# Dynamic lot-size model

{{ safesubst:#invoke:Unsubst||\$N=Use dmy dates |date=__DATE__ |\$B= }} 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 ${\displaystyle D_{t}}$ 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 ${\displaystyle S}$ incurred for each order and there is an inventory holding cost ${\displaystyle H}$ per item per period (S and H can also vary with time if desired). The problem is how many units 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.

## References

1. Harvey M. Wagner and Thomson M. Whitin, "Dynamic version of the economic lot size model," Management Science, Vol. 5, pp. 89–96, 195
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.

• Lee, Chung-Yee, Sila Çetinkaya, and Albert PM Wagelmans. "A dynamic lot-sizing model with demand time windows." Management Science 47.10 (2001): 1384-1395.
• Federgruen, Awi, and Michal Tzur. "A simple forward algorithm to solve general dynamic lot sizing models with n periods in 0 (n log n) or 0 (n) time." Management Science 37.8 (1991): 909-925.
• Jans, Raf, and Zeger Degraeve. "Meta-heuristics for dynamic lot sizing: a review and comparison of solution approaches." European Journal of Operational Research 177.3 (2007): 1855-1875.
• H.M. Wagner and T. Whitin, "Dynamic version of the economic lot size model," Management Science, Vol. 5, pp. 89–96, 1958
• H.M. Wagner: "Comments on Dynamic version of the economic lot size model", Management Science, Vol. 50 No. 12 Suppl., December 2004