Dynamic lot-size model

The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in 1958.^[1]^[2]

Problem setup

We have available a forecast of product demand $d t$ over a relevant time horizon (for example we might know how many widgets will be needed each week for the next 52 weeks). There is a setup cost $s t$ incurred for each order and there is an inventory holding cost $i t$ per item per period ( $s t$ and $i t$ can also vary with time if desired). The problem is how many units $x t$ to order now to minimize the sum of setup cost and inventory cost.

Wagner and Whitin gave an algorithm for finding the optimal solution by dynamic programming. Because this method was perceived by some as too complex, a number of authors also developed approximate heuristics (e.g., the Silver-Meal heuristic) for the problem. Also, the capacity constraint is not considered in Dynamic lot-size model. In this case, to find optimal solution mathematical model can be used, or to have near-optimal solution, heuristic algorithms can be applied.^[3]

$I=I_{0}+\sum _{j=1}^{t-1}x_{j}-\sum _{j=1}^{t-1}d_{j}\geq 0$

$f_{t}(I)={\underset {x_{t}\geq 0 \atop I+x_{t}\geq d_{t}}{min}}\left[i_{t-1}I+H(x_{t})s_{t}+f_{t+1}\left(I+x_{t}-d_{t}\right)\right]$

References

^ Harvey M. Wagner and Thomson M. Whitin, "Dynamic version of the economic lot size model," Management Science, Vol. 5, pp. 89–96, 1958
^ Wagelmans, Albert, Stan Van Hoesel, and Antoon Kolen. "Economic lot sizing: an O (n log n) algorithm that runs in linear time in the Wagner-Whitin case." Operations Research 40.1-Supplement - 1 (1992): S145-S156.
^ Malakooti, Behnam (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons. ISBN 978-1-118-58537-5.

External links

[1] Harvey M. Wagner and Thomson M. Whitin, "Dynamic version of the economic lot size model," Management Science, Vol. 5, pp. 89–96, 1958

[2] Wagelmans, Albert, Stan Van Hoesel, and Antoon Kolen. "Economic lot sizing: an O (n log n) algorithm that runs in linear time in the Wagner-Whitin case." Operations Research 40.1-Supplement - 1 (1992): S145-S156.

[MalakootiMCDM-3] Malakooti, Behnam (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons. ISBN 978-1-118-58537-5.

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Problem setup

References

Further reading

External links