Optimal Control of a Remanufacturing System

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Optimal Control of a Remanufacturing System

• K. Nakashima, H. Arimitsu, T. Nose and S.Kuriyama

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What is Product Recovery?

• Collection, Disassembly, Cleaning, Sorting,
  Reparing, Reconditioning, Reassembly and Testing
• Why Product Recovery
• Escalating Deterioration of Environment
• Profit Motives

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Inventory

• Actual Product Inventory
• Virtual Inventory
• The state is defined considering both
  inventories.
• Then optimal production policy is obtained to
  minimize the expected average cost per period.

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Literature Review

• Various Models
• Periodic review models
• Collected products are directly used
• Continuous review models
• Remanufacturing system with non-zero lead time
  and control policy with traditional (Q,r) rule
• Push and pull strategy
• Optimal policy for a one-product recovery
  system with lead time
• In all these models, demand and procurement are
  considered independent of each other
• This papers deals with product recovery system
  with a single class of product cycle.

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Remanufacturing System
Customers
Factory
k
?J(t)
J(t)
I(t)
D(t)
Imax
µJ(t)
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Model
Transition of each inventory
The action space
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Transition Proability
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Expected Cost per period
CH Holding cost per unit
CN Manufacturing cost
CR Remanufacturing cost
CB and Co are backorder and out of date costs
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Policy Iteration

• The optimality condition to minimize the expected
  average cost g satisfies

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Numerical example and summary
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Parameter Values and Demand Distribution

• For the numerical example, the demand
  distribution is given as follow

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Optimal control policy

• Given below is the optimal control policy for the
  remanufacturing system when
• variance 0.5. It was seen that the minimum
  expected cost per period, g 11.5

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Sensitivity Analysis

• The variation of the of the minimum cost w.r.t
  remanufacturing rate and demand variance are
  depicted in the following figure.

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Summary

• A remanufacturing system is formulated as an
  undiscounted Markov decision process.
• The stages in the system are characterized using
  the Actual inventory and Virtual inventory.
• The optimal production quantity that will
  minimize expected average cost is determined
  using the policy iterative method.