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

Algorithm 2

Rolling horizon heuristic (FT, BT).

For each stage 𝑡=1 to 𝑇

 For each node 𝑛 at stage 𝑡

  For each initial inventory 𝑠_𝑚∈{𝑑_0,𝑚−𝑑_0,𝑎(𝑛)≥0∶𝑚∈RH_FT,BT(𝑛)}

  Set 𝐻_𝑃(𝑛,𝑠_𝑚)=𝐻_𝑁𝑃(𝑛,𝑠_𝑚)=+∞; (if 𝑡=1,  set 𝑠_𝑚=0)

   step 1: If 𝑚∈𝐷(𝑛)⧵{𝑛}, go  to step 3; otherwise calculate 𝐻_𝑃(𝑛,𝑠_𝑚)

    by (3.15)

   step 2: If 𝑡−𝑡(𝑚)=BF or 𝑑_0,𝑛−𝑑_0,𝑚<0, goto step 3; otherwise

    calculate 𝐻_𝑁𝑃(𝑛,𝑠_𝑚) by (3.12)

   step 3: Calculate 𝐻(𝑛) by (3.13)

  End For Iteration (𝑠_𝑚)

 End For Iteration (𝑛)

End For Iteration (𝑡)