- Email: [email protected]
Mitigation of Bullwhip Effect in Supply Chain Inventory Management Model
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 174 (2017) 1229 – 1234
13th Global Congress on Manufacturing and Management, GCMM 2016
Mitigation of Bullwhip Effect in Supply Chain Inventory Management Model Jianhua Dai*, Shengbo Peng, Shibiao Li School of Economics and Management, Communication University of China, Beijing, 100020, China
Abstract This article starts with the reasons to bullwhip effect phenomenon, analyzes how to enhance inventory management strategy to reduce the bullwhip effect in supply chain management. And then, we study the case of McDonald's and its third-party logistics system HAVI cooperation to explore the cooperation mode between the two companies. Assuming that McDonald's stores as a logistics activities supply chain leader adopts the upper and lower inventory management strategy, according to the HAVI’s distribution for McDonald's stores, we develop a one-multi distribution model, and build a mathematical model for reducing inventory and improve service level. 2016The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © 2017 © Published by Elsevier Ltd. This Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management Keywords: bullwhip effect; inventory management; one-multi distribution; control model;
1. Introduction Bullwhip Effect refers to a kind of distortion occurring in the process of transmitting order information upstream, which is a bigger fluctuation in upstream order quantity caused by the fluctuation of downstream demands. This is a common phenomenon in supply chain. The existence of Bullwhip Effect makes it difficult for enterprises to grasp market demands, causing an overstock and reducing the operational efficiency for the whole supply chain. The best way to solve Bullwhip Effect is to reduce knots of supply chain as far as possible, thus to greatly ensure accuracy of information. Using efficient supply chain management system can reduce Bullwhip Effect and realize real-time response, directly reducing operating costs of enterprises. The factors causing Bullwhip Effect include the following
* Corresponding author. Tel.: 13811722338. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management
doi:10.1016/j.proeng.2017.01.291
1230
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
several aspects which are demand forecast amendment, fluctuations in prices, order quantity decision, shortages game, inventory imbalances, lead time, etc. Guo Haifeng applies vendor managed inventory strategy to reforge the physical process of supply chain(Sponsored by China Postdoctoral Science Foundation “A Study on Interconnection Charges during China's Integration of Telecommunications, Broadcasting and Internet Networks” (No.: 20110490258)) [1]. The simulation demonstrates that the inventory strategy of vendor management is an effective way to reduce Bullwhip Effect. Based on pre-existing documents on Bullwhip Effect problem research, this article analyzes and summarizes how to reduce Bullwhip Effect by vendor control inventory strategy combined with cases. Nomenclature
O P V Lw Ld Q
The time required for goods from distribution centers to stores Daily average demand of the goods in the stores. The standard variance of the goods in the stores. Upper limit of the stores. Lower limit of the stores. Order Quantity of stores.
2. Vendor Control Inventory Strategies under Management of Supply Chain Supply chain management is to realize optimization of supply chain operation with least costs, in order to make the supply chain efficiently operate in the whole process from purchasing to satisfying the final customers including workflow, material flow, fund flow, information flow, etc. And customers get appropriate products with a reasonable price accurately and timely. Its basic idea is “Horizontal Integration” and makes full use of external resources [2]. Enterprises always manage their own stock independently in the operation and have their vendor control inventory strategy in every knot of material flow chain. As everyone has their different but open inventory strategy, it gives rise to a distortion in demands, causing to enlarge demand variation and not able to accurately master up streaming customers’ demands for suppliers. As to this problem, there appear some new inventory control methods. In the practical application, we can find that all kinds of vendor managed inventory strategies do not independently exist, and different ideas can cross, in order to better realize vendor managed inventory strategy. 2.1. Vendor Managed Inventory Vendor managed inventory management system is a cooperative strategy between user and vendor with an availability at lowest costs and optimizing products for both parties. And guided by an integrated target framework, the vendor manages inventory, transferring inventory management function to be charged by vendor. The key measures of VMI strategy are as follows. x The first one is team spirit. While implementing this strategy, both vendor and customer should have a better team spirit, with mutual trust and information transparency being equally important. x The second one is to have the minimum cost for both parties. This strategy can be used to reduce the inventory costs in the whole supply chain, which will benefit to both of them. x The third one is goal congruence principle. The two parties should know their own responsibility and reach unanimous ideas. x The fourth one is continuous improvement principle. A closed-loop system is formed, has continuous feedback and eliminates waste gradually. 2.2. Joint Managed Inventory Management Joint managed inventory management is an effective method to solve a requirement amplification phenomenon caused by mutual different inventory operation mode with node enterprises in supply chain system, and improve
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
1231
synchronization degree of supply chain. It emphasizes the two parties’ participation in the meantime to make inventory plan together. Every inventory director (vendor, manufacturer and distributor) in the process of supply chain should think about their mutual congruousness and keep pace with the expected requirements from inventory director between the two nodes, in order to eliminate the phenomenon of demand variation amplification. The demand determination of every adjacent node is a result of coordination of both supply and demand parties. The inventory management is no longer separate operation process but a link of supply and demand as well as coordination center. Joint managed inventory management principle is a management mode of risks sharing [3]. 2.3. Third Party Logistics System Third party logistics system is a means of supply inheritance, providing all kinds of services like product transportation, inventory management and order choice for customers. Enterprises can be more focused on their own core businesses by delegating some of the functions of inventory management to third party logistics system. Third party logistics system takes a role as a bridge to contact vendor and user. 3. Model Establishment About the policy conditions of “Universal build” wireless cities, a briefly analysis is as follows. 3.1. Case Study The HAVI is a third-party logistics company for McDonald. The company works for McDonald's restaurants, ordering, storage, transportation and distribution of a series of work, including information processing, inventory control, labeling, production and quality control and other aspects. All of this can reduces the McDonald's stock greatly, and product inventory to meet the minimum principle [4]. What McDonald only need is to let the suppliers know their demand information continually and timely, and the suppliers can forecast the future demand of the user by this demand information. According to this forecast, suppliers develop their own production plans and delivery plans, take the initiative to small quantities frequency to the user to supplement the inventory of goods, both to ensure to meet user demand and inventory of goods for at least minimum waste. With the VMI purchasing the biggest beneficiaries is McDonald, it can get rid of the cumbersome procurement business, freed from the Procurement, even the inventory and transport are also burden by HAVI with elevated service rate [5]. HAVI is that, not only played the role of third party logistics companies, but also bear the responsibilities of suppliers. McDonald's has commissioned a third party logistics agent for their manufacture, storage, distribution and management. On the other hand, he takes the form of suppliers, agents, master of McDonald's stock by the vendor, purchasing is done by HAVI, McDonald's and its suppliers, HAVI, is completely became a partner Whether HAVI as third-party logistics companies, or as a vendor, who is in the entire logistics operation has played an important role in the process [6]. For more than 30 years, HAVI and McDonald's cooperation without a contract, both the long-term relationship of mutual trust cooperation between the two has the lowest cost of trust. Partnership between McDonald's and HAVI is good proof of the above deals to supply inventory management on policy, the joint management of inventory strategy and strategy of third-party logistics. HAVI mainly rely on information systems management to create value, its average inventory is much lower than its competitors. The logistics products loss rate of McDonald's is only one out of 10,000. The following papers will be analysis its management model. 3.2. Upper and Lower Inventory Control Method The automatic monitoring technology of McDonald's stores is very advanced, from order to achieve transparent management of the stock has a set of automation equipment. Here we assume that the upper and lower inventory control method has been used on the device.
1232
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
When the stores system detects the minimum store inventory down to Ld , the so-called upper and lower inventory control model will generated the orders automatically with order quantity Q to the distribution center orders. When goods have been delivered to the stores, the expected maximum inventory level L w is achieved. When calculate the upper and lower limits, we must calculate the sales forecast based on past sales data, this article does not examine in detail the demand forecast. 1) The assumptions of model x Commodities daily sales data is a normal distribution, according to the principle of normal distribution function, we know that the standard deviation and the mean ratio k is a constant, but due to the sample data obtained k and k there is a deviation, thus allowing the presence of constant bias. x Distribution Center by FCL distribution to stores replenishment. 2) The description of mathematical symbol The number of specifications of the goods per case. O : The time required for goods from distribution centers to stores. P : Daily average demand of the goods in the stores. V : The standard variance of the goods in the stores. Lw : Upper limit of the stores. Ld : Lower limit of the stores. Q : Order Quantity of stores. 3) Model establishment The average demand in the period O is PO ˈits standard deviation is V O ˈand: (1) μ λ =λ×μ , σλ k u μ λ σ / μ u λ μ σ u λ . Also recorded in the period t O , the safety stock is SSˈso: (2) SS=σλ z( p) σ O z( p) . We can calculate the lower of the stores: (3) Ld μ λ SS λ u μ σ λ z(p) . The order of the stores: (4) Q=[(Ld -SS)/B] B [O P /B] B . Upper of the stores: Lw Q SS > λ μ / B@ u B σ λ z(p) . (5) 3.3. Distribution center and 1-N distribution model of retail store To abstract the distribution relationship between Havi Logistics Company and retail store of McDonalds, virtually it is a distribution relationship between a distribution center and many retail stores (1-N). The order quantity of optimal inventory strategy can be obtained by mathematical model. 1) Hypothesis x Inventory fee is composed by inventory storage fee and shortage cost. This paper argues that retail stores will lose selling profits directly if the commodities in the retail stores are out of stock. The loss costs of each unit of commodities are the profits, shared by distribution center and retail stores in different proportion. x
Customers’ requirements to retail stores are supposed to change randomly, but each requirement is independent. The external customers’ requirements in t period are supposed to be yt , the density function to be f t ( y) , and distribution function to be f t ( y) , besides they are continuous, transcending and differentiable.
x
The retail stores of MacDonald adopt continuous checking (s j , Q j ) inventory strategy, in which the order point is s j , and the order quantity is Q j ˄ Q j is constant˅.
x
Havi Distribution Center adopts the continuous checking S0 inventory strategy which holds inventory level.
2) Meaning of variable symbolic y j : goods in the stores j day sales. Y j ( L j ) : goods in the stores j day sales, during period L j . Y j ( L0 ) : goods in the stores j day sales, during Period L0 . P j : average daily sales of merchandise in the store j. L0 : lead time for goods from suppliers to distribution centers. L j : lead time for goods from distribution centers to stores j. O j : production orders of store j obeys to the Poisson distribution in which parameter is λ. D : proportional share
1233
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
coefficient of the supply chain shortage cost. h0 : distribution centers per unit time inventory holding costs. h j : per unit time inventory holding costs of store j. P: unit shortage cost no matter cost of goods out of stock in which stores. Q j : each order quantity of store j. s j : inventory levels when store j generate an order automatically. s0 : the maximum inventory level of the distribution center. HC0 : inventory holding costs of distribution center during period t. HC j : inventory holding costs of store j during period t. LC0 : distribution centers to share the cost of inventory loss during period t. LC j : store j to share the cost of inventory loss during period t. TC0 : distribution center inventory costs in period t. TC j : store j inventory costs in period t. TC : total inventory cost of the supply chain system in period t. In all above, j 1, 2,..., N . 3) Model Establishment Inventory holding costs of store j during period t:
1 hj ( Qj s j P j L j ) , 2 The shared cost of inventory loss during period t of store j:
HC j
LC j
f
D P ³ [Yj ( L j ) s j ] f [Y j ( L j )]dYj ( L j ) . sj
(6)
(7)
We get: TC j
HC j LC j
. f 1 h j ( Q j s j P j L j ) D P ³ [Y j ( L j ) s j ] f [Y j ( L j )]dY j ( L j ) sj 2
(8)
We assume the distribution centers per unit time inventory holding costs is h0, so inventory holding costs of distribution center during period t:
1 N h0 [S0 (S0 ¦ j 1 O L0 Q j ) ] , 2 And distribution centers to share the cost of inventory loss during period t: HC0
LC0
¦ (1 D ) P ³
f
sj
[Yj ( L j ) s j ] f [Yj ( L j )]dYj ( L j ) ,
(9)
(10)
So, TC0
HC0 LC0
f 1 N h0 [ S0 ( S0 ¦ j 1 O L0 Q j ) ] ¦ (1 D ) P ³ [Y j ( L j ) s j ] f [Y j ( L j )]dY j ( L j ) . s j 2 By the above formula, we can get the supply chain system, the total inventory costs in period t is:
TC
(11)
TC0 ¦ j 1TC j N
f 1 1 N h0 [ S0 ( S0 ¦ j 1 O L0 Q j ) ] ¦ h j ( Q j s j P j L j ) ¦ P ³ [Y j ( L j ) s j ] f [Y j ( L j )]dY j ( L j ) . sj 2 2 (12) We obtain a set of solutions (s1 , s2 ,...sN , s0 ) that makes the TC minimum. When make the solution of the model. We can use the heuristic method, and select the value of a series of α, compared to the actual supply chain inventory management, as long as that relative to an optimal solution.
1234
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
4. Summary Starting from reasons for Bullwhip effect phenomenon, this article stresses the emphasis on analyzing how to reduce Bullwhip effect under supply management circumstance. This article takes MacDonald and its third party logistics Havi Company as an example, to discuss their ways of cooperation. Retail stores of MacDonald, as a leading part for supply logistics activities, are supposed to adopt up and bottom limitation inventory management strategy, and abstract the distribution situation between Havi Company and retail stores of MacDonald to 1-N distribution Module, thus to build mathematics modeling, so as to reach the target of lowering stock as well as improving service. The special circumstance that distribution center stock S_0 is less than the total order quantities of the entire retail store isn’t taken into consideration in this article when minimizing in the 1-N distribution module, which is worth to mention and needs to improve in the module. The more this module corresponds with the practical condition, the better of the simulation results to data as well as the less of enterprises’ costs. At the same time, it is an effective way for enterprises to raise profits by way of reducing nodes of supply chain, linearization of information transmitting, and utilizing advanced information management system, thus to eliminate, to some extent, Bullwhip effect phenomenon. Acknowledgements This paper was supported by the National Natural Science Foundation of China (No. 71203202), the Program for Young Scholars of Beijing (No. YETP0633) and the Research Task of Communication University of China (No. 3132014XNG1458, CUC16A17). References [1] H.F. Guo, X.Y. Huang, Impact of Vendor Managed Inventory on the Bullwhip Effect, Control Engineering, 1 (2007)111-114. [2] R.Q. Chen, S.H. Ma, Production and operations management, third ed., Higher Education Press, Beijing, 2011. [3] L.B. Zhang, Y.Q. Han, J. Chen, System cost & bullwhip effect in quantity-based VMI consolidation replenishment system, Computer Integrated Manufacturing System, 2 (2007) 410-416. [4] P. Xiao, An Inventory Model for Convenience Store in Two-stage Supply Chain with One-DC and N-Stores, Master Thesis of Tongji University, 2007. [5] L.Z. Huang, X. Li, Q.P. Wang, Optimation of the Order Policy in a Distribution Center of Super-Market System, Tongji University (Natural Science), 34 (2006) 275-279. [6] Y.G. Ma, Y.F. Huang, N.Q. Jiang, W.J. Cao, Bullwhip Effect Based on Retailers’ and Customers’ Forecasting Behaviors, Systems Engineering, 58 (2011) 14-20.
ScienceDirect Procedia Engineering 174 (2017) 1229 – 1234
13th Global Congress on Manufacturing and Management, GCMM 2016
Mitigation of Bullwhip Effect in Supply Chain Inventory Management Model Jianhua Dai*, Shengbo Peng, Shibiao Li School of Economics and Management, Communication University of China, Beijing, 100020, China
Abstract This article starts with the reasons to bullwhip effect phenomenon, analyzes how to enhance inventory management strategy to reduce the bullwhip effect in supply chain management. And then, we study the case of McDonald's and its third-party logistics system HAVI cooperation to explore the cooperation mode between the two companies. Assuming that McDonald's stores as a logistics activities supply chain leader adopts the upper and lower inventory management strategy, according to the HAVI’s distribution for McDonald's stores, we develop a one-multi distribution model, and build a mathematical model for reducing inventory and improve service level. 2016The TheAuthors. Authors. Published by Elsevier Ltd. is an open access article under the CC BY-NC-ND license © 2017 © Published by Elsevier Ltd. This Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management Keywords: bullwhip effect; inventory management; one-multi distribution; control model;
1. Introduction Bullwhip Effect refers to a kind of distortion occurring in the process of transmitting order information upstream, which is a bigger fluctuation in upstream order quantity caused by the fluctuation of downstream demands. This is a common phenomenon in supply chain. The existence of Bullwhip Effect makes it difficult for enterprises to grasp market demands, causing an overstock and reducing the operational efficiency for the whole supply chain. The best way to solve Bullwhip Effect is to reduce knots of supply chain as far as possible, thus to greatly ensure accuracy of information. Using efficient supply chain management system can reduce Bullwhip Effect and realize real-time response, directly reducing operating costs of enterprises. The factors causing Bullwhip Effect include the following
* Corresponding author. Tel.: 13811722338. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 13th Global Congress on Manufacturing and Management
doi:10.1016/j.proeng.2017.01.291
1230
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
several aspects which are demand forecast amendment, fluctuations in prices, order quantity decision, shortages game, inventory imbalances, lead time, etc. Guo Haifeng applies vendor managed inventory strategy to reforge the physical process of supply chain(Sponsored by China Postdoctoral Science Foundation “A Study on Interconnection Charges during China's Integration of Telecommunications, Broadcasting and Internet Networks” (No.: 20110490258)) [1]. The simulation demonstrates that the inventory strategy of vendor management is an effective way to reduce Bullwhip Effect. Based on pre-existing documents on Bullwhip Effect problem research, this article analyzes and summarizes how to reduce Bullwhip Effect by vendor control inventory strategy combined with cases. Nomenclature
O P V Lw Ld Q
The time required for goods from distribution centers to stores Daily average demand of the goods in the stores. The standard variance of the goods in the stores. Upper limit of the stores. Lower limit of the stores. Order Quantity of stores.
2. Vendor Control Inventory Strategies under Management of Supply Chain Supply chain management is to realize optimization of supply chain operation with least costs, in order to make the supply chain efficiently operate in the whole process from purchasing to satisfying the final customers including workflow, material flow, fund flow, information flow, etc. And customers get appropriate products with a reasonable price accurately and timely. Its basic idea is “Horizontal Integration” and makes full use of external resources [2]. Enterprises always manage their own stock independently in the operation and have their vendor control inventory strategy in every knot of material flow chain. As everyone has their different but open inventory strategy, it gives rise to a distortion in demands, causing to enlarge demand variation and not able to accurately master up streaming customers’ demands for suppliers. As to this problem, there appear some new inventory control methods. In the practical application, we can find that all kinds of vendor managed inventory strategies do not independently exist, and different ideas can cross, in order to better realize vendor managed inventory strategy. 2.1. Vendor Managed Inventory Vendor managed inventory management system is a cooperative strategy between user and vendor with an availability at lowest costs and optimizing products for both parties. And guided by an integrated target framework, the vendor manages inventory, transferring inventory management function to be charged by vendor. The key measures of VMI strategy are as follows. x The first one is team spirit. While implementing this strategy, both vendor and customer should have a better team spirit, with mutual trust and information transparency being equally important. x The second one is to have the minimum cost for both parties. This strategy can be used to reduce the inventory costs in the whole supply chain, which will benefit to both of them. x The third one is goal congruence principle. The two parties should know their own responsibility and reach unanimous ideas. x The fourth one is continuous improvement principle. A closed-loop system is formed, has continuous feedback and eliminates waste gradually. 2.2. Joint Managed Inventory Management Joint managed inventory management is an effective method to solve a requirement amplification phenomenon caused by mutual different inventory operation mode with node enterprises in supply chain system, and improve
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
1231
synchronization degree of supply chain. It emphasizes the two parties’ participation in the meantime to make inventory plan together. Every inventory director (vendor, manufacturer and distributor) in the process of supply chain should think about their mutual congruousness and keep pace with the expected requirements from inventory director between the two nodes, in order to eliminate the phenomenon of demand variation amplification. The demand determination of every adjacent node is a result of coordination of both supply and demand parties. The inventory management is no longer separate operation process but a link of supply and demand as well as coordination center. Joint managed inventory management principle is a management mode of risks sharing [3]. 2.3. Third Party Logistics System Third party logistics system is a means of supply inheritance, providing all kinds of services like product transportation, inventory management and order choice for customers. Enterprises can be more focused on their own core businesses by delegating some of the functions of inventory management to third party logistics system. Third party logistics system takes a role as a bridge to contact vendor and user. 3. Model Establishment About the policy conditions of “Universal build” wireless cities, a briefly analysis is as follows. 3.1. Case Study The HAVI is a third-party logistics company for McDonald. The company works for McDonald's restaurants, ordering, storage, transportation and distribution of a series of work, including information processing, inventory control, labeling, production and quality control and other aspects. All of this can reduces the McDonald's stock greatly, and product inventory to meet the minimum principle [4]. What McDonald only need is to let the suppliers know their demand information continually and timely, and the suppliers can forecast the future demand of the user by this demand information. According to this forecast, suppliers develop their own production plans and delivery plans, take the initiative to small quantities frequency to the user to supplement the inventory of goods, both to ensure to meet user demand and inventory of goods for at least minimum waste. With the VMI purchasing the biggest beneficiaries is McDonald, it can get rid of the cumbersome procurement business, freed from the Procurement, even the inventory and transport are also burden by HAVI with elevated service rate [5]. HAVI is that, not only played the role of third party logistics companies, but also bear the responsibilities of suppliers. McDonald's has commissioned a third party logistics agent for their manufacture, storage, distribution and management. On the other hand, he takes the form of suppliers, agents, master of McDonald's stock by the vendor, purchasing is done by HAVI, McDonald's and its suppliers, HAVI, is completely became a partner Whether HAVI as third-party logistics companies, or as a vendor, who is in the entire logistics operation has played an important role in the process [6]. For more than 30 years, HAVI and McDonald's cooperation without a contract, both the long-term relationship of mutual trust cooperation between the two has the lowest cost of trust. Partnership between McDonald's and HAVI is good proof of the above deals to supply inventory management on policy, the joint management of inventory strategy and strategy of third-party logistics. HAVI mainly rely on information systems management to create value, its average inventory is much lower than its competitors. The logistics products loss rate of McDonald's is only one out of 10,000. The following papers will be analysis its management model. 3.2. Upper and Lower Inventory Control Method The automatic monitoring technology of McDonald's stores is very advanced, from order to achieve transparent management of the stock has a set of automation equipment. Here we assume that the upper and lower inventory control method has been used on the device.
1232
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
When the stores system detects the minimum store inventory down to Ld , the so-called upper and lower inventory control model will generated the orders automatically with order quantity Q to the distribution center orders. When goods have been delivered to the stores, the expected maximum inventory level L w is achieved. When calculate the upper and lower limits, we must calculate the sales forecast based on past sales data, this article does not examine in detail the demand forecast. 1) The assumptions of model x Commodities daily sales data is a normal distribution, according to the principle of normal distribution function, we know that the standard deviation and the mean ratio k is a constant, but due to the sample data obtained k and k there is a deviation, thus allowing the presence of constant bias. x Distribution Center by FCL distribution to stores replenishment. 2) The description of mathematical symbol The number of specifications of the goods per case. O : The time required for goods from distribution centers to stores. P : Daily average demand of the goods in the stores. V : The standard variance of the goods in the stores. Lw : Upper limit of the stores. Ld : Lower limit of the stores. Q : Order Quantity of stores. 3) Model establishment The average demand in the period O is PO ˈits standard deviation is V O ˈand: (1) μ λ =λ×μ , σλ k u μ λ σ / μ u λ μ σ u λ . Also recorded in the period t O , the safety stock is SSˈso: (2) SS=σλ z( p) σ O z( p) . We can calculate the lower of the stores: (3) Ld μ λ SS λ u μ σ λ z(p) . The order of the stores: (4) Q=[(Ld -SS)/B] B [O P /B] B . Upper of the stores: Lw Q SS > λ μ / B@ u B σ λ z(p) . (5) 3.3. Distribution center and 1-N distribution model of retail store To abstract the distribution relationship between Havi Logistics Company and retail store of McDonalds, virtually it is a distribution relationship between a distribution center and many retail stores (1-N). The order quantity of optimal inventory strategy can be obtained by mathematical model. 1) Hypothesis x Inventory fee is composed by inventory storage fee and shortage cost. This paper argues that retail stores will lose selling profits directly if the commodities in the retail stores are out of stock. The loss costs of each unit of commodities are the profits, shared by distribution center and retail stores in different proportion. x
Customers’ requirements to retail stores are supposed to change randomly, but each requirement is independent. The external customers’ requirements in t period are supposed to be yt , the density function to be f t ( y) , and distribution function to be f t ( y) , besides they are continuous, transcending and differentiable.
x
The retail stores of MacDonald adopt continuous checking (s j , Q j ) inventory strategy, in which the order point is s j , and the order quantity is Q j ˄ Q j is constant˅.
x
Havi Distribution Center adopts the continuous checking S0 inventory strategy which holds inventory level.
2) Meaning of variable symbolic y j : goods in the stores j day sales. Y j ( L j ) : goods in the stores j day sales, during period L j . Y j ( L0 ) : goods in the stores j day sales, during Period L0 . P j : average daily sales of merchandise in the store j. L0 : lead time for goods from suppliers to distribution centers. L j : lead time for goods from distribution centers to stores j. O j : production orders of store j obeys to the Poisson distribution in which parameter is λ. D : proportional share
1233
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
coefficient of the supply chain shortage cost. h0 : distribution centers per unit time inventory holding costs. h j : per unit time inventory holding costs of store j. P: unit shortage cost no matter cost of goods out of stock in which stores. Q j : each order quantity of store j. s j : inventory levels when store j generate an order automatically. s0 : the maximum inventory level of the distribution center. HC0 : inventory holding costs of distribution center during period t. HC j : inventory holding costs of store j during period t. LC0 : distribution centers to share the cost of inventory loss during period t. LC j : store j to share the cost of inventory loss during period t. TC0 : distribution center inventory costs in period t. TC j : store j inventory costs in period t. TC : total inventory cost of the supply chain system in period t. In all above, j 1, 2,..., N . 3) Model Establishment Inventory holding costs of store j during period t:
1 hj ( Qj s j P j L j ) , 2 The shared cost of inventory loss during period t of store j:
HC j
LC j
f
D P ³ [Yj ( L j ) s j ] f [Y j ( L j )]dYj ( L j ) . sj
(6)
(7)
We get: TC j
HC j LC j
. f 1 h j ( Q j s j P j L j ) D P ³ [Y j ( L j ) s j ] f [Y j ( L j )]dY j ( L j ) sj 2
(8)
We assume the distribution centers per unit time inventory holding costs is h0, so inventory holding costs of distribution center during period t:
1 N h0 [S0 (S0 ¦ j 1 O L0 Q j ) ] , 2 And distribution centers to share the cost of inventory loss during period t: HC0
LC0
¦ (1 D ) P ³
f
sj
[Yj ( L j ) s j ] f [Yj ( L j )]dYj ( L j ) ,
(9)
(10)
So, TC0
HC0 LC0
f 1 N h0 [ S0 ( S0 ¦ j 1 O L0 Q j ) ] ¦ (1 D ) P ³ [Y j ( L j ) s j ] f [Y j ( L j )]dY j ( L j ) . s j 2 By the above formula, we can get the supply chain system, the total inventory costs in period t is:
TC
(11)
TC0 ¦ j 1TC j N
f 1 1 N h0 [ S0 ( S0 ¦ j 1 O L0 Q j ) ] ¦ h j ( Q j s j P j L j ) ¦ P ³ [Y j ( L j ) s j ] f [Y j ( L j )]dY j ( L j ) . sj 2 2 (12) We obtain a set of solutions (s1 , s2 ,...sN , s0 ) that makes the TC minimum. When make the solution of the model. We can use the heuristic method, and select the value of a series of α, compared to the actual supply chain inventory management, as long as that relative to an optimal solution.
1234
Jianhua Dai et al. / Procedia Engineering 174 (2017) 1229 – 1234
4. Summary Starting from reasons for Bullwhip effect phenomenon, this article stresses the emphasis on analyzing how to reduce Bullwhip effect under supply management circumstance. This article takes MacDonald and its third party logistics Havi Company as an example, to discuss their ways of cooperation. Retail stores of MacDonald, as a leading part for supply logistics activities, are supposed to adopt up and bottom limitation inventory management strategy, and abstract the distribution situation between Havi Company and retail stores of MacDonald to 1-N distribution Module, thus to build mathematics modeling, so as to reach the target of lowering stock as well as improving service. The special circumstance that distribution center stock S_0 is less than the total order quantities of the entire retail store isn’t taken into consideration in this article when minimizing in the 1-N distribution module, which is worth to mention and needs to improve in the module. The more this module corresponds with the practical condition, the better of the simulation results to data as well as the less of enterprises’ costs. At the same time, it is an effective way for enterprises to raise profits by way of reducing nodes of supply chain, linearization of information transmitting, and utilizing advanced information management system, thus to eliminate, to some extent, Bullwhip effect phenomenon. Acknowledgements This paper was supported by the National Natural Science Foundation of China (No. 71203202), the Program for Young Scholars of Beijing (No. YETP0633) and the Research Task of Communication University of China (No. 3132014XNG1458, CUC16A17). References [1] H.F. Guo, X.Y. Huang, Impact of Vendor Managed Inventory on the Bullwhip Effect, Control Engineering, 1 (2007)111-114. [2] R.Q. Chen, S.H. Ma, Production and operations management, third ed., Higher Education Press, Beijing, 2011. [3] L.B. Zhang, Y.Q. Han, J. Chen, System cost & bullwhip effect in quantity-based VMI consolidation replenishment system, Computer Integrated Manufacturing System, 2 (2007) 410-416. [4] P. Xiao, An Inventory Model for Convenience Store in Two-stage Supply Chain with One-DC and N-Stores, Master Thesis of Tongji University, 2007. [5] L.Z. Huang, X. Li, Q.P. Wang, Optimation of the Order Policy in a Distribution Center of Super-Market System, Tongji University (Natural Science), 34 (2006) 275-279. [6] Y.G. Ma, Y.F. Huang, N.Q. Jiang, W.J. Cao, Bullwhip Effect Based on Retailers’ and Customers’ Forecasting Behaviors, Systems Engineering, 58 (2011) 14-20.