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

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

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.

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.

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

Model Transition of each inventory The action space

Transition Proability

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Cost per period CH Holding cost per unit CN Manufacturing cost CR Remanufacturing cost CB and Co are backorder and out of date costs

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

Numerical example and summary

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

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

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

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.