A linear programming model to support e-fulfillment strategies in warehouse-based supermarket chains

The input parameters have been collected from the database of the company under study. The values have been structured according to the indexes defined in the MILP model to develop the case study. With this information, the model can be replicated in future research. The parameters have been structured according to the indexes defined in the model. The index ‘i’ represents the orders, the index ‘j’ defines the time window, the index ‘k’ symbolizes the truck and the index ‘z’ describes the region. 

Specialized formats or other abbreviations used: 

i: Index of orders
j: Index of time windows
k: Index of trucks
z: Index of regions
CCi: {(1 if the order i is click&collect or click&drive; 0 otherwise)}
NiD: Number of dry products boxes per order i
NiFR: Number of fresh products boxes per order i
NiFZ: Number of frozen products boxes per order i
MPCjD: Maximum picking capacity for preparing dry products boxes at time window j
MPCjFR: Maximum picking capacity for preparing fresh products boxes at time window j
MPCjFZ: Maximum picking capacity for preparing frozen products boxes at time window j
PCjD: Order picking cost per box of dry products at time window j
PCjFR: Order picking cost per box of fresh products at time window j
PCjFZ: Order picking cost per box of frozen products at time window j
TWUCj: Availability cost of order picking time window j
MTCjkD: Maximum transport capacity of dry products boxes per truck k at time window j
MTCjkFR: Maximum transport capacity of fresh products boxes per truck k at time window j
MTCjkFZ: Maximum transport capacity of frozen products boxes per truck k at time window j
KMCk: Delivery cost per kilometer of the truck k
PTCFk: Payment function of truck k in the previous horizon
TUCk: Availability cost of each truck k in the planning horizon considered
Lz: Delivery distance from the warehouse to the main store of the region z
WFz: Wiggle Factor for region z
Rz: Average distance within which home delivery orders are made in region z