Mathematical Modeling of Integrated Order Batching and Distribution Scheduling in a Warehouse with Multiple Pickers Using Batch Picking

The orders received from customers in retail companies must be picked in the warehouse before delivery to customers. Order picking is the most costly and time-consuming process in a warehouse and customer orders are usually batched and picked in common tours to reduce travel distance and picking time. On the other hand, the widespread use of the internet and e-commerce has significantly increased the number and decreased the size of orders issued by customers and as a result, the order batching and picking operations in the warehouse has become more complicated. Besides, adopting appropriate policies to distribute orders among customers by taking into account issues such as the time and cost of distributing orders and due dates, is of great importance. Moreover, considering the operations of order picking and distribution in an integrated manner can significantly reduce costs and increase the level of service provided to customers. In this research, the order batching and distribution operations are considered integratedly and a mathematical model is proposed to address the integrated problem by considering minimization of total tardiness as objective function. respectively. For model validation purposes, an iterated local search metaheuristic approach is proposed to solve the proposed model. By using the generated data, it has been shown that the metaheuristic algorithm is able to obtain quality solutions for the problem. Due to the fact that an optimization solver is unable to optimize a small size problem in a realistic time, an upper bound was defined for the purpose of comparing the algorithm results with that. Our comparison of results indicates that for relatively larger sized sample problem the quality of obtained solutions by meta-heurietsic algorithm, in comparion with upper bound, having suitable quality as expected.