congress Subject Headings (LCSH):	Production planning -- Mathematical models, Stochastic programming, Stochastic models
Official Date:	November 1981
Dates:	Date Event November 1981 Submitted
Institution:	University of Warwick
Theses Department:	School of Industrial and Business Studies
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Dyson, Robert G.
Sponsors:	Science Research Council (Great Britain)
Format of File:	pdf
Extent:	263 pages
Language:	eng

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