Fast solution and detection of minimal forecast horizons in dynamic programs with a single indicator of the future: applications to dynamic lot-sizing models
Article Abstract:
An optimal decision at a certain stage relies on limited information in several dynamic planning problems. To address this problem, a study is conducted to identify a general class of dynamic programs where an efficient forward algorithm can be developed to solve the problem and identify minimal forecast horizons. A forecast horizon procedure is used. This facilitates identification of optimal decisions when there is precise information over a limited space or space horizon only. The class of dynamic programs identified includes thee single-item dynamic lot-sizing model with general concave costs, both with and without backlogging. Other problems belonging to the class of dynamic programs are scheduling, molecular biology, equipment replacement, geology, bond refunding and speech recognition problems.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1995
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Learning in setups: analysis, minimal forecast horizons, and algorithms
Article Abstract:
The dynamic lot-sizing model is considered in which the setup costs are contingent upon the number of setups incurred so far. Unlike other learning models, the production model examined is more general in that it allows for a general nondecreasing total setup cost function. Its tight relationships with special cases of the classical dynamic lot-sizing model are examined. Minimal forecast and planning horizons for the model are found. These influence the first decision regarding the resolution of the model based on a rolling horizon. An algorithm is provided for solving the model in the absence of a forecast horizon, as well as for solving the finite horizon problem. Results offer insights that can be applied to other models with a similar cost behavior.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1996
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A simple forward algorithm to solve general dynamic lot sizing models with n periods in 0(n log n) or 0(n) time
Article Abstract:
The general dynamic lot size model, also referred to as the Wagner-Whitin model, is examined. A simple algorithm which solves the general model in 0 (n log n) time and 0 (n) space is described. A linear algorithm is presented for two special cases: models without speculative carrying stock motives and models with setup costs that are nondecreasing. Conditions for monotone optimal policies are also derived and then related to known results.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1991
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