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Dynamic lot sizing: exact solution of the Wagner-Whitin model

The optimal solution of the Single-Level Uncapacitated LotSizing Problem (SLULSP) is computed with the dynamic programming procedure due to Wagner and Whitin.

The algorithm is also available in the module MRP successive planning .


i index of periods
s(i) setup cost in period i
h(i) holding cost in period i
p(i) variable production cost in period i
d(i) demand in period i
f(i) minimum costs for a production plan covering the first i periods
q(i) lot size in period i


  • deterministic dynamic demands
  • deterministic setup costs, holding costs and production costs
  • no capacity consideration


- Nahmias (1997), Chapter 6.4

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