An Algorithm and Implementation Based on an Agricultural EOQ Model

With the improvement of living quality, the agricultural supermarket gradually take the place of the farmers market as the trend. But the agricultural supermarkets’ inappropriate inventory strategies are wasteful and inefficient. So this paper will put forward an inventory strategy for the agricultural supermarkets to lead the conductor decides when and how much to shelve the product. This strategy has significant meaning that it can reduce the loss and get more profit. The research methods are based on the inventory theory and the EOQ model, but the authors add multiple cycles’ theory to them because of the agricultural products’ decreasing characteristics. The research procedures are shown as follows. First, the authors do research in the agricultural supermarket to find their real conduction, and then put forward the new strategy in this paper. Second, the authors found out the model. At last, the authors search the specialty agriculture document to find the data such as the loss rate and the fresh parameters, and solve it out by MATLAB. The numerical result proves that the strategy is better than the real conduction in agricultural supermarket, and it also proves the feasibility.

utility or loss of marginal value of a commodity that results in decreasing usefulness from the original one.Several researchers studied a deteriorating inventory system in recent decades.In recent year, many scholars dedicated to researching the EOQ model of perishable products which is based on the freshness and the loss rate of the products.Wu [7] discussed an EOQ model with time-varying demand, considering deterioration and shortages.Lietal [8] analyzed views on inventory management for deteriorating items.Mishra and Singh [9] developed an inventory model with constant rate of deterioration and time-dependent demand.Yan et al [10] developed an integrated inventory model of production for a deteriorating inventory item.Balkhi [11] presented an optimal ordering policy for deteriorating items based on different supplier trade credits and considered a finite horizon.The Freshness and loss rate that determines the EOQ model of perishable products is different from the basic EOQ model.
The main strategy presented in this paper is several shelves for one ordering.When the manager purchases a number of agricultural products, or just shelves a section, others will be stored into the refrigerators to keep them fresh and reduce the loss.When the remains of the shelved section are few or sold out, then take out another section from the refrigerators until all the products are taken out.In the strategy, there are two stock environments leading to two pairs of freshness and loss rate which make the inventory system difficult to control.Several papers have made some research on several periods of agricultural products inventory strategy.Changyuan Yan built a model which is related to integration of multiple period inventory [12] ; Bing Luo [13] and Po-Chung Yang [14] set up a perishable product EOQ model considering backlogging rates, demand and purchase price; Chen considered the strategy of twice shelves.When the first batch of agricultural products is with a low degree of freshness after a sales period remains few, the managers abandon the remains and shelve the second batch [15] .Singhetal considered perishable items with power demand and partial backordering [16] .Mishra and Singh put out an inventory ordering policies of delayed deteriorating items based on permissible delay in payments [17] .The documents mentioned above are involved in considering not only one period, however, no one considered the strategy of several shelves in a period which can reduce the decay of quality and quantity when the managers store most of agricultural products in most of time.The objective function is the revenue maximization.
In this paper, we proposed an agricultural products inventory strategy of several shelves for one ordering, and built a deterministic agricultural products inventory model assuming that this inventory strategy has better practical guiding significance for the agricultural supermarket.The organization of the paper is shown as follows.

MATHEMATICAL MODELING AND ANALYSIS
The mathematical model considering the integrated raw material, production and distribution is developed based on the following assumptions: (a)The demand within the scope of the supermarkets' service is only decided by the freshness of the agricultural products shelved.
(b)The agricultural products after purchased are net worth.They are not needed to be cleaned and selected and other processing.
(c)The replenishment for buyer is instantaneous.
(d)Shortage and returns are not allowed (e)Deterioration of the agricultural products is considered only after they have been received into the inventory.
(f)The freshness function is exponentially distributed, and the loss rate is a constant.
The parameters are set as follows: is m q .And the agricultural products which have not been shelved will suffer from the decay in the refrigerator more slightly than on the shelves.After the agricultural products on the shelves are at a certain level, there is not much left but with low freshness, and abandon the remains (Its amount is r q ).Managers can decide the " m q "and " r q "to control the inventory.
The demand function of the n-th product shelved is Put them into the function, and obtain a recurrence relations of each n t which are related to m q and r q .
2 1 T E E

T T T T E T E
This is the most important equation in this paper which establishes the link between the m q , r q and the time node to shelve.In other word, managers just need to decide how many to shelve and how many to abandon.From Figure 1 it can be analyzed that in the system of refrigerator environment and the shelves environment, freshness of the agricultural products which is firstly shelved is determined (because they are just shelved and completely fresh).Then just decide how many to shelve, and it is to be controlled that how this curve goes.Then the manager should decide when to replenish the second batch of "qm".This moment should be decided by "qr".When the inventory level is reduced to "qr", they make the decision.Since the inventory function curve of the first batch is known, "t1" is determinate."t1" is just the intersection of "qr" and the inventory function of first batch.The second batch of agricultural products has been stored in the refrigerator for "t1", so their freshness is determinate.Just like the first batch, the whole function curve can be decided when the "qm" and "qr" are decided.Just as the presented equation, all the "tn" can be solved with the decided "qm", "qr" and "t0=0"."n" is the number of shelves which cannot be too large, and it can increase the decay and the inventory costs through increasing the storage time.From the fact, the sales time is limited by the operation of the agricultural supermarket.So set n [1,10] in the solution section as follows.(1 ) , because the n-th batch which is shelved will be stored in the refrigerator for "tn-1".The inventory cost on the shelves is 2) Purchase cost.The n-th batch of agricultural products has suffered for "tn-1", and its number is  ( ) The final model is shown as follows: max ( , , )

Parameter setting
Referring the document [18] , [19], the parameters are set as follows:

Algorithm
The recursive relationship equation is an exponential equation with parameters, which "tn" cannot be expressed by "qm" and "qr".So referring to the document [20] and [21], we use Taylor formula to deal with the exponential.The solution is shown in Figure 2.

ANALYSIS
The result is presented that when "n=5", "qm=396" and the "qr=19.656",the subjective function is maximized.When "n=1", the model is degraded to the traditional model.And from the result, it can be seen that this strategy of several shelves for one ordering is better than the traditional strategy.

CONCLUSION
Based on the traditional QOE model, this paper puts out an innovative strategy of several shelves for one ordering, and then sets up the corresponding model.The last section is the solution.Although there are many innovations in this paper, there are many shortcomings as well.The opening time of agricultural supermarkets is regular, which is from 9:00 to 19:00, but it didn't be taken into consideration.And the approach of the Taylor formula is improper, it will be improved in the future study.The result is shown as follows:

K
θ freshness pararmeters on the shelves θ freshness pararmeters in the r β the loss rate on the shelves β the loss rate in the r the agricultural on the shelves h unit inventory costs of the agricultural in the r traditional demand function of the perishable products is (t) t D ye T , called t e T freshness.And the differential equations related to the invention function are ( ) -(t)-( ) =Q (Q is the purchase volume) and I(T)=0 (T is the sale period).Almost all the inventory theories of agricultural products are based on the research foundation.But in the strategy of this paper, the agricultural products are totally shelved n times, each amount Web of Conferences MATEC 01054-p.2

4 )
Labor cost.It includes the fixed labor cost and the variable labor cost: m C+rnq C is fixed labor cost r is variable labor cost 5) Sales revenue.