Joint Order Batching and Picker Routing Proble

In 2016, the Gross Domestic Product (GDP) of the United States hit $18.57 trillion (Kearney, 2017). 7.5% of the GDP was from logistic costs, which is $1.4 trillion. Out of this $1.4 trillion the cost for warehousing has increased despite the fall in GDP compared to 2015. Total United States expenditures on public and private warehousing rose by 1.8 percent to $143.5 billion last year (Kearney, 2017). Moreover, the forecasters have predicted a steady industry growth of 3 percent annually through 2021. Warehouse companies face various overheads such as rise in labor cost, transportation cost along with high demand uncertainties. As the challenges increase in warehouse operating costs, there is a pressing need to mitigate the inefficiencies in warehouse management. Thus, it is important to discover areas where there is scope for the overhead cost to be avoided. Focusing on this problem area, it is identified that around 26% of logistics cost ($36 billion) is accounted by warehousing (van den Berg and Zijm, 1999). Upon analyzing the areas of various warehousing cost activities it is noted that order picking accounts to atleast 50% of the total cost. Thereby, with the increasing order picking challenges due to long travel time it is essential to build holistic and flexible solutions that are capable of providing fulfilment of customer orders.;In this research the order picking process is addressed through joint order batching and picker routing problem. Here the order to batch assignment problem is handled by order batching problem and the picker routing problem in the warehouse addresses efficient vehicle movement in the warehouse. This research proposes a new mathematical model to determine the batch size, allocation of all orders to one of the batches available and then the picker routing for all tours. Unlike the other models for joint order batching and picker routing problem, the proposed model in this study considers both the quantities of each items of an order and also the weight of each item. The objective is to minimize the total picker routing distance of the order picking vehicle to pick all the orders and handling all batches. While there has been considerable research in both order batching and picker routing problems separately, there has not been much research conducted on the joint order batching and picker routing problem. In order to understand the scope and importance of this joint problem, a comparison study between sequential order batching and picker routing problem and joint order batching problem and picker routing problem has been carried out. The experimental results show that the joint order batching and picker routing problem has an improvement of 31.64% in the objective values. This is because the joint problem minimizes the total picker routing by not only choosing optimal order picker route but also the orders are also batched by minimizing total number of batches required to handle all the orders. Moreover, it is noted that for Large Warehouse size some of the experiments could not be solved to optimality as CPLEX runs into Memory Error. Thus, this could have affected the improvement. Similarly, the computational time of the joint problem was also significantly lesser than that of sequential problem (64% improvement). Thus, a comparison study of how the objective values are affected based on Warehouse Sizes (Small, Regular and Large) and similarly for Problem Sizes (Low, Moderate and High) have been carried out. For future work there are several directions to expand the problem scope. One such approach would be to consider warehouse layout along with the joint order batching and picker routing problem to understand the impact of the order picking efficiency on the basis of the warehouse layout. Yet another problem to consider would be joint optimization of order batching and picker routing along with storage location allocation based on order demand. This problem would provide clarity on how whether or not the storage location allocation affects the joint problem.