Research on Distribution Network Spare Parts Demand Forecasting and Inventory Quota

Zengyu Wang1 School of Electric Power, South China University of

Technology Guangzhou, China, 510640

Dong Hua3 School of Electric Power, South China University of

Technology Guangzhou, China, 510640 E-mail: dhua@scut.edu.cn

Jiyin Wen2 Guangzhou Power Supply Co. Ltd.

Guangzhou, China, 510000

Abstract—Due to the professionalism and particularity of the power equipment, a reasonable inventory equipment quota forecasting and purchasing plan can guarantee the electrical power construction and maintenance work smoothly. Furthermore, an accurate quota forecasting can also save a large volume of liquid funds for the power companies. This paper establishes a reasonable spare parts demand forecasting and inventory quota model based on SVM algorithm which takes material historical demand, repair schedule, the failure rate of the equipment and operating environment into full consideration. Moreover, the spare parts of electrical equipment in distribution network are divided into Class A, Class B1 and Class B2 through the activity based classification, through which the inventory quota method based on the different types of inventory management model is established. Finally, the calculation results of actual distribution power network show that the proposed SVM model is of high prediction accuracy, providing a simple and effective solution for inventory equipment management of electricity equipment.

Index Terms—Distribution network; Spare parts; Activity based classification; Demand forecasting; Inventory quota

I. INTRODUCTION Spare parts inventory is playing a very important role in

the distribution network equipment management, concerning how to improve the operational reliability of power supply by arranging a reasonable maintenance for spare parts. As a technology and capital intensive enterprise, the power company spends lots of funds on electric equipment every year. Therefore, how to establish reasonable spare parts demand forecasting model and inventory quota model are the issues about which the operation and equipment department in power industry really concern.

Researches on spare parts inventory of enterprises began from 1950s, and then inventory management became a branch of enterprise logistics, being an important part of the normal operation of enterprises management. Equipment spare parts are the support materials for equipment maintenance, which is the important factor to guarantee the equipment in good condition. With the development of science and technology, inventory costs are gradually increased for the equipment is more and more complex and expensive, which would cost much more liquidity and affect the enterprise economic benefit. There are some research achievements on the spare parts inventory from Telecom, nuclear and military, but the inventory research related to power system is still less. Currently, the research of spare part inventory management is divided into three parts, including spare parts inventory classification, demand forecasting and inventory management strategy.

Spare parts inventory are sorted by analytic hierarchy process (AHP) based on a variety of factors in reference paper [1]. In reference paper [2], fuzzy evaluation theory is applied to sort the spare parts inventory by quantizing the fuzzy vector and getting the comprehensive evaluation to divide the material importance. Reference [3] adopted the Bayesian algorithm as demand forecasting algorithm for which the demand was not obeying any distribution. In reference paper [4], a new intermittent demand forecasting method called the Bootstrap algorithm sampled virtual data from historical data to forecast the possibility of lead time demand, and then obtained the forecast demand of per unit time. Paper [5] applied the data mining technology to building a flexible and accurate forecasting database and used the inventory demand forecasting model based on exponential smoothing model to forecast the inventory demand. A synthesized forecasting model which involves both the time series and the multi-

Corresponding author: Dong Hua, Email: dhua@scut.edu.cn This work was supported by “the Fundamental Research Funds for the

Central Universities” 978-1-4799-7537-2/14/$31.00 2014 IEEE

regression methods is established by analyzing the factors influencing the demand in paper [6]．Paper [7] proposes the BP neural network model for the forecast of the inventory by simulating the expert in forecasting the enterprise inventory. But the distribution network spare parts demand is discrete and intermittent, and the relevant historical data is usually not enough, so the methods of the previous references is not suitable for distribution network spare parts demand forecasting. Support Vector Machine (SVM) algorithm, as a kind of novel machine learning method, is implemented with a great deal of experience especially in small sample forecasting problem.

In this paper, the regression forecasting algorithm based on SVM is used to predict the distribution network spare part demand through the study of inventory demand forecasting theory and the feature of distribution network spare parts. The SVM forecasting model takes material historical demand, repair schedule, the failure rate of the equipment and operating environment into full consideration, and then the feasibility of the demand forecast algorithm is verified by the data of column circuit breaker from a power supply enterprise in Guangdong. The spare part inventory quota management algorithm adopted in distribution network is also presented in this paper. The distribution network spare parts of the power supply enterprise are divided into A, B (including B1 and B2) two classes, through which the inventory quota models are established respectively for the two classes. Finally, the corresponding examples show the practical application of stock quota management algorithm.

II. SPARE PARTS CLASSIFICATION Activity based classification (ABC) method can sorted the

spare parts into A (the particularly important inventory), B (the general inventory), C (the secondary inventory) classes according to the cost of items and amount of usage [8]. The core idea of ABC method is to distinguish between the higher cost spare parts account for a smaller portion of the all inventory and a large number of the secondary spare parts according to the technical or economic characteristics of equipment.

The classification steps are as follows [9]: 1) The cost of each spare parts is calculated as a

percentage of the total cost of spare parts inventory. 2) The spare parts are ranked in descending order of the

percentage of each spare parts inventory cost to the total inventory cost.

3) The graph is plotted with percentage of spare part inventory used on X axis and the percentage of its cost on the Y axis as shown in Figure. 1.

Figure.1 Activity based classification for spare parts inventory

Considering the importance of repair materials and the particularity of power supply enterprise, the distribution network spare parts inventory are divided into A, B (including B1 and B2) two classes in this paper.

III. SPARE PARTS DEMAND FORECASTING

A. Basic principle of SVM forecasting algorithm Based on the statistical learning theory, Support Vector

Machine (SVM) algorithm is a kind of novel machine learning method compared with Neural network’s heuristic learning mode, which is implemented with a great deal of experience and of a more rigorous theoretical and mathematical foundations[10]. The basic idea of SVM is applying the kernel function to nonlinearly map the training set from the input space to a high-dimensional space, solving convex optimization problems (typical quadratic programming problem) in the high-dimensional space to get the global optimal solution [11].

The training set can be expressed as{( , ), 1,2,..., }i iy i l=x , and 1 2[ , ,..., ]i i i T

i dx x x=x , which is the i-th input column vector of training sample, iy is the corresponding output value. The regression problem is to find a mapping from the input space to the output space, f : dR R→ , ( )f y=x . For linear problems, SVM regression function can be expressed as follows [1]:

( ) ( )y f b= = ⋅ +x w x (1)

The regression function was established by minimizing the objective function as follows [2]:

2

1

1min [ ( )]2

, 1, 2,...,s.t.

0, 0

l

i ii

i i i

i i i

i i

C

y b i ly b

ξ ξ

ε ξε ξ

ξ ξ

∗

=

∗

∗

⎧ + +⎪⎪⎪ ⎧ − ⋅ − ≤ + =⎨

⎪⎪ − + ⋅ + ≤ +⎨⎪ ⎪ ≥ ≥⎪ ⎩⎩

∑w

w xw x

(2)

Where iξ and iξ ∗ are the slack variables, ε is the insensitive loss function, and C is the penalty factor.

The above formula can be converted to dual form by introducing Lagrange multipliers as follows [3]:

* *

1 1

* *

1 1

*

1

*

1max [ ( )( )( )2

( ) ( ) ]

( ) 0s.t.

00

l l

i i j j i ji j

l l

i i i i ii i

l

i ii

i

i

y

CC

α α α α

α α ε α α

α α

αα

= =

= =

=

⎧ − − −⎪⎪⎪

− + + −⎪⎪⎨

⎧⎪ − =⎪⎪ ⎪⎪ ⎨ ≤ ≤⎪ ⎪⎪ ⎪ ≤ ≤⎩⎩

∑∑

∑ ∑

∑

x x

(3)

For nonlinear problems, we can nonlinearly map the training set from the original input space to a high-dimensional space by adopting the kernel function to replace the dot product, which can be described as follows [4]:

*

1( ) ( ) ( , )

l

i i ii

f x K bα α=

= − +∑ x x (4)

Where ( , )iK x x is the Gauss radial basis function as follows [5].

2

2( , ) exp(- )iiK

σ−

=x x

x x (5)

Where C and 2σ are the key parameter in SVM model, respectively.

B. SVM forecasting model for spare parts inventory 1) Characterizing attributes of sample set in SVM model

Based on the characteristics of distribution network equipment, distribution network operation experience and the spare parts historical demand, four characterizing attributes are considered for the SVM forecasting model in this paper, as below.

1 2 3 4[ , , , ]i i i i Ti x x x x=x (6)

Where 1x means spare parts history demand for repair,

2x is repair schedule, 3x is operating environment of distribution network equipment and 4x means the failure rate of equipment. The four attributes can be specified in details as below.

a) The hisitorical demand data of spare parts for repairing: The historical demand data of each type material in each month are got through gathering statistics on outgoing record for the repair material.

b) repair schedule: The demand of repair material for a certain period is closely tied to overhaul and repair schedules. The spare parts demand will increase during the repair schedule period. The paper quantizes the attribute 2x

by monthly repair schedule, assigning 2x as 1 when there has repair schedule in the month1,or 2x is 0.

c) Operating environment of distribution network equipment: the electricity equipment undertakes different loading rates under different operating environments. The harsh operating environment would lead to equipment failure rate increased, resulting in the demand of spare parts increasing. This paper take the monthly maximum temperature to quantify this index as follows [7].

3 2

0 1515( ) 15

20

Tx T T

<⎧⎪= −⎨ ≥⎪⎩

(7)

d) Failure rate of distribition equipment: the higher the distribiton equipment failure rate, the greater demand for the equipment spare parts. The failure rate of equipment is quantified by summarizing the scale of distribution network equipment and the number of failure caused by various faults and defects.

2) Spare parts demand forecasting process based on SVM The flow chart of spare parts demand forecasting based on

SVM is shown in Figure.2.

Quantize the characterizing attributes

Construct the training samples

Train the SVM forecasting model

Input the model parameters

Meet the accuracy requirement

Optimal parameters of SVM model

Get the forecasting results

Save the SVM forecasting model

Increase the training samples

Figure.2 The flow chart of spare parts demand forecasting based on SVM

IV. SPARE PARTS INVENTORY QUOTA The different inventory quota models are established

respectively for spare parts of Class A and Class B in this section.

A. Fixed order quantity model Fixed order quantity (FOQ) model is the “event-driven”,

that is, whenever the inventory fell to a certain level, the spare parts will be ordered with a fixed quantity. The order may occur at any time, so it is mainly determined by the spare part demand. For FOQ model, the warehouse keeper must

continuously monitor the remaining inventory and refresh the inventory record to judge whether the inventory has reached the reorder point.

It is necessary to closely monitor the inventory of Class A for their importance, so FOQ model is suitable for setting the inventory quota for spare parts Class A. On one hand, on the premise of meeting the spare parts demand, the expensive spare parts of Class A should be maintained in the lowest safe stock level; on the other hand, a certain safety inventory can reduce the impact of the prediction inaccuracy and supplier delivery delay.

Here assuming that the spare parts demand obey normal distribution, the mean value is d, standard deviation is σ , the lead time is LT, then the safety inventory can be calculated as follows.

D LT d= ⋅ (8)

D LTσ σ= ⋅ (9)

DSS Z Z LTσ σ= ⋅ = ⋅ ⋅ (10)

Where D is the average demand during the lead time, Dσ is the standard deviation of demand during the lead time, SS is the safety inventory, ZZ is the safety factor.

Reorder level (ROL) is equal to the sum of the safety inventory and the demand during lead time.

ROL D SS LT d Z LTσ= + = ⋅ + ⋅ ⋅ (11)

The economic order quantity model which considering ordering cost, carrying cost and material purchasing cost is used to calculate the order quantity as following equations (12) and (13).

12

yy

D STC Q H C D

Q⋅

= + ⋅ + ⋅ (12)

Where yD is the annual demand, S refers to the ordering cost of each order, Q means the per order amount, H is the carrying cost of the unit material, C is the purchasing cost of the unit material, and TC means the annual total cost.

The fix order quantity is calculated by differentiating the annual total cost, of which result is shown as below.

2 yD S

QH

⋅= (13)

B. Periodic review model The periodic review model is the “time-driven”, that is,

the orders occur at regular intervals with different amount. According to the actual demand, the periodic review model adopts the different orders at regular intervals to offset the effects of the uncertainty factors. Adopting this method, the actual inventory levels would be checked regularly, periodically replenishing the stock and keeping the inventory above the target level.

For class B of the spare parts, the paper applies the periodic review model to calculate the inventory quota due to their high demand and low prices. According to different inspection cycle, the class B can be further divided into Class B1 with review period at month and Class B2 at one quarter.

The target inventory level can be calculated as follow function.

( ) ZTSL d T LT T LTσ= ⋅ + + ⋅ ⋅ + (14)

Where TSL is the target inventory level, T is the inspection cycle.

V. CASES STUDIES This paper takes the distribution network spare parts

inventory of a power supply enterprise in Guangdong as a practical example, verifying the proposed methods.

Firstly, we apply the ABC method to classify the spare parts inventory. The classification principles and results are shown in Table I and Table II.

TABLE I. CLASSIFICATION PRINCIPLES OF ACTIVITY BASED CLASSIFICATION FOR SPARE PARTS

Category Cumulative percentage of spare parts inventory (%)

Cumulative percentage of inventory cost (%)

Class A 0%一 41% 0%一 83% Class B1 41%一 81% 83%一 98% Class B2 81%一 100% 98%一 100%

TABLE II. CLASSIFICATION RESULTS OF ACTIVITY BASED CLASSIFICATION FOR SPARE PARTS

Spare parts

Cumulative percentage of spare parts

inventory (%)

Cumulative percentage of

inventory cost (%)

Category

SF6 load switch cabinet 12.35 38.47 A High voltage cable 18.52 59.75 A

Column circuit breaker 27.16 73.58 A Oil-filled transformer 40.74 82.81 A Outdoor switch box 45.68 86.03 B1

Low-voltage switchgear 53.09 89.24 B1 Dry-type transformer 56.79 92.05 B1 Box-type transformer 61.73 94.75 B1

Low tension wire 71.60 96.37 B1 Cable accessories 80.25 97.48 B1 Low-tension cable 85.19 98.16 B2

Outdoor low voltage distribution box 87.65 98.80 B2

Column load switch 90.12 99.42 B2 Overhead insulation-

covered lines 92.59 99.80 B2

PT 93.83 99.93 B2 Steel core aluminum

stranded wire 96.30 99.97 B2

Cement pole 100 100 B2

The SVM forecasting model is adopted to predict the spare parts demand based on the demand data of the power supply enterprise from 2005 to 2013. And then this paper

takes the column circuit breaker as example to verify the accuracy of the proposed model.

The parameter selection of C and 2σ for SVM model is of a great influence on forecasting accuracy [12-13]. The penalty factor C determines the complexity of model and the punishment for the prediction bias, which can be selected according to the characteristics of the sample data and forecasting models. The setting of parameter 2σ too large in the radial basis function will cause the SVM model under-fitting, while too small value of 2σ would lead to the problem of over-fitting.

In order to quickly determine the reasonable interval of the parameters, the particle swarm optimization algorithm (PSO) and genetic algorithm (GA) are used to optimize the parameters, among which the population and iterations times of PSO and GA are both set as 20 and 200, respectively. The value range of C and 2σ are set as [0.1, 100] and [0.01, 1000], respectively. Finally, the grid traversal algorithm is adopted for two dimensional optimization after obtaining the approximate parameter space by PSO and GA algorithm. The process and results of the parameters optimization in this forecasting example of the column circuit breaker are shown in Table III.

TABLE III. SVM PARAMETER OPTIMIZATION RESULTS

Parameters optimization stage C 2σ PSO optimization 4.214 13.93 GA optimization 4.539 12.67

Grid traversal optimization 3.764 13.62

In addition, the paper adopts the BP neural network forecasting algorithm to compare the forecasting accuracy of SVM model. The forecasting results of the column circuit breaker are shown in Figure.3 and Table IV.

Figure.3 The 2013 prediction results of the column circuit breaker

TABLE IV. THE 2013 PREDICTION RESULTS OF THE COLUMN CIRCUIT BREAKER

Model Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.SVM 5 1 5 9 12 4 13 10 7 0 4 5 BP 4 2 6 7 6 6 8 7 7 1 1 3

Actual demand 4 0 4 10 10 4 12 8 6 0 2 6 As can be seen from the table IV, the SVM forecasting

model shows more accurate than BP method. The ratio of

occurrence accuracy (ROA) and the mean squared error (MSE) of SVM model are 91.67% and 1.58 respectively, while the two indices of BP model are 83.33% and 5.5. The BP neural network is based on the gradient descent method to optimize the weight, of which unusually plunges into local optima [14]. On contrast, the essence of SVM forecasting algorithm is to solve the quadratic programming problem with linear constraint, according to equation (3) to (5), generally, the traditional methods for solving linear optimization problem is able to get a satisfactory solution, avoiding local optima. In addition, the demand data of distribution network spare parts in the Power supply enterprise is too limited, and many studies suggest that SVM is suitable for small sample prediction problem, because SVM algorithm can also find out the optimal hyperplane even with small sample. However, BP neural network algorithm need many historical demand data to train the model.

Finally the representative items of each class are selected for inventory quota calculation as samples. The Averages and standard deviations of the spare parts introduced in Part IV can be calculated based on the demand forecasting results. Here selects SF6 load switch cabinet (Class A), cable accessories (Class B1) and column load switch (Class B2) as the examples.

The averages and standard deviations of SF6 load switch cabinet is 13.58 and 9.90 according to the forecasting results, the lead time is 1 month, the ordering cost of each order is 800 Yuan, the carrying cost of the unit material is 280 Yuan, the service level is 99.9% and Z is 3.The quota results of SF6 load switch cabinet are shown as below.

3 9.90 1 30DSS Z Z LTσ σ= ⋅ = × × = × × ≈ (15)

1 13.58 30 44ROL LT d SS= × + = × + ≈ (16)

2 2 12 13.58 800= 31

280yD S

QH

⋅ × × ×= ≈ (17)

The averages and standard deviations of cable accessories is 10.21 and 10.06, the lead time is 1 month, the inspection cycle is 1 month, and the service level is 99.9%. The quota results of cable accessories are shown as follows.

3 10.06 2 43DSS Z Z T LTσ σ= ⋅ = ⋅ ⋅ + = × × ≈ (18)

( ) 10.21 2 43 64TSL d T LT SS= ⋅ + + = × + ≈ (19)

For the column load switch, all of the parameters are the same to cable accessories (B1) except for the inspection cycle. According to the periodic review model for Class B2, the inspection cycle of column load switch is 3 months. We can get the results from formula [20] to [21].

3 0.83 3 1 5DSS Z Z T LTσ σ= ⋅ = ⋅ ⋅ + = × × + ≈ (20)

( ) 0.46 4 5 7TSL d T LT SS= ⋅ + + = × + ≈ (21)

VI. CONCLUSION The distribution network spare parts inventory demand

forecasting method based on SVM is proposed in this paper

and the column circuit breaker is taken as a practical example to verify that the accuracy of the SVM forecasting model is superior to BP model. In addition, the spare parts are divided into Class A, Class B1 and Class B2 through the activity based classification, and then the inventory quota method based on the different types of inventory management model is put forward and some typical spare parts of different classes are selected as example of inventory quota calculation. The calculation results of actual distribution power network show that the proposed SVM model is of high prediction accuracy, providing a simple and effective solution for inventory equipment management of electricity equipment.

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