1. Optimal Control of a Remanufacturing System
K. Nakashima, H. Arimitsu, T. Nose and S.Kuriyama

2. What is Product Recovery?
Collection, Disassembly, Cleaning, Sorting, Reparing, Reconditioning, Reassembly and Testing
Why Product Recovery
Escalating Deterioration of Environment
Profit Motives

3. 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.

4. 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.

5. Remanufacturing System
Factory
Customers k
λJ(t)
J(t)
I(t)
D(t)
Imax
μJ(t)

6. Model
Transition of each inventory
The action space

7. Transition Proability

8. 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CB and Co are backorder and out of date costs

9. Policy Iteration
The optimality condition to minimize the expected average cost g satisfies

10. Numerical example and summary

11. Parameter Values and Demand Distribution
For the numerical example, the demand distribution is given as follow:

12. 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

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

14. 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.