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A diffusion model for a two product inventory system Ling, Daymond
Abstract
This thesis presents the results of an investigation of a continuous-time two product inventory model in which the stock level of two divisible commodities is represented by a two dimensional diffusion process. Two classes of replenishment policies are considered. One is a two dimensional analog of the stationary one dimensional (s,S) policy; i.e., when either the inventory of product one declines to s₁ or when the inventory of product two declines to s₂, both stocks are instantaneously replenished, product one up to S₁, and product two up to S₂. This is referred to as the (s₁,s₂,S₁,S₂) policy. The inventory is then allowed to decline again and is replenished. These cycles continue indefinitely. There are costs associated with the replenishment of stock and maintaining a given inventory. The objective is to choose values for (s₁,s₂,S₁,S₂,) to minimize the long-run average cost of opirating such a system. The appropriate theory of diffusion processes is heuristically developed and then applied to evaluate this cost. In general, analytic solutions cannot be obtained., Classical numerical analysis methods are used to obtain the average costs for given (s₁,s₂,S₁,S₂) values and to select the best such values. One dimensional diffusion models are a special case of the present model and Puterman's [21] results are used to verify the results obtained. The other policy examined differs from the two dimensional (s₁,s₂,S₁,S₂) policy in that the lower levels, s₁ and s₂, of the stock levels are coupled in the form of an elliptic arc. Numerical solution of this policy can be obtained and comparisons of the two policies are made.
Item Metadata
| Title |
A diffusion model for a two product inventory system
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1978
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| Description |
This thesis presents the results of an investigation of a continuous-time two product inventory model in which the stock level of two divisible commodities is represented by a two dimensional diffusion process. Two classes of replenishment policies are considered. One is a two dimensional analog of the stationary one dimensional (s,S) policy; i.e., when either the inventory of product one declines to s₁ or when the inventory of product two declines to s₂, both stocks are instantaneously replenished, product one up to S₁, and product two up to S₂. This is referred to as the (s₁,s₂,S₁,S₂) policy. The inventory is then allowed to decline again and is replenished. These cycles continue indefinitely. There are costs associated with the replenishment of stock and maintaining a given inventory. The objective is to choose values for (s₁,s₂,S₁,S₂,) to minimize the long-run average cost of opirating such a system. The appropriate theory of diffusion processes is heuristically developed and then applied to evaluate this cost. In general, analytic solutions cannot be obtained., Classical numerical analysis methods are used to obtain the average costs for given (s₁,s₂,S₁,S₂) values and to select the best such values. One dimensional diffusion models are a special case of the present model and Puterman's [21] results are used to verify the results obtained. The other policy examined differs from the two dimensional (s₁,s₂,S₁,S₂) policy in that the lower levels, s₁ and s₂, of the stock levels are coupled in the form of an elliptic arc. Numerical solution of this policy can be obtained and comparisons of the two policies are made.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2010-02-23
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0094229
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.