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The purpose of this research is to minimize the total cost of the overall system in the process of replenishment, to maximize the overall system profits. This paper regards all affiliated stores of chain supermarket as a system to do some research about the replenishment of fresh agricultural products. Then, this paper proposes the lateral replenishment strategy, analyzes its advantages, and applies the strategy thinking to the solution of the surplus or shortage of fresh agricultural products. Through the establishment of the inventory cost model, we compare the system inventory total cost between taking the lateral replenishment and deployment strategy and not using the lateral replenishment and deployment strategy, and get that there is lower total cost. Through the establishment of lateral replenishment transportation model, the optimal dispatching scheme between the surplus supermarket and the shortages supermarket is given. And then, the sensitivity analysis presents the variable range of the fresh agricultural products increment and decrement that does not affect this optimal dispatching scheme. This paper can provide a reference for the chain supermarket to deal with the shortage or surplus of fresh agricultural products so as to improve sales margins of agricultural products, to reduce the total inventory costs of the whole the chain supermarket system, and to improve the customer service levels.

With the improvement of living standards, there are increasingly high requirements for fresh agricultural products. People attach more importance to the quality, variety, nutritional value, and many other factors of fresh agricultural products. When consumers buy fresh agricultural products, the fresh, green, organic and healthy are the important factors to be taken into consideration. In China, the main sources of the supply of fresh agricultural products include farmers’ markets and supermarkets. Compared with farmers’ markets and others, supermarkets are more secure in fresh quality and security. Unified procurement, processing, distribution and strict checks of various aspects can meet the special requirements in the circulation with irreplaceable advantages. Therefore, chain supermarkets become the primary place for consumers to buy fresh agricultural products. However, as more and more people choose to go to the chain supermarket to buy fresh agricultural products, the uncertainty of demand for fresh produce leads to the inaccurate forecasts of supermarket for fresh agricultural products demand. Thus, to a certain extent, this causes the stockpiles or shortages of fresh agricultural products of supermarket, affects the consumer demand for fresh agricultural products, and finally causes some damage of the supermarkets interests. Therefore, researching the transverse replenishment policy of chain supermarkets fresh agricultural products can not only ensure the individual needs of consumers for fresh produce, improve customer satisfaction, but also reduce the inventory costs and improve the profits of supermarket.

Some scholars previously have done certain related researches about the shortage, surplus, replenishment of fresh agricultural products. Chaaben Kouki et al. (2015) [

Previous scholars have made some researches on inventory management and replenishment strategy of the chain supermarket fresh agricultural products, but only focused on individual supermarkets to find the optimal strategy to achieve a certain type of supermarket inventory management and not to apply the lateral replenishment strategy to the inventory management. This paper will regard all sub supermarket stores of the chain supermarket as a system and apply the lateral replenishment strategy to the inventory management of the fresh agricultural products. And the optimal replenishment strategy of system will advance to the optimal replenishment strategy of a single-goods store. This research not only optimizes the inventory cost and restocking fee of fresh agricultural products of each store, but also lays more emphasis on the realization of the optimal inventory replenishment transfer cargo policy of the entire system. On the basis of our research, through the store inventory control and supervision, the chain supermarket can effectively minimize the whole inventory costs of fresh agricultural products and improve the profits and margins of the whole system.

Lateral replenishment thinking applied to the replenishment of fresh agricultural products of the chain supermarket is a relatively new approach. That conduct lateral replenishment of fresh agricultural products between supermarket stores is when there is shortage, or surplus of supermarket stores, appropriate to transport the surplus fresh agricultural products of the supermarket stores to the shortage fresh agricultural products of the supermarket stores in some period of time, thus timely and effectively solving the shortage, or surplus problems of fresh agricultural products of the supermarket stores. Through the lateral replenishment, it can have the following advantages:

1) Regard all sub supermarket stores of the chain supermarket as a system. When there is shortage or surplus of fresh agricultural products of some supermarket stores, then the shortage of the part of supermarket stores do not represent the shortage of the chain supermarket system, the surplus stock of the part of supermarket stores can not represent the surplus of the chain supermarket system. The lateral replenishment strategy can optimize inventory adjustment fresh agricultural products from the perspective of system.

2) Since all sub chain supermarket stores are unified managed by the headquarters, there is not a problem that unstable partnership occurs between the sub chain supermarket stores.

3) The replenishment price of fresh agricultural products is relatively stable, which can be controlled between the purchase price of the distribution center and the selling price of the supermarket stores. And it can be priced by headquarters to reduce the replenishment costs.

4) When the sub supermarket stores transfer fresh agricultural products from a store to another store, the distance between them should be taken into consideration. Therefore, transfer goods between stores can improve arrival rate. For the supermarket stores out of stock, the transport costs of transfering fresh agricultural products from other supermarket stores are much lower than the supply center. And for small quantities of fresh agricultural products out of stock, transfer fresh agricultural products from other sub-goods supermarket stores will be more convenient. This can help short the replenishment time, to a certain extent, improve customer service levels.

5) After adding lateral replenishment, fresh agricultural products between the supermarket stores will be allocated optimally to improve the overall profits. Also, this can reduce profits loss of the shortage situation when the supermarket stores take no notice of the shortage situation, and this can reduce profits loss of the surplus situation when the supermarket stores treat the surplus fresh agricultural products at discount prices.

In summary, the lateral replenishment has more advantages. It can be used in supermarkets fresh agricultural products replenishment, but it needs to combine the use of traditional replenishment strategy so as to play their strengths. Because it cannot exclude the situation that the inventory shortage or excess of the entire chain supermarket will occur, the lateral replenishment of fresh agricultural products between stores needs to combine traditional way to provide services of the chain supermarket.

Because the distribution center is relatively far from the supermarket stores, or due to the certain small demand of fresh agricultural products not up to the required amount of the distribution center, the distribution center is not to carry out the distribution, resulting in the shortage situation of fresh agricultural products. Because when some supermarket stores predict the demand of fresh agricultural products, there is large deviation, which results in excessive accumulation of fresh agricultural products. For the cases above, the lateral replenishment will be applied to supermarket stores, which will be more rational to use the resources fresh agricultural products to further reduce losses and reduce costs.

The purpose of lateral replenishment of the chain supermarket fresh agricultural products is to make the optimal allocation of reasonable inventory of the supermarket fresh agricultural products, to minimize the total costs, and to get the entire optimal system. To solve the issue of the replenishment of the fresh agricultural pro- ducts between the chain supermarket stores, the lateral replenishment inventory model can be established. On the one hand, to make the whole system to the minimum inventory costs, on the other hand, to make optimal replenishment strategies of all stores to the lowest cost.

Assume that the operational status of each supermarket store is same. The demand of fresh agricultural products is independent and is in keeping with poisson distributions. The order lead time of fresh agricultural products is same and unchanged. All supermarket stores apply (s, S) storage strategy. When the stock fresh agricultural products are less than s, then they restock to S. In the case of each supermarket stores appear out of fresh agricultural products, only when the existing inventory below the safety stock quantity, there is replenishment applications from the supermarket stores, which stock stores is greater than the safety stock.

The symbols and meanings involved in the model are as follows:

1) i, j represents each chain supermarket stores, and the total number is N.

2) S_{0} represents the fresh agricultural products inventory of the chain supermarket system, S_{i} represents the fresh agricultural products stocks of store i.

3) C_{r} represents the ordering cost of fresh agricultural products of each chain supermarket stores.

4) C_{h} represents the unit time fee of fresh agricultural products of each chain supermarket stores.

5) C_{l} represents the Shortage Costs of fresh agricultural products of each chain supermarket stores.

6) C_{ij} represents the lateral transportation costs of fresh agricultural products of each chain supermarket stores, represents the average transportation cost of the chain supermarket stores i.

7) a_{i} represents probability of supermarket store i meeting the demand of fresh agricultural products with its own stocks.

8) b_{i} represents probability of supermarket store i meeting the demand of fresh agricultural products rely on lateral replenishment.

9) l_{i} represents the probability that the fresh agricultural products of supermarket store i out of stock. Because only when the fresh agricultural products of entire system is out of stock, then the fresh agricultural products of each supermarket store may is out of stock, therefore, the probability of the shortage of system fresh agricultural products: l = l_{i}.

10) e represents the expectation customer service levels of the chain supermarket system.

11) D_{i} represents the demand of fresh agricultural products of unit time of supermarket stores i; D_{0} represents the demand of fresh agricultural products of system; m_{i} represents the average demand of each supermarket store; D_{ij} represents the replenishment quantities from store i to stores j.

12) L_{i} represents the replenishment lead time of fresh agricultural products of each chain supermarket stores. It is the time that from the issue replenishment orders to the commodity storage.

Inventory costs include order costs, storage costs, lateral transportation costs, the shortage loss costs.

Order costs C_{R}: the order cost of fresh agricultural products can be represented a product by a single order costs and the total number of orders.

In the formula,

Storage costs C_{H}: the order cost of unit time of fresh agricultural products can be represented a product by the unit storage cost and the Average inventory quantities.

Because the model is based on the premise allowing out of stock, so the average inventory quantities do not include the demand quantities in the period of lead time. The average inventory quantities is

Then, get the storage costs:

Lateral transportation costs C_{T}: the ateral transportation costs is related with the average transportation costs, the average demand rate of fresh agricultural products and the probability of meeting the demand of fresh agricultural products through ateral transportation.

Throughout the chain supermarket system, there are three cases about the stock demand of fresh agricultural products: a) the fresh agricultural products of stores can be met through the original stock, then the probability is a_{i}; b) the fresh agricultural products of stores can be met through lateral transportation, the probability is b_{i}; 3) the entire supermarket system is out of stock, the fresh agricultural products cannot be met, then the probability is l_{i}. And, a_{i} + b_{i} + l_{i} = 1.

According to independent demand inventory model, in the period of order lead time, the demand of store i is D_{i} L_{i}, then:

If the system is out of stock, it does not meet the conditions of lateral replenishment. Then, the store i is out of stock in the period of optimal ordering, while other stores j is in the lead time or in the period of order cycle. And the demand is always greater than the actual stocks of stores. Then, the probability is as follows:

The lateral transportation costs of the whole chain supermarket system can be obtained from the above equation as follows:

The shortage loss costs of the whole chain supermarket system are as follows:

In summary, the inventory total cost model of fresh agricultural products of the chain supermarket system is as follows:

If there is no lateral transportation between supermarket store, the model becomes the follows:

When store i has the surplus of fresh agricultural products goods stores, the surplus that has excess safety stock, needs to be transported to the stores is out of fresh agricultural products. On the contrary, when there is shortage of store i, the store i need to make replenishment application to other stores that owning more fresh agricultural products. Assume that eventually all fresh agricultural products of the chain supermarket system is distributed to all the sub stores of the chain supermarket system, the model will be the supply and demand balance transport model. m represents the stores that has Surplus, referred to as A_{1}, A_{2}, A_{3},…, A_{m}. n represents the stores that has shortage, denoted by B_{1}, B_{2}, B_{3}, …, B_{n}. The quantities of shortage is recorded as b_{1}, b_{2}, b_{3}, …, b_{n}. s_{ij} is the transporting capacity of the chain supermarket which is transported from store A_{i} owning surplus to store B_{j} that has shortage (i = 1, 2, 3, …, m, j = 1, 2, 3, …, n). c_{ij} represents the unit transportation costs from store A_{i} to store B_{j}. l_{ij} is the distance from store A_{i} to store B_{j}, but it will be affected by traffic in the actual transportation process. If it is considered only in distance or unit transportation costs, there will be inaccurate to the distribution program of the whole system. And the traffic situation the day is not the same in each time. rij represents traffic situation coefficients from store A_{i} to store B_{j}. p_{ij} is only in 0 - 1. The more it is closer to 1, the better the traffic situation it is. On the contrary, it is worse.

Then, the lateral replenishment transportation model is established on the basis of the traditional transportation model as follows:

A supermarket is a national chain supermarket and is the large-scale retail enterprises. There are a total of seven regional chain stores in Beijing. These stores are replenished by the same fresh agricultural products distribution center. In recent years, in order to increase traffic, improve the market competitiveness of industry peers, a chain supermarket increases a significant operating proportion of fresh agricultural products in supermarkets stores, and regards the fresh agricultural products as highlights and features.

Since the distribution center is relatively far from the supermarket stores, or due to the certain small demand of fresh agricultural products not up to the required amount of the distribution center, the distribution center is not to carry out the distribution, resulting in the shortage situation of fresh agricultural products. Because when some supermarket stores predict the demand of fresh agricultural products, there is large deviation, which results in excessive accumulation of fresh agricultural products. And the fresh agricultural products cannot be sold due to the rot, then the profit margins of the fresh agricultural products will be reduced. For the cases above, the lateral replenishment will be applied to A supermarket, which will be used to solve the shortage and the surplus problems of fresh agricultural products.

The operational status of the seven chain stores is same. The demand of fresh agricultural products is independent and is in keeping with poisson distributions. The order lead time of fresh agricultural products is same and unchanged. All supermarket stores apply (s, S) storage strategy.

Related data are as follows:

1) The S_{i}, s_{i} of each supermarket store, the average transportation cost:

2) The single ordering cost: C_{r} = 1000 yuan, the inventory holding costs of a single piece of fresh produce of unit time: C_{h} = 5 yuan, the shortage loss costs of a single piece of fresh agricultural products: C_{l} = 20 yuan.

3) The demand of fresh produce stores varies every day. Criteria to the demand of a month, the average daily demand m_{i} of the store is as shown in

The above data are into the formula (1) and formula (2), then the order costs, storage costs can be obtained under the conditions of not allowing lateral replenishment.

4) The demand of fresh agricultural products is in keeping with poisson distributions: D_{i} ~ P(s_{i});

Take store 1 as example, Use the Matlab 7.0 to describe demand probability distribution of the fresh agricultural products. And the demand probability distribution is shown in

The fresh agricultural products of stores can be met through the original stock, and the probability is a_{i}. According to the equation (3) and the probability formula of poisson distributions, the

can be got. And the results are shown in

Number of stores | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

S_{i} (piece) | 550 | 580 | 480 | 460 | 520 | 500 | 540 |

s_{i} (piece) | 50 | 60 | 55 | 40 | 50 | 55 | 45 |

3 | 4 | 3 | 5 | 5 | 4 | 3 | |

L_{i} (day) | 2 | 1.5 | 2.5 | 2 | 1.5 | 1.5 | 2 |

m_{i }_{}(piece) | 55 | 80 | 60 | 70 | 60 | 50 | 65 |

Number of stores | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

s_{i} | 30 | 45 | 25 | 24 | 38 | 40 | 26 |

S_{i}/L_{i} | 25 | 40 | 22 | 20 | 33.33 | 36.67 | 22.5 |

a_{i} | 0.2084 | 0.2555 | 0.3175 | 0.2426 | 0.2365 | 0.2963 | 0.2517 |

When the chain supermarket system is out of stock, it will does not meet the conditions of lateral replenishment. Then, supermarket stores at this time needs to place an order to suppliers or distribution center, the rate of shortage is l_{i}, b_{i}. According to Equation (4) and the formula a_{i} + b_{i} + l_{i} = 1, the results obtained are shown in

5) The above data are into the formula (5) and formula (6), then the lateral transportation costs, the shortage loss costs can be obtained.

6) The order costs, storage costs can be obtained under the conditions of allowing lateral replenishment .

7) According to the inventory cost model, the total cost of inventory can be obtained under the conditions of allowing lateral replenishment.

8) When the chain supermarket system does not meet the needs of fresh agricultural products, supermarket stores at this time needs to place an order to suppliers or distribution center. Then, there will be no lateral transportation costs, and the total cost of inventory is as follows.

From the two inventory costs of allowing the lateral replenishment and not allowing the lateral replenishment, it can be got that the total inventory cost of allowing the lateral replenishment is lower than the total inventory cost of not allowing the lateral replenishment.

When the supermarket adopt the lateral replenishment, even though the loss caused by shortages is much lower than ordering directly to the distribution centers, even though it needs bear the cost of transporting in the lateral transportation, and even though the storage costs are slightly higher than the cost of the replenishment adopted by distribution center or supplier, there but is a relatively small impact on the total cost of inventory. Therefore, the supermarket adopt the lateral replenishment can make the total inventory costs of the entire chain supermarket x system lower. And achieve the overall system optimization.

The lateral replenishment inventory model obtains the total inventory cost of allowing the lateral replenishment is lower than the total inventory cost of not allowing the lateral replenishment.

It can be provided for the chain supermarket to reduce the loss of fresh agricultural products. After the analysis and calculation of inventory cost model, we can transport the fresh agricultural products from stores owning surplus to store owning shortage. Then, the best transportation plan should be designed in order to transport the fresh agricultural products with the lowest transportation costs. And, the sensitivity analysis of the lateral replenishment inventory model should be given.

According to the lateral replenishment transport model, we use an excel to get the optimal solution. The optimal solution is as shown in

The lateral replenishment transport model above get the optimal dispatching scheme between stores, and the sensitivity analysis of this transportation program, get the variable range of the fresh agricultural products increment and decrement that does not affect this optimal dispatching scheme. That is, within this range, the optimal dispatching scheme remains the same.

In this paper, all the sub-supermarket stores of the chain supermarket are regarded as a whole system to be researched. The goal of the research is to minimize the total inventory cost of the overall system in the process of replenishment, to maximize the overall system profits. This paper applies the lateral replenishment thinking to the replenishment of the chain supermarket, provides the solution to deal with the shortage or surplus of chain supermarket fresh agricultural products, and the shortcomings issue of traditional replenishment methods, and provides the solution to deal with the shortcomings issue of only considering the local interest of the traditional replenishment thinking. By the establishment of the lateral replenishment inventory model and the analysis of the actual examples, it can be got that the total inventory cost of allowing the lateral replenishment is lower than the total inventory cost of not allowing the lateral replenishment. Through the establishment of lateral replenishment transportation model, the optimal dispatching scheme between the surplus supermarket and the shortages supermarket is given. And then, the sensitivity analysis presents the variable range of the fresh agricultural

Number of stores | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

l_{i} | 0.2317 | 0.2831 | 0.2267 | 0.2603 | 0.2194 | 0.2451 | 0.2354 |

b_{i} | 0.5599 | 0.4614 | 0.4558 | 0.4971 | 0.5441 | 0.4586 | 0.5129 |

l_{ij} | B_{1} | B_{2} | B_{3} | B_{4} | Surplus quantity |
---|---|---|---|---|---|

A_{1} | 10 | 5 | 7 | 3 | 400 |

A_{2} | 5 | 7 | 2 | 5 | 600 |

A_{3} | 6 | 9 | 4 | 8 | 300 |

Shortage quantity | 300 | 450 | 350 | 200 |

C_{ij} | B_{1} | B_{2} | B_{3} | B_{4} |
---|---|---|---|---|

A_{1} | 6 | 3 | 4 | 3 |

A_{2} | 3 | 4 | 2 | 4 |

A_{3} | 5 | 1 | 2 | 1 |

B_{1} | B_{2} | B_{3} | B_{4} | |
---|---|---|---|---|

A_{1} | 0.2 | 0.5 | 0.7 | 0.9 |

A_{2} | 0.4 | 0.3 | 0.8 | 0.2 |

A_{3} | 0.6 | 0.1 | 0.3 | 0.5 |

B_{1} | B_{2} | B_{3} | B_{4} | |
---|---|---|---|---|

A_{1} | 0 | 400 | 0 | 0 |

A_{2} | 250 | 0 | 350 | 0 |

A_{3} | 50 | 50 | 0 | 200 |

Name | Final value | Decreasing costs | Target type coefficient | Allow increments | Allowed reduction |
---|---|---|---|---|---|

A_{1} B_{1} | 0 | 310 | 300 | ∞ | 310 |

A_{1} B_{2} | 400 | 0 | 30 | 54 | ∞ |

A_{1} B_{3} | 0 | 82.5 | 40 | ∞ | 82.5 |

A_{1} B_{4} | 0 | 54 | 10 | ∞ | 54 |

A_{2} B_{1} | 250 | 0 | 37.5 | 12.5 | 9.166666667 |

A_{2} B_{2} | 0 | 15.83333333 | 93.33333333 | ∞ | 15.83333333 |

A_{2} B_{3} | 350 | 0 | 5 | 9.166666667 | ∞ |

A_{2} B_{4} | 0 | 96.5 | 100 | ∞ | 96.5 |

A_{3} B_{1} | 50 | 0 | 50 | 9.166666667 | 12.5 |

A_{3} B_{2} | 50 | 0 | 90 | 15.83333333 | 54 |

A_{3} B_{3} | 0 | 9.166666667 | 26.66666667 | ∞ | 9.166666667 |

products’ increment and decrement that does not affect this optimal dispatching scheme.

This paper can provide a reference for the chain supermarket to deal with the shortage or surplus of fresh agricultural products. And, this will help the chain supermarket to improve sales margins of agricultural products, to reduce the total inventory costs of the whole the chain supermarket system, and to improve the customer

Name | Final value | Shadow price | Constraint value | Allow increments | Allowed reduction |
---|---|---|---|---|---|

A1 surplus quantities | 400 | −60 | 400 | 50 | 0 |

A2 surplus quantities | 600 | −12.5 | 600 | 50 | 0 |

A3 surplus quantities | 300 | 0 | 300 | ∞ | 0 |

Shortage quantities B_{1} | 300 | 50 | 300 | 0 | 50 |

Shortage quantities B_{2} | 450 | 90 | 450 | 0 | 50 |

Shortage quantities B_{3} | 350 | 17.5 | 350 | 0 | 50 |

Shortage quantities B_{4} | 200 | 16 | 200 | 0 | 200 |

service levels. This paper will have the certain significance for the further research of the ateral replenishment strategy of the chain supermarket fresh agricultural products.

GuangshuXu,ZilongSong,ShangjunPiao, (2015) Analysis Research on the Lateral Replenishment Strategy of the Chain Supermarket Fresh Agricultural Products. Journal of Service Science and Management,08,619-630. doi: 10.4236/jssm.2015.84062