In many modern logistic systems, automated carousal conveyors are frequently used for storing/retrieving small to medium items to fulfil the customer's demand. The system is used to process a sequence of orders from customers in a dynamic fashion. Each order includes one or several items to be picked from the carousal storage or bin. The sequence between orders and the sequences among items within each order are to be determined, to minimise the total order processing or associated picking cost. This multi-order picking problem is formulated as 0-1 integer programming model, which resembles the well-known Multi-travelling salesman problem. Some important properties of this unique order processing system are described. New theoretical properties are established to characterise the optimal retrieval sequence in an order with multiple items to be picked. Based on these properties, efficient and effective heuristics are developed to solve this multi-order picking problem. The computational detail of these approaches is illustrated by an example. Numerical experiments with problem sizes up to 500 items for a batch of 50 orders are performed, where different order densities and order rates are considered.
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