Abstract: It is an important issue to integrate the order picking with delivery problem under shorter time and lower cost by picking the items from the shelves, packaging them and delivering to customers. A nonlinear mathematical model is proposed to minimize the time required to complete picking the orders, delivering to customer and returning to the distribution center, which solves the joint decision-making problem such as order picking sequence, picking process method and vehicle routing. For this NP-hard problem, a three-phase heuristic algorithm is designed. Firstly, the "clustering-vehicle routing" method is used to get delivery solutions. Secondly, the similarity-based order batching rules are used to optimize each route's orders. Thirdly, picking sequence is sorted based on the descending order of each route's delivery time. The experiments are proposed to test the efficiency of the model. The results are compared with the traditional optimization algorithm, which show that the three-phase algorithm can reduce the throughput time, decrease the vehicle's wait time and improve the delivery resource utilization. integrated scheduling; order picking; vehicle route; three-phase algorithm; genetic algorithmAbstract:
With the development and wide-spread use of mobile technology, customers can shop anytime and anywhere through a business-to-consumer (B2C) e-commerce shopping platform. However small lot-size and high frequency customer orders make order picking and delivery difficult to implement. In order to accelerate the whole order fulfillment process, orders should be picked and delivered to customers in a very short lead time. It is therefore critical to integrate scheduling order picking and distribution under B2C e-commerce. Research on order picking problems, however, seldom takes delivery constraints into consideration.
The integrated order picking and distribution scheduling (IOPDS) problem is studied to minimize the time required to complete picking the orders, delivering to customer and returning to the distribution center to meet the demand of a given set of customers. The picking processing method is order bathing optimization and distribution characteristic is batching delivery with vehicle routing problem. The problem is NP-hard in strong sense. A three-phase heuristic algorithm is proposed, analyze upper bounds and low bounds of the algorithm are analyzed. The first phase uses the "clustering-vehicle routing" method to get delivery solutions; the second phase uses the similarity-based order batching rules to optimize each route's orders; the third one sorts picking sequence based on the descending order of each route's delivery time. The traditional sequential approach is also proposed, which optimizes order picking and delivery processes separately.In order to verify the effectiveness of the proposed model and algorithms for IOPDS, several examples are tested. The locations for 300 customers are randomly generated in the 100*100 square, where the warehouse is in the center of the square. The three-phase algorithm's relative difference from the lower bounds is good. The results are also compared with the traditional algorithm, which show several enlightening findings:1) the throughput time of the three-phase algorithm is 17.11% shorter than the one of the traditional algorithm, which means it is significant to integrate order picking and distribution; 2) the average improvement of the three-phase algorithm is 13.03%, shows that it is helpful to improve the whole efficiency of the picking and distribution system; 3) it decreases the vehicle's wait time and improve the delivery resource utilization.Theoretically the IOPDS model and algorithm in the work expand the order picking optimization theory and improve the scheduling of production and distribution problem. Moreover, it is beneficial to the e-commerce shopping platform, which can promote the shipping efficiency, save vehicle resources and improve customer satisfaction.

Key words: integrated scheduling, order picking, vehicle route, three-phase algorithm, genetic algorithm