A Strategic Supply Chain Network Model with Safety Stock

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A Strategic Supply Chain Network Model with
Safety Stock

• Guoyong Lv
• Mikio Kubo
• CORS/INFORMS Joint International Meeting
•  May 16-19 2004  

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Agenda

• Strategic supply chain network model
• Safety stock cost
• A strategic supply chain network model with
  safety stock
• Dynamic cut-adding algorithm
• Conclusions

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Strategic Supply Chain Network Model
---Long-term Network Design Model

• Supply Chain Network Configure
• Node and Arc
• Flow
• When to use it
• Determine the optimal number, location of
  warehouses and/or plants
• Determine optimal sourcing strategy
• Which plant/vendor should produce
  which product
• Determine best distribution channels
• Which warehouse should service which
  customer
• Maintain optimal network as business changes
• Strategic network design is deciding which DCs
  and plants you are going to use to serve your
  customers

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Strategic Supply Chain Network Model

• Output from the model
• Optimal node locations --- which node?
• Optimal transport routing of productions between
  the nodes --- which arc?
• The throughput of those nodes --- how big the
  flow?
• Minimize the total costs
• ---most cost-effectively satisfy
  customer demand.
• Node related cost
• Fixed Cost Node Holding cost, opening a new
  node or close an old node
• Arc related cost
• Transport cost and procurement cost
• Node and production related cost ---node variable
  cost
• Production cost and Warehouse cost
• Inventory (pipeline inventory, cycle inventory,
  safety stock) cost

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Literature review about Strategic supply chain
network model

• A. Geoffrion and G. Graves, Multicommodity
  distribution system design by Benders
  decomposition 1974
• G.G. Brown, G.W. Graves, and M.D. Honczarenko,
  Design and operation of a multicommodity
  production/distribution system using primal goal
  decomposition 1987
• Determine the locations of warehouses as well as
  the flow of multiple commodities from plants
  through warehouses, and on to customers.
• Fixed warehouse cost, Inbound and outbound
  transport cost, Warehouse handling cost
• Plant locations, assignment of production
  facilities to plants

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Literature review about Strategic supply chain
network model

• M.A. Cohen and H.L. Lee, Resource deployment
  analysis of global manufacturing and distribution
  networks 1989
• Maximize global after-tax profits
• Incorporate country-specific offset constraints
• Transfer prices, exchange-rate
• S. Lakhal, A. Martel, O. Kettani, and M. Oral, On
  the optimization of supply chain networking
  decisions, 2001
• Activity Base Cost
• Maximize the value-added of the internal
  activities.

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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?

• Network design models
• Large-scale MIP problem
• linear function of flow
• Node location variable binary variable
• Treatment of uncertainty
• Supply and demand as deterministic
• Facility location model
• Dastin formulated facility locations problems
  with safety stock
• Warehouse location between customers
• Not a network design model
• We try to involve safety stock into strategic
  supply chain network model

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Agenda

• Strategic supply chain network model
• Safety stock cost
• A strategic supply chain network model with
  safety stock
• Dynamic cut-adding algorithm
• Conclusions

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Safety Stock Cost --Example of One
DC N Retailers

• N retailers in SC, demand , then
• Demand in DC
• Risk pool effect

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An assumption

• Variance-to-mean ratio of the demand
• Safety Stock in DC

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• The summation of the demand is the flow coming
  out of it.
• Formulation using the flow to express safety
  stock
• Square root function of a variable

flow
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Agenda

• Strategic supply chain network model
• Safety stock cost
• A strategic supply chain network model with
  safety stock
• Dynamic cut-adding algorithm
• Conclusions

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Network model and inventory model

• Respective Optimization
• Solve the the network model (not include
  inventory cost)? optimal supply chain
  infrastructure
• Solve the inventory model ? utilize the network
  configure generated from network model
• Inventory model return nothing back to the
  network design model
• Integrate network and inventory model
• Inventory model delivers optimal inventory
  deployment, it could impact the cost used in
  network model

Traditional Network Model
Inventory cost Parameter
Inventory Model
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Integrate Network and Inventory model
Traditional Network Model

• Iterative process Integration --- By inventory
  cost
• Schneider Logistics (presentation in 2004
  informs conference on OR/MS practice applying
  science)
• Inventory model return inventory cost to the
  network model, which provide network configure to
  inventory model
• Iterative process loop until both reached the
  same supply chain total cost.

Inventory cost
Network configure
Inventory Model
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Integrate Network and Inventory Models
--- our approach

• Iterative process integration --- By Lead time
• Lead time is a parameter in our strategic supply
  network model
• Lead time is the decision variable in inventory
  placement model
• Iterative process loop until reach the same lead
  time

Network Model with safety stock
Lead Time
Network configure
Inventory Model
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Integrate Network and Inventory Models--- to
extend

• Incorporate the transport mode into strategic
  network model
• Incorporate the transport mode into inventory
  placement model
• Use transport mode and leadtime as the data to
  transfer between two models.

Network Model with safety stock
transport mode
Transport mode
Network configure
Inventory Model
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Supply Chain Network Model
Solve the non-linear problem ?
Logistics cost
Facility cost

Safety stock cost
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Agenda

• Strategic supply chain network model
• Safety stock cost
• A strategic supply chain network model with
  safety stock
• Dynamic cut-adding algorithm
• Conclusions

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Supply Chain Network Model

• Relax Concave function to piece-wise linear
  function
• Multiple Choice Model
• Incremental Model
• Convex Combination Model

Cs
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Agenda

• Strategic supply chain network model
• Safety stock cost
• A strategic supply chain network model with
  safety stock
• Dynamic cut-adding algorithm
• Conclusions

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Summary and Conclusions

• Incorporate safety stock into supply chain
  network design model
• Dynamic cut-adding algorithm is used to solve the
  model with concave function
• Network design model with safety stock and
  inventory model is congenial, because of using
  Leadtime as iterative process parameter.