Indices

i , j

index of items, i, j = 1, ..., N

o

index of orders, o = 1, ..., O

m

index of pods, m = 1, ..., M

Parameters

N

total number of items

O

total number of orders

M

total number of pods

Q

number of inventory bins in one pod; Q=8 in this article

B_i

number of inventory bins for the item i needed to be assigned

S_ij

similarity value between the item i and j, it is equal to the support count between item i and j

S

item similarity matrix

Decision variables

x_im

x_im = 1 if the item i is put on the pod m;

x_im = 0 , otherwise

y_im

number of inventory bins that item i occupies on the pod m