# A Modified Bayesian Network Model to Predict Reorder Level of Printed Circuit Board
## 1 Introduction  
A printed circuit board (PCB) is found in practically all electrical and electronic equipment. It is the base of the electronics industry [1]. Due to increased competition and market volatility, demand for highly individualized products promotes a rapid growth of orders with a small batch of purchase and production. Some orders even with the relatively large volume have been placed separately and repeatedly at different times by customers. Dynamic fluctuation of market demands for PCB can easily bring great production imbalance, which is a waste of production capacity during the idle period with fewer orders from customers. However, during the busy period, it results in tardiness among many orders. Multi-batches of the same PCB product produced separately always require higher preparation and production cost with a higher scrap rate. Identifying orders with high reorder frequency and combining different batches of these orders during a reasonable period (e.g., an idle period) as batchand inventory-oriented production can reduce production cost, benefit production capacity balance, and facilitate on time delivery. Taking an example from a PCB manufacturer named Guangzhou FastPrint Technology Co., Ltd. (called FastPrint in this paper), few orders were manually selected each month for batch production during the idle period based on reorder frequency and cumulative delivery area in the past 30 months. The reorder frequency is the number of times a customer places the same type of orders to a manufacturer in a given period. The delivery area of each order corresponds to the amount (quantity) of PCB products the customer orders multiplied by the area of each piece of PCB. The cumulative delivery area is the accumulation of the delivery area of the same type of orders in a given period. If 80% of the manually selected orders for batch production can be purchased by customers within six months (i.e., the maximum storage period in the manufacturer's inventory can be ordered by most of customers), then the manufacturer can profit from better utilization of idle resources and the reduction of repeated production preparation and cost. However, the manual selection process is experience-dependent and time-consuming. Meanwhile, the accuracy needs to be improved because only the reorder frequency and the cumulative delivery area are taken into consideration. The selection of orders for batch production is not based on the accurate reorder frequency within a certain period but always according to the range of predicted reorder frequency (e.g., reorder frequency \(\geq\) 3) in practice. Moreover, it is difficult to accurately determine the reorder frequency within a certain period for each PCB order in advance. Therefore, we transform the repeated orders identification problem into a reorder level prediction problem in which the reorder frequency within six months was divided into four reorder levels (i.e., 1, 2, 3, and 4) corresponding to the reorder frequency (0, 1-2, 3-5, and >5, respectively). On this basis, orders with a highly predicted reorder level corresponding to the range of high reorder frequency placed within six months are taken as candidates for batch production. The reorder level prediction is similar to the data mining based customer identification (also referred to as customer acquisition) problem as an important task of customer relationship management (CRM) [2]. The former can be conducted by analyzing characteristics of the orders and subdividing them into different groups in which the order groups with higher reorder levels (e.g., 3 and 4) can be taken as candidates for batch production. The latter, on the other hand, is to seek the profitable customer segments by analyzing their underlying characteristics and subdividing an entire customer base into smaller customer segments, which are comprised of customers who are relatively similar within each specific segment [2; 3]. Identification of the most profit-generating customers and segmentation of customers are quite vital [3].