1. OPTIMAL CONTROL OF REMANUFACTURING SYSTEM by K.Nakashima et al.
Journal Article Review by
Anand Ghurka, Sasidhar Malladi and Shantha Daniel
Final Presentation
Spring 2005

2. Presentation Outline Recap of the Model. Details of Numerical Example.
Results of the Numerical Example.
Analysis of paper.
Future directions.

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

4. Model Details State space: Transition of each inventory:
The action space:
Transition Probability:

5. Expected Cost per period and Solution Methodology
CH Holding cost per unit
CN Manufacturing cost
CR Remanufacturing cost
CB and Co are backorder and out of date costs
SOULTION METHODOLOGY: Policy Iteration
The optimality condition to minimize the expected average cost g satisfies

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

7. 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

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

9. 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.

10. Analysis of the paper The premise of the paper is
“ The virtual inventory and hence the remanufacturing system, can be controlled by deciding the optimal production quantity at each state”
The model in the paper, tries to accomplish this by using the trade-off between the holding cost and the backorder cost.
The model also tries to account for the variable nature of demand.

11. Short comings and contributions of the model
The model is too general/simple to be applied in reality.
The impact of the out-of date cost has been neglected.
Though the model is aimed at controlling the re-manufacturing system, the goal is not accomplished.
The sensitivity analysis w.r.t remanufacturing rate does not account for the interaction between the holding cost and backorder cost.
Contribution:
The model can serve as a base model for a more detailed and realistic study of remanufacturing systems.
The model shows the advantages of modeling the remanufacturing system as a MDP- the availability of solution methodologies.

12. Future Directions
A model with a more perceptible representation of the interaction between the holding costs and background costs.
A model with variable remanufacturing rate and discarded rate.