Dynamic Programming and Heuristic for Stochastic Uncapacitated Lot-Sizing Problems with Incremental Quantity Discount

Algorithm 1

Dynamic programming algorithm.

For each stage 𝑡=1 to 𝑇

 For each node 𝑛 at stage 𝑡

  For each possible initial inventory 𝑠_𝑚=𝑑_0,𝑚−𝑑_0,𝑎(𝑛)≥0,  𝑚∈𝑁

  (if 𝑡=1, set 𝑠_𝑚=0)

   step 1: Calculate 𝐻_𝑃(𝑛,𝑠_𝑚) by (3.11)

   step 2: Calculate 𝐻_𝑁𝑃(𝑛,𝑠_𝑚) by (3.12) if 𝑑_0,𝑚−𝑑_0,𝑛>=0,

    otherwise 𝐻_𝑁𝑃(𝑛,𝑠_𝑚)=+∞

   step 3: Calculate 𝐻(𝑛) by (3.13)

  End For Iteration (𝑠_𝑚)

 End For Iteration (𝑛)

End For Iteration (𝑡)