Inventory control is a key factor for reducing supply chain cost and increasing customer satisfaction. However, prediction of inventory level is a challenging task for managers. As one of the widely used techniques for inventory control, standard BP neural network has such problems as low convergence rate and poor prediction accuracy. Aiming at these problems, a new fast convergent BP neural network model for predicting inventory level is developed in this paper. By adding an error offset, this paper deduces the new chain propagation rule and the new weight formula. This paper also applies the improved BP neural network model to predict the inventory level of an automotive parts company. The results show that the improved algorithm not only significantly exceeds the standard algorithm but also outperforms some other improved BP algorithms both on convergence rate and prediction accuracy.

Inventory control is one of the key topics for supply chain management. Usually inventory takes the form of raw material, work in process (WIP) products, semifinished products, or finished products. Inventory cost is the main cost for supply chain management. A drop of just several percentage points of inventory cost can greatly increase the profits of the whole supply chain. In addition, sound inventory level can prevent shortage of material, maintain the continuity of the production process, and quickly satisfy customers' demand. Thereby, exploring the optimal inventory level is very necessary and valuable for supply chain management.

To date, the following inventory control problems need to be addressed [

There are highly nonlinear models which are hard to process.

There are qualitative indicators which are hard to deal with.

The unchangeable indicators of inventory control lack self-adaptation.

Information of inventory control models is always indirect and the collection of information is time-consuming and of low efficiency.

Inventory control models always ignore the influence of uncertain factors, such as lead time, transportation conditions, and change of demand.

Considering the above problems, traditional inventory control theory is hard to meet the requirement posed by the new environment. Thanks to the uncertain feature of inventory control and the strengths of neural network in model prediction, this paper chooses to use BP neural network to establish inventory model and predict inventory level.

BP neural network is a kind of nonlinear feed forward network which has good nonlinear mapping ability. Theories have proved that BP network can approach any nonlinear mapping relationship given enough input and hidden layers while there is no necessity to establish a mathematical model. Furthermore, by learning and training, BP network can store information systematically in weight matrix

However, it is acknowledged that BP neural network also has such problems as slow convergence and easily converging to local minimum when forecasting. Considering the shortcomings of standard BP algorithm, this paper proposes a new fast convergent BP neural network model for predicting inventory level. By adding an error offset, this paper deduces the new chain propagation rule and the updated weight formula. The application of the improved BP neural network model to predict the inventory level of an automotive parts company shows that the improved algorithm significantly outperforms the standard algorithm and some other improved BP algorithms both on convergence rate and prediction accuracy.

This paper proceeds as follows: Section

Recently, more and more scholars have applied neural network technique to inventory control. Bansal et al. used a neural network-based data mining technique to solve the problem of inventory of a large medical distribution company [

Although there are various neural network models, BP neural network is the most widely used model because of its simple structure and strong ability to learn. In fact, it has been widely used in inventory control. Zhang et al. used the reinforcement learning technique and the BP neural network to propose a new adaptive inventory control method for supply chain management [

The BP neural network we mentioned above is referring to the standard BP neural network. The standard BP neural network is based on the Widrow-Hoff rule and uses the gradient descent method to transfer the mapping of a set of inputs to its correct output into nonlinear optimal problems. However, the standard BP algorithm has inherent disadvantages such as slow convergence, problem of converging to local minimum, complication of system, and random network structure selection [

Aiming at the weaknesses of standard BP neural network, scholars have made further studies and proposed different improved BP neural network models [

By adding an error offset to the error function, this paper puts forward a direct improvement on standard BP neural network. Based on a dataset of an automotive parts company, it proves that the improved BP algorithm not only exceeds the standard BP algorithm both on convergence rate and prediction accuracy but also outperforms some other improved BP neural networks.

Back-propagation algorithm or BP algorithm, one of the most widely used algorithms in artificial neural network, is a kind of supervised learning algorithm. Its main purpose is to adjust weight matrix according to the squared error between the actual output and target output. The squared error is expressed as follows:

Here,

Here,

Here,

Suppose that

When the

If the

From the above analysis, we can know that the standard BP algorithm updates the weights of its output layer and hidden layer just according to the above formula. Regarded as a part of the weights, the update of bias is quite similar to that of weights so we will not give further details about its deduction.

To improve the convergence rate of standard BP algorithm, we propose a new algorithm, which can achieve the goal by adding an error offset.

The essence of BP algorithm is the forward propagation of data and backward propagation of errors. The weight value is revised according to the errors in back propagation. However, the convergence rate of standard BP algorithm is slow and often cannot satisfy the requirements when applied. Therefore, we propose a new method: adding an error offset in back propagation to greatly improve the convergence rate. The latter experiment illustrates that its effect is quite outstanding. Here, we redefine the squared error as follows:

For the right-hand side of (

The new weight formula is

If

The new weight formula is

This paper uses the dataset of an automotive parts company to train the improved BP neural network. As we know, nowadays automobiles are comprised of lots of parts. These parts are produced on the demand of automobile manufacturers and then are sent to assembly factories to form a complete product. In this way, the whole production process of an automobile exists in the form of a supply chain. To realize the highest overall efficiency, it needs cooperation of all the suppliers, manufacturers, wholesalers, and retailers. Inventory control is an important aspect which reflects such kind of cooperation. In the following part, this paper will use the improved BP neural network to forecast the inventory level of bearings—one of the components for an automobile.

Usually accurate inventory level is the precondition for good inventory management. For inventory management, inventory controlling cost and customers’ service levels as well as inventory controlling quality are the main factors to estimate the inventory level. Therefore, in the design of inventory control system, we mainly use these factors to predict. They are described as follows [

This paper chooses the historical data of factors which influence the safety inventory level and inventory data of bearing of an automotive parts production company in one of the middle provinces of China from March 2012 to March 2013 as a sample to train the improved BP neural network. We mainly choose 100 groups of the data to train the network and then check its prediction ability. The number of training samples cannot be too small; otherwise, the network cannot learn enough which may result in low prediction ability. However, too large samples will lead to redundancy. At this time, the network will be overfitted. Therefore, this paper chooses 100 groups of data as input to train and predict and chooses inventory level as output to establish the BP neural network model. In this case, because the system is nonlinear, the initial value plays very important role in achieving local minimum. Therefore, the input sample needs to be normalized and the purpose is to make the big input values also fall in the range with large gradients of activation function.

Before network training, we normalized the training data according to

Normalized data of stock-influencing factor.

Data | Storage cost | Ordering cost | Shortage cost | Transportation cost | Demand level | Supply level | Quantity of substitutes | Waiting time | Service level | Actual inventory level |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1.0 | 0.88 | 0.94 | 1 | 0.65 | 0.8 | 0.25 | 0.00 | 0 | 0.33 |

2 | 0.7 | 1.00 | 1.00 | 0 | 1.00 | 1.0 | 1.00 | 0.25 | 0 | 0.38 |

3 | 0.5 | 0.40 | 0.31 | 0 | 0.22 | 0.0 | 0.25 | 0.58 | 0 | 0.50 |

4 | 0.0 | 0.08 | 0.13 | 0 | 0.43 | 0.0 | 0.00 | 0.50 | 1 | 0.13 |

5 | 0.5 | 0.40 | 0.38 | 1 | 0.65 | 0.4 | 0.00 | 0.54 | 0 | 0.25 |

6 | 0.7 | 0.60 | 0.31 | 1 | 0.74 | 0.4 | 0.00 | 0.87 | 1 | 0.38 |

7 | 0.4 | 0.32 | 0.13 | 1 | 0.30 | 0.2 | 0.00 | 0.37 | 1 | 0.50 |

8 | 0.3 | 0.20 | 0.00 | 0 | 0.00 | 0.0 | 0.00 | 0.79 | 1 | 0.00 |

9 | 0.3 | 0.00 | 0.13 | 0 | 0.13 | 0.0 | 0.25 | 1.00 | 1 | 1.00 |

10 | 0.5 | 0.78 | 0.63 | 1 | 0.43 | 0.4 | 0.25 | 0.08 | 1 | 0.13 |

Any continuous function can be realized by a three-layer artificial neural network. Therefore, this paper adopts the three-layer BP neural network structure. When all information is input into the network, the information starts by being transmitted from input layer to hidden layer. With the work of activation function, the information is then transmitted to output layer. There are 9 input factors and the output is inventory level. The selection of variables of the network is as follows.

According to empirical formula

This paper uses the neural network tool package of MATLAB 7.6 to program the model for safety inventory level based on BP neural network. In the BP neural network model established in this paper, there are 9 inputs and the number of neurons is relatively large. We preliminarily set the training variables as follows: times of training are 10000, training target is 0.01, and learning rate is 0.1. The code and training result is as follows:

net. trainParam. Epochs = 10000;

net. trainParam. goal = 0.1;

LP. lr = 0.1;

net-train(net, P, T);

after 1000 trainings, the training is finished.

After network finishes training, the network gets tested. We use the data of March 2013 to test. The code of prediction is as follows:

Out = sim (net,

By comparing Figures

Training convergence effect of improved algorithm.

Training convergence effect of standard algorithm.

From Table

Comparison of training convergence rate among standard algorithm, other improved algorithms, and improved algorithm of this paper.

Parameter depiction | Standard BP algorithm | Improved BP algorithm [ |
Improved BP algorithm [ |
Improved BP algorithm of this paper |
---|---|---|---|---|

Maximum iteration times | 9897 | 6245 | 4268 | 4432 |

Minimum iteration times | 1456 | 841 | 985 | 756 |

Average iteration times | 5423.4 | 2315.8 | 2013.9 | 1968.7 |

As prediction accuracy is concerned, from Figure

Prediction effect of improved algorithm.

Suppose

Comparison of error among standard algorithm, other improved algorithms, and improved algorithm of this paper.

Parameter depiction | Standard BP algorithm | Improved BP algorithm [ |
Improved BP algorithm [ |
Improved BP algorithm of this paper |
---|---|---|---|---|

Prediction set error | 0.002687 | 0.000938 | 0.000921 | 0.000780 |

We conclude the following with the practical importance of our findings. First, this paper proposes a new, fast convergent BP algorithm and deduces new chain propagation rules of neural network by introducing an error offset. Secondly, this paper applies it to the prediction of inventory level of an automotive parts company and achieves good effect. From the experimental results, we can see that using neural network to predict inventory is effective. The improved BP algorithm not only significantly exceeds the standard algorithm both on convergence time and prediction effect but also outperforms some other improved BP algorithms on these two main indicators. In this sense, this paper provides a valuable reference for inventory control of supply chain. However, this paper also has limitations. There are still some problems that need to be solved such as how to decide the number of nodes of hidden layer and the optimization of whole structure of network. Apart from that, the introduction of the error offset is based on experiences. The theoretical explanation for it still needs to be further discussed. All these problems wait to be further explored in future research.

This work is supported by the NSFC (71361013 and 71163014) and The Education Department of Jiangxi Province Science and Technology Research Projects (11728).