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  • Mr. Chairman, ladies and Gentlemen, I am very delighted to be here. Today I want to talk to you about our model, that is A strategic supply chain network model with safety sock. My name is Lv guoyong and Professor Kubo is co-author of this model
  • So the agenda is like here. Firstly, I want to make an introduction to the strategic supply chain network model
  • This is generally regarded as long-term network design model we hope to get the optimal solution of the supply chain network configure through this model. In details, We want through the network design model to know which supplier to use, where is the product made, which Distribution Center through to Provide to customers. In additionally, we also can know the flow and the stock. Therefore, if the company need to make a decision of the optimal number, location of warehouses, and/or plants, the model can be used. And it also help to decide which plant/vendor should produce which product. And which warehouses should make a service to which customers. In a word, we can say: the strategic network design model is deciding which DC’s and plants you are going to use to serve your customers.
  • In this slide, I want to discuss all the cost detail. First is the fixed cost, this is the node holding cost and when a new node is to open there is opening cost and if a old node need to be closed, we have to pay the closing cost. Second is the transport cost. The transport cost exist in all the link. Such as when import from supplier, transport product from plants to DCs and distribute them to customers, We need to pay the transport cost. This cost is calculated base of the distance of the link for every products or parts. It means for a items transported through a link, the transport cost is just the unit of transport fee multiply the flow. The third is the production and the warehouse cost. We see those cost as variable cost in the node, is the linear function of the flow. Special to say, the warehouse in here is just the handling cost in warehouse not include any inventory cost. At last there are inventory costs. We consider three inventory cost in our model. Pipeline inventory cost, cycle inventory and safety stock cost. Pipeline inventory mean the inventory carried due to transportation in the supply chain. And cycle inventory is the inventory carried at intervals of replenishment. And in our model, since we treat the demand as uncertain, we need to keep safety stock for the demand variation. We think this is very important to the supply chain, and it is a big cost can affect the design of the network.
  • Then I want to discuss the safety stock cost.
  • Here let consider the safety stock, when a dc make a service to N retailers. First in every retailer, assume the demand is uncertain and belong to the normal distribution (u, σ). As shown in previous slide, the safety stock is formulated as this. Then the demand at DC is also belong to the normal distribution, and its mean is the summation of the all retailer average demand and So is the variance. The safety stock in DC is formulated like this. By this, we can understand the risk pool effect, that is the variance in DC, the square root of summation, is smaller than the summation of the variance in all retailer, which is the summation of the square root.
  • Here we want to introduce an important assumption: that is the variance to mean ratio of the demand is identical for all customers. We use γ to express it, then we can change the safety stock formulation using the mean of the demand, instead of the variance. Why we should do like this, we can see in the next slide.
  • Since the summation of the average demand is equal to the flow coming out a node, we can use it to express the safety stock. As mentioned before, the flow is the decision variable in our model, This safety stock formulation is the square root function of variable, the flow. Then I will show our algorithm how to solve this non-linear programming.
  • Before show the algorithm, I want still want to use a little time to show how the safety stock in our model, a strategic supply chain network model
  • We use this formulation to express the objective function of our model. A square root function of variable is included there.
  • Now I want to introduce the our algorithm to solve the concave function
  • It is easy to consider that we can treat concave function as piece –wise linear function. To do this, there are three equivalent models. Here we use the first model to transfer concave function to piece –wise linear function. To do this, first we divide the section between Low bound and unbound into several small section. We use bs to express the section’s unbound, and bs-1 to express the low bound. Then at the section s, we can know the slope cs and the cost-intercept fs by the low and up bound of the section.
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    1. 1. A Strategic Supply Chain Network Model with Safety Stock Guoyong Lv Mikio Kubo CORS/INFORMS Joint International Meeting   May 16-19 2004  
    2. 2. Agenda <ul><li>Strategic supply chain network model </li></ul><ul><li>Safety stock cost </li></ul><ul><li>A strategic supply chain network model with safety stock </li></ul><ul><li>Dynamic cut-adding algorithm </li></ul><ul><li>Conclusions </li></ul>
    3. 3. Strategic Supply Chain Network Model <ul><li>Supply Chain Network Configure </li></ul><ul><ul><li>Node and Arc </li></ul></ul><ul><ul><li>Flow </li></ul></ul><ul><li>When to use it </li></ul><ul><ul><li>Determine the optimal number, location of warehouses and/or plants </li></ul></ul><ul><ul><li>Determine optimal sourcing strategy </li></ul></ul><ul><ul><li>Which plant/vendor should produce which product </li></ul></ul><ul><ul><li>Determine best distribution channels </li></ul></ul><ul><ul><li>Which warehouse should service which customer </li></ul></ul><ul><ul><li>Maintain optimal network as business changes </li></ul></ul><ul><li>Strategic network design is deciding which DC’s and plants you are going to use to serve your customers </li></ul>---Long-term Network Design Model
    4. 4. Strategic Supply Chain Network Model <ul><li>Output from the model: </li></ul><ul><ul><li>Optimal node locations --- which node? </li></ul></ul><ul><ul><li>Optimal transport routing of productions between the nodes --- which arc? </li></ul></ul><ul><ul><li>The throughput of those nodes --- how big the flow? </li></ul></ul><ul><li>Minimize the total costs </li></ul><ul><li>--- most cost-effectively satisfy customer demand. </li></ul><ul><ul><li>Node related cost </li></ul></ul><ul><ul><ul><li>Fixed Cost : Node Holding cost, opening a new node or close an old node </li></ul></ul></ul><ul><ul><li>Arc related cost </li></ul></ul><ul><ul><ul><li>Transport cost and procurement cost </li></ul></ul></ul><ul><ul><li>Node and production related cost ---node variable cost </li></ul></ul><ul><ul><ul><li>Production cost and Warehouse cost </li></ul></ul></ul><ul><ul><ul><li>Inventory (pipeline inventory, cycle inventory, safety stock) cost </li></ul></ul></ul>
    5. 5. Literature review about Strategic supply chain network model <ul><li>A. Geoffrion and G. Graves, Multicommodity distribution system design by Benders decomposition 1974 </li></ul><ul><li>G.G. Brown, G.W. Graves, and M.D. Honczarenko, Design and operation of a multicommodity production/distribution system using primal goal decomposition 1987 </li></ul><ul><ul><li>Determine the locations of warehouses as well as the flow of multiple commodities from plants through warehouses, and on to customers. </li></ul></ul><ul><ul><li>Fixed warehouse cost, Inbound and outbound transport cost, Warehouse handling cost </li></ul></ul><ul><ul><li>Plant locations, assignment of production facilities to plants </li></ul></ul>
    6. 6. <ul><li>M.A. Cohen and H.L. Lee, Resource deployment analysis of global manufacturing and distribution networks 1989 </li></ul><ul><ul><li>Maximize global after-tax profits </li></ul></ul><ul><ul><li>Incorporate country-specific offset constraints </li></ul></ul><ul><ul><li>Transfer prices, exchange-rate </li></ul></ul><ul><li>S. Lakhal, A. Martel, O. Kettani, and M. Oral, On the optimization of supply chain networking decisions , 2001 </li></ul><ul><ul><li>Activity Base Cost </li></ul></ul><ul><ul><li>Maximize the value-added of the internal activities. </li></ul></ul>Literature review about Strategic supply chain network model
    7. 7. <ul><li>Network design models </li></ul><ul><ul><li>Large-scale MIP problem </li></ul></ul><ul><ul><ul><li>linear function of flow </li></ul></ul></ul><ul><ul><ul><li>Node location variable – binary variable </li></ul></ul></ul><ul><ul><li>Treatment of uncertainty </li></ul></ul><ul><ul><ul><li>Supply and demand as deterministic </li></ul></ul></ul><ul><li>Facility location model </li></ul><ul><ul><li>Dastin formulated facility locations problems with safety stock </li></ul></ul><ul><ul><ul><li>Warehouse location between customers </li></ul></ul></ul><ul><ul><ul><li>Not a network design model </li></ul></ul></ul><ul><li>We try to involve safety stock into strategic supply chain network model </li></ul>Strategic Supply Chain Network Model Demand is uncertain in real world, therefore the inventory buffer should be necessary. Then the safety stock cost should be considered into the model, how to do this?
    8. 8. Agenda <ul><li>Strategic supply chain network model </li></ul><ul><li>Safety stock cost </li></ul><ul><li>A strategic supply chain network model with safety stock </li></ul><ul><li>Dynamic cut-adding algorithm </li></ul><ul><li>Conclusions </li></ul>
    9. 10. Safety Stock Cost --Example of      One DC N Retailers <ul><li>N retailers in SC, demand , then </li></ul><ul><li>Demand in DC </li></ul><ul><li>Risk pool effect : </li></ul>
    10. 11. <ul><li>Variance-to-mean ratio of the demand </li></ul><ul><li>Safety Stock in DC </li></ul>An assumption γ is identical for all customers Assumption :
    11. 12. <ul><li>The summation of the demand is the flow coming out of it. </li></ul><ul><li>Formulation using the flow to express safety stock </li></ul><ul><li>Square root function of a variable </li></ul>flow ∑ μ
    12. 13. Agenda <ul><li>Strategic supply chain network model </li></ul><ul><li>Safety stock cost </li></ul><ul><li>A strategic supply chain network model with safety stock </li></ul><ul><li>Dynamic cut-adding algorithm </li></ul><ul><li>Conclusions </li></ul>
    13. 14. Network model and inventory model <ul><li>Respective Optimization </li></ul><ul><ul><li>Solve the the network model (not include inventory cost)-> optimal supply chain infrastructure </li></ul></ul><ul><ul><li>Solve the inventory model ← utilize the network configure generated from network model </li></ul></ul><ul><ul><li>Inventory model return nothing back to the network design model </li></ul></ul><ul><li>Integrate network and inventory model </li></ul><ul><ul><li>Inventory model delivers optimal inventory deployment, it could impact the cost used in network model </li></ul></ul>Traditional Network Model Inventory Model Inventory cost Parameter
    14. 15. Integrate Network and Inventory model <ul><li>Iterative process Integration --- By inventory cost </li></ul><ul><ul><li>Schneider Logistics ™ (presentation in 2004 informs conference on OR/MS practice applying science) </li></ul></ul><ul><ul><li>Inventory model return inventory cost to the network model, which provide network configure to inventory model </li></ul></ul><ul><ul><li>Iterative process loop until both reached the same supply chain total cost. </li></ul></ul>Traditional Network Model Inventory Model Inventory cost Network configure
    15. 16. Integrate Network and Inventory Models --- our approach <ul><li>Iterative process integration --- By Lead time </li></ul><ul><ul><li>Lead time is a parameter in our strategic supply network model </li></ul></ul><ul><ul><li>Lead time is the decision variable in inventory placement model </li></ul></ul><ul><ul><li>Iterative process loop until reach the same lead time </li></ul></ul>Network Model with safety stock Inventory Model Lead Time Network configure
    16. 17. <ul><li>Incorporate the transport mode into strategic network model </li></ul><ul><li>Incorporate the transport mode into inventory placement model </li></ul><ul><li>Use transport mode and leadtime as the data to transfer between two models. </li></ul>Integrate Network and Inventory Models --- to extend Network Model with safety stock & transport mode Inventory Model Transport mode Network configure
    17. 18. Supply Chain Network Model Logistics cost Facility cost Safety stock cost Solve the non-linear problem ?
    18. 19. Agenda <ul><li>Strategic supply chain network model </li></ul><ul><li>Safety stock cost </li></ul><ul><li>A strategic supply chain network model with safety stock </li></ul><ul><li>Dynamic cut-adding algorithm </li></ul><ul><li>Conclusions </li></ul>
    19. 20. Supply Chain Network Model <ul><li>Relax Concave function to piece-wise linear function </li></ul><ul><ul><li>Multiple Choice Model </li></ul></ul><ul><ul><li>Incremental   Model </li></ul></ul><ul><ul><li>Convex Combination Model </li></ul></ul>C s F s S S-1 B s-1 B s
    20. 23. Agenda <ul><li>Strategic supply chain network model </li></ul><ul><li>Safety stock cost </li></ul><ul><li>A strategic supply chain network model with safety stock </li></ul><ul><li>Dynamic cut-adding algorithm </li></ul><ul><li>Conclusions </li></ul>
    21. 24. Summary and Conclusions <ul><li>Incorporate safety stock into supply chain network design model </li></ul><ul><li>Dynamic cut-adding algorithm is used to solve the model with concave function </li></ul><ul><li>Network design model with safety stock and inventory model is congenial, because of using Leadtime as iterative process parameter. </li></ul>