Order picking plan to maximize the order fill rate

In distribution centers, some orders may not be fulfilled due to the shortage of inventory. We consider the case where an order is picked and shipped only when all items in the order is available in the inventory; and the unfulfilled orders are transferred to the next day with higher priority. Given daily inventory and a set of orders arrived during a day, the problem is to assign the inventory to the orders so as to maximize the order fill rate (OFR). We formulate this problem as a linear programming problem. We also consider the weighted OFR to reflect the importance of each order. Simulation results indicate that the proposed LP approach outperforms the existing simple rules; and, more importantly, the improvement ratio increases as the number of items and/or orders increases.