Cost Optimization of Supply Chain of Green Agricultural Product Basing on Particle Swarm Optimization

As the basic industry, the modernization of agriculture has the advantage with low cost and instant effect, which is an important choice for the cities. However, the irrational cost control of supply chain makes a great contribution to the price rising of green agricultural products. On the basis of analysing the cost structure of supply chain, this study structures the target cost model and gives an optimizing solution to the problem based on Particle Swarm Optimization. Moreover, this study takes one of green agricultural product supply chains in China for empirical research to examine the above optimizing method, the results shows that the target cost of green agricultural product supply chain can be obtained by the method of improved Particle Swarm Optimization.


Introduction
As one of typical business models for the cooperation between investors and local farmers, contract farming is the main development direction of agricultural production, which is supported by great majority of government departments in the world.However, there are a great deal of problems existing in various aspects of cost control owing to the irrational supply chain management of green agricultural product, which lead the market price to remain an unbearable level.In the current inflation era, it is urgent to explore a scientific and practical method of the cost control of green agricultural product supply chain.Therefore, according to the development model of contract farming at present, this paper aims to structure the target cost model of green agricultural product supply chain and give an optimizing solution to the problem based on Particle Swarm Optimization, which can offer the reference for the development of green agriculture in the world.

Cost of Supply Chain
The operation mode of green agricultural product supply chain is shown in Figure 1.As shown in Fig. 1, the market demands are the driving force of the whole supply chain.On one hand, the information flow of green agricultural product supply chain proceeds from the customer's demand, and transmits to every link reversely until the peasants receive the order information.On the other hand, as the main material flow of green agricultural product supply chain, green agricultural products transmit toward the consumers along the supply chain.Usually, the cost of supply chain is equal to the total cost of all activities including material procurement, production, transportation and consumption.The cost of green agricultural products supply chain is relatively complicated owing to it is relatively strict with the quality and shelf life of the final products [1].This research will divide the cost of green agricultural product supply chain into six parts, namely information processing cost, direct production cost, indirect production cost, quality control cost, transaction cost and time control cost.

Information Processing Cost
Due to various node enterprises of green agricultural product supply chain arrange for the production and operation in accordance with the orders, the whole supply chain is relatively strict with the ability of information collection and processing, which brings relatively high information processing expenses [2].Usually, the higher information sharing degree during supply chain enterprises often mean the higher information processing cost, the formula weighing information processing cost of green agricultural product supply chain is shown in Equation (1).
Among them, p stands for the market occupation rate of the products, β stands for the information sharing degree, n stands for the quantity of batches, shows the information processing expenses of unit batch.
Among them, p stands for the market occupation rate of the products, β stands for the information sharing degree, n stands for the quantity of batches, f shows the information processing expenses of unit batch.

Direct Production Cost
This kind of cost is the expense in the production and processing activities of green agricultural products, which not only includes the cost of raw materials, but also includes the charges of equipment depreciation and labour cost.The formula of calculating the direct production cost of unit product is shown in Equation (2).
Among them, P*stands for the expenses of unit raw materials (include the expenses of seed and fertilizer, etc.) and labour cost of unit product, which is a fixed value; C* stands for the value of the equipment; n•m stands for the average processing quantity of equipment within its life cycle.Therefore, there is an inverse proportion relation between the batch counts n and production quantity m of every batch.

Indirect Production Cost
This kind of cost is the expense of various auxiliary activities when carrying on the production activities of green agricultural products, such as relevant administrative expenses, transportation cost of raw materials and products, etc.The formula of calculating the indirect production cost of unit product is shown in Equation (3). 3 1 Among them, f stands for the average expenses of each management activity of unit product, n1 stands for the frequency of management activities needed by unit product; F stands for the total transportation cost of every batch of unit mileage, m stands for the quantity of every batch, S stands for the mileage of the transportation.

Product Quality Cost
Due to the strict requirement for the product quality, the value of green agricultural products would not be realized until the products meet all quality requirements in the reprocessing activities of the products.Therefore, it is necessary to monitor and control the quality of green agricultural products before they are sold, the cost brought by these activities is just the product quality cost, meanwhile, the product quality cost still includes the losses caused by unqualified quality [3].Thus, the calculation formula of the quality cost of green agricultural products is shown in Equation (4).
Among them, QJ C stands for the testing cost of unit product; QN C stands for the internal fault cost of unit product (include the rework cost); α stands for the defective product rate; ĉ stands for the price of unit product.

Transaction Cost
This cost refers to the cost brought by transaction activities between various node enterprises or between internal enterprises and external enterprises of green agricultural product supply chain .Usually ,there is high information sharing degree and low transaction cost between the nodal enterprises with a long-term cooperation [4].Therefore, the formula which weighs the transaction cost is shown in Equation (5).

(1 )
Among them, β stands for the information sharing degree, namely the cooperative degree between enterprises; c is average default loss of every batch of products.

Time Control Cost
There is certain quality guarantee period for every green agricultural product, so it will suffer the loss of the decline in the quality if taking excessive time to produce, transport or store the green agricultural product for some unexpected factors [5].Therefore, it is necessary that time is controlled strictly in the course of producing, transporting and selling green agricultural products, which will bring certain cost accordingly.Usually, the formula which weighs the time control cost is shown in Equation ( 6).
Among them, t1 stands for the actual growth time of agricultural products, t is the average growth time of agricultural products; t2 stands for the actual sales time of agricultural products, t is the average keeping time of agricultural products; γ stands for the actual spoilage rate of green agricultural products, ĉ is the actual market price of this kind of agricultural products.

Target Cost Model
According to the above cost analysis, the target function of the target cost optimization model of green agricultural product supply chain can be constructed by working out weighted sum of the above cost.
is a fixed value.

Solution Of Target Cost Model
Due to the excessive non-linear variables and constraints in the above optimizing model, it is difficult to obtain the optimum conclusion by general solving methods, so the model of improved Particle Swarm Optimization (PSO) will be used to solve the problem in this research.In computer science, PSO is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality [6].The main methods in the model are detailed.
Firstly, determine weight factor ω: It can be found out from above-mentioned formula that the weight factor influences the searching velocity of the particle mainly.The larger value of ω means the wider search-space of the particle.According to the research experience, a better searching ability can be obtained when the value of ω is controlled within [0.9, 1.2].Meanwhile, ω is assigned a value of 1 when there is a small maximum velocity νmax, and ω is assigned a value of 0.9 when there is a large maximum velocity νmax.We can also carry on adaptive adjustment according to the number of iterations, the basic formula is Equation (8).according to the experience [7].Thirdly, determine particles number and searching dimensions: Generally speaking, searching dimensions keep up with the dimensions of solution space, and the determination of particles number should take account of the actual conditions, the number of particles is less than 100 for the simple problems while it is more than 100 for the complicated problems.
Besides, in order to avoid falling into the predicament of local extremum, the algorithm should be carried on a variation processing, here two problems of variation time and variation method should be paid close attention to.
Firstly, determine variation time: We can carry on a variation processing to the particles swarm when the algorithm is convergent but not obtain global extremum, namely meet two conditions of σ2 < λ2 and fg -ft > λ at the same time, among them λ is the precision of algorithms, fg is the fitness of the particle when the algorithm obtains global extremum, ft is the value of global extremum the overall situation which is obtained according to the experience or the theoretical research.
Secondly, determine variation method: The method of velocity upgrading will mainly be adopted when the particle is found out to lie in local extremum instead of global extremum, the formula of velocity upgrading is Equation (9).
The variation operator is added to this formula of velocity variation, here * k values 0 when the algorithm starts, and it values 1 when the particle swarm falls into local extremum.According to the experience, the value of the velocity influence factor μ is shown in Equation (10).min ,1 It can be found out that the value of μ depends on the disparity between actual value and theoretical value of the global extreme fitness of the algorithm, there will be large velocity variation if the disparity is relatively large, so the global search can be realized; There will be small velocity variation if the disparity is relatively small, so the further improvement of the optimizing precision can be realized.

Data and Empirical Analysis
As a modern agricultural scientific & technical corporation in China, Wuhan Justeasy Agricultural Science &Technologies Co., Ltd is devoted to the supply of green agricultural products for the urban population, which constructs a modernized agricultural product supply chain made up of planting base, processing factories, supermarkets and consumers.The planting base can plant two hectares of green agricultural products on each batch at most, the growth cycle of vegetables is three months on average, there is 600 yuan / mu cost of seeds, fertilizer and labor on average in growth stage, the logistics cost from planting base to the vegetables processing factory is 170 yuan on each batch, and every batch can transport 6.5 tons of vegetables at most.The processing capacity of the vegetables processing factories is 730 kilograms per day in maximum volume, the fixed processing cost of each ton vegetables is 350 Yuan, the logistics cost from processing factories to the logistics centre is 210 Yuan on each batch, and every batch can transport 4.5 tons of vegetables at most.According to the market of green vegetables at present, it can be known that are the largest sales of this vegetables is 2.3 tons per day, the greatest stock of the vegetables processing factories is 8 tons, the greatest quantity in short supply allowed is 2 tons.Meanwhile, the greatest stock of the logistics centre is 4 tons, and its greatest quantity in short supply allowed is 1.5 tons.
We adopt the method of improved PSO algorithms to obtain the target cost of the abovementioned green agricultural product supply chain.According to the experience, let the weight factor ω=1.0, let the accelerate factor c1= c2=2, set the number of particles N=100.According to the characteristic of the above cost analysis, we can let the searching dimensions be 6, the initial position of every particle is of random distribution, and provide the initial velocity of every particle within [0.7, 0.9] at random.
With the help of the programming software of Matlab 7.0, the result of cost optimization can be drawn that the total cost of the green vegetables each kilogram is: C=02316+0.5208+0.1077+0.1729+0.2961+0.6281=1.9617(yuan / kg) Seeing that the actual market price of the green vegetables is 5.4 yuan / kg, more than 1.5 times of profit can be obtained through the above cost optimization.
According to the improved PSO algorithm, the curve of the relation between evolution generations and particle fitness of the cost optimization of green agricultural product supply chain is shown in Figure 2.
Figure 2 Relation curve between evolution generations and particle fitness.

Measures of Cost Control
After confirming the target cost of supply chain, various activities of supply chain need to be optimized and controlled in order to get the actual cost moving toward the target cost.

Encourage Information Sharing
Win-win cooperation can be realized when nodal enterprises or farmers can obtain the market information timely and effectively.The profit incentive measures can be taken properly to improve the enthusiasm of information sharing, in this way, which can also reduce the sharing cost brought by the mandatory measures to a certain extent.

Improve the Transaction Efficiency
The transaction cost and risk can be reduced effectively by establishing the long-term cooperation relation during various members of supply chain.Meanwhile, credit rating should be implemented, the members of supply chain with high credit degree should be encouraged to obtain more orders; On the contrary, the members with poor credit degree should suffer the loss of reducing the cooperative chance.

Standardize the Procedure
In order to reduce the losses brought by the subquality products and improve the efficiency of quality inspection of green agricultural products, the advanced testing equipment and instruments should be applied rationally; meanwhile, sampling process should also be standardized and rationalized to avoid the cost increase.

Introduce Advanced Technologies
On the premise that product quality can be guaranteed, the rational adoption of advanced planting technologies can shorten the Marketing cycle of the products effectively; meanwhile, the advanced production and fresh-keeping technologies can be adopted to extend the freshness period of the products.The above measures can reduce the time control cost of green agricultural products effectively.

Implement Lean Logistics
The necessary logistics integration should be implemented, and the relevant activities of packing, transporting, delivering etc. should be optimized.Meanwhile, the logistics cost can be and reduced through the batch processing, which can improve the benefit of the whole supply chain.

Conclusions
This research applies PSO algorithm to the problem of cost control of green agricultural product supply chain, and has predicted the target cost of green agricultural product supply chain.First of all, this research divides the cost of green agricultural product supply chain into six parts, namely information processing cost, direct production cost, indirect production cost, quality control cost, transaction cost and time control cost.Secondly, this study structures the target cost model and gives an optimized solution to the problem based on PSO.Moreover, this study takes one green agricultural product supply chain in China for example to verify the above method, the results shows that the method of improved PSO is practicable and effective in controlling the cost of green agricultural product supply chain.Nevertheless, PSO algorithm still has some deficiencies, it is very important to improve the algorithm further in the future research work.

Figure 1
Figure 1 Operation mode of green agricultural product supply chain.
to obtain global extremum and moderate velocity of the particle, and strengthen the searching ability, we usually let1